Spectrophotometry is an analytical method used to determine the concentration of a substance by measuring how much light of a specific wavelength is absorbed by a solution.
In university analytical chemistry experiments, a calibration curve is often prepared from standard solutions, and the concentration of an unknown sample is determined from its absorbance.
In a spectrophotometry report, it is important to discuss not only the measured absorbance values, but also the linearity of the calibration curve, the correlation coefficient, calculation of the unknown sample concentration, the measurement range, blank correction, cell contamination, and dilution errors.
This article clearly explains points that are useful when discussing spectrophotometry, how to interpret calibration curves and correlation coefficients, how to determine unknown concentrations, sources of error, and discussion examples that can be used in reports.
Note:
This article is a reference intended to assist with discussions of results obtained in chemistry experiments at universities and similar institutions.
For the actual experimental procedures, measurement conditions, wavelengths used, and handling of reagents, always follow the instructions in your university’s laboratory manual and those given by your instructor or TA.
- What Is Spectrophotometry?
- Beer-Lambert Law
- Results to Examine in Spectrophotometry
- Reference Experimental Values for Absorbance and an Example of Concentration Analysis Using a Calibration Curve
- Reference Experimental Conditions
- Beer-Lambert Law
- Example of Absorbance Measurements of Standard Solutions
- Example of a Calibration-Curve Equation
- Example of Calculating an Unknown Sample Concentration
- Example Considering the Dilution Factor
- Example of Multiple Measurements of an Unknown Sample
- Example of Deviation From the Linear Range of the Calibration Curve
- Difference With and Without Blank Correction
- Example of a Calibration Curve With an Outlier
- Example of Comparing Calibration Curves
- When the Unknown Sample Is Outside the Calibration-Curve Range
- Example of Relative Error and Recovery
- Main Sources of Error
- Example of How to Write the Results
- Points to Connect to the Discussion
- Example Discussion Text
- Summary
- What Is a Calibration Curve?
- How to Read the Calibration-Curve Equation
- How to Interpret the Correlation Coefficient and Coefficient of Determination
- How to Determine an Unknown Concentration
- Whether the Unknown Sample Lies Within the Calibration-Curve Range
- Meaning of Blank Measurement
- Selection of the Measurement Wavelength
- Errors Caused by Cell Contamination and Air Bubbles
- Effects of Cell Orientation and Optical Path Length
- Errors in Standard-Solution Preparation
- Errors Caused by Dilution Procedures
- Why the High-Concentration Side Deviates From the Straight Line
- Why Errors Appear Larger at Low Concentrations
- Discussion When There Is an Outlier
- Discussion When the Correlation Coefficient Is Low
- When the Absorbance of the Unknown Sample Is Too High
- When the Absorbance of the Unknown Sample Is Too Low
- Discussion When Measurements Are Repeated
- When the Result Can Be Considered Good
- Example Discussion When the Experiment Did Not Go Well
- How to Write Points for Improvement
- Difference Between a Superficial Discussion and a Good Discussion
- Examples of Expressions That Can Be Used in Reports
- Points to Check When Discussing Spectrophotometry
- Summary
What Is Spectrophotometry?
Spectrophotometry is a method for determining the concentration of a component in a solution by passing light through a sample solution and measuring how much light is absorbed.
Because different substances absorb different wavelengths of light more readily, measurements are made at a wavelength that is strongly absorbed by the target substance.
In general, as the concentration of a solution increases, the amount of light absorbed increases and the absorbance also becomes larger.
Using this relationship, the absorbances of standard solutions with known concentrations are measured and a calibration curve is prepared.
The concentration of an unknown sample is then determined by applying its absorbance to the calibration curve.
Spectrophotometry is a relatively simple method of quantitative analysis, but the results can change depending on the measurement wavelength, cell condition, concentration range of the sample, blank correction, and dilution procedure.
Therefore, these factors must be examined in the discussion.
Beer-Lambert Law
The Beer-Lambert law forms the basis of spectrophotometry.
According to this law, under constant conditions, absorbance is proportional to the concentration of the solution and the optical path length.
A = εcl
Here, A is absorbance, ε is the molar absorptivity, c is concentration, and l is the optical path length of the cell.
In ordinary experiments, the same cell is used, so the optical path length remains constant and absorbance A is proportional to concentration c.
Example Discussion:
In the calibration curve, absorbance increased as the concentration increased.
This is because, according to the Beer-Lambert law, absorbance is proportional to concentration when the optical path length is constant.
Within the measured concentration range, an approximately linear relationship between absorbance and concentration is considered to have been established.
Results to Examine in Spectrophotometry
In spectrophotometry results, organize the concentrations and absorbances of the standard solutions, the equation of the calibration curve, the correlation coefficient, the absorbance of the unknown sample, and the concentration of the unknown sample.
It is also necessary to check whether any measured values deviate greatly from the calibration curve and whether the absorbance of the unknown sample lies within the range of the calibration curve.
Main Items to Include in the Results
- Measurement wavelength
- Concentrations of the standard solutions
- Absorbance of each standard solution
- Graph of the calibration curve
- Equation of the calibration curve
- Correlation coefficient or coefficient of determination
- Absorbance of the unknown sample
- Concentration of the unknown sample determined from the calibration curve
- If dilution was performed, the concentration after accounting for the dilution factor
- Variation or outliers in measured values
Example of How to Write the Results:
A calibration curve was prepared with the concentration of the standard solution on the horizontal axis and absorbance on the vertical axis.
The equation of the obtained regression line was y = 0.125x + 0.003, and the correlation coefficient was 0.998.
Because the absorbance of the unknown sample was 0.503, substitution into the calibration curve gave an unknown sample concentration of 4.00.
Reference Experimental Values for Absorbance and an Example of Concentration Analysis Using a Calibration Curve
Here, reference experimental values are organized for preparing a calibration curve from absorbance measurements and determining the concentration of an unknown sample.
Standard-solution concentration, absorbance, blank correction, the calibration-curve equation, correlation coefficient, unknown sample concentration, dilution factor, outliers, and measurement errors are summarized in a form that is easy to use in reports.
In absorbance analysis, standard solutions of known concentrations are measured to prepare a calibration curve, and the concentration of an unknown sample is determined by applying its absorbance to the calibration curve.
Within the range where the Beer-Lambert law holds, absorbance is proportional to concentration.
However, linearity may break down on the high-concentration side or in a range where absorbance is too high, so it is important to confirm the range of the calibration curve.
Reference Experimental Conditions
| Item | Details |
|---|---|
| Measurement target | Colored complexes, metal ions, proteins, dyes, reaction products, etc. |
| Measurement method | UV-visible spectrophotometry |
| Measurement wavelength | Use a wavelength near the absorption maximum |
| Cell length | 1.00 cm |
| Evaluation items | Absorbance, blank correction, calibration-curve equation, correlation coefficient, unknown sample concentration, dilution factor |
| Main sources of error | Standard-solution preparation, blank correction, cell contamination, air bubbles, turbidity, wavelength setting, measurement outside the range |
Beer-Lambert Law
Absorbance A is expressed using molar absorptivity ε, cell length l, and concentration c as follows.
A = εlc
| Symbol | Meaning | Unit | Use in the Calibration Curve |
|---|---|---|---|
| A | Absorbance | None | Placed on the vertical axis |
| ε | Molar absorptivity | L mol−1 cm−1 | Indicator of sensitivity |
| l | Cell length | cm | Usually 1.00 cm |
| c | Concentration | mol/L, mg/L, μg/mL, etc. | Placed on the horizontal axis |
If the cell length is constant, absorbance A is proportional to concentration c.
This relationship is used to prepare the calibration curve.
Example of Absorbance Measurements of Standard Solutions
The following is a reference example in which standard solutions from 0 to 10.0 mg/L were prepared for a colored component and their absorbances were measured.
The blank absorbance was taken as 0.015 and corrected.
| Standard Solution | Concentration | Measured Absorbance | Absorbance After Blank Correction | Assessment |
|---|---|---|---|---|
| Blank | 0.0 mg/L | 0.015 | 0.000 | Reference |
| Standard 1 | 2.0 mg/L | 0.167 | 0.152 | Good |
| Standard 2 | 4.0 mg/L | 0.319 | 0.304 | Good |
| Standard 3 | 6.0 mg/L | 0.471 | 0.456 | Good |
| Standard 4 | 8.0 mg/L | 0.623 | 0.608 | Good |
| Standard 5 | 10.0 mg/L | 0.776 | 0.761 | Slightly on the high-concentration side |
Using absorbance values after blank correction makes it possible to subtract absorption by the solvent and reagents themselves.
Normally, absorbance values after blank correction are used for the calibration curve.
Example of a Calibration-Curve Equation
Suppose linear regression of the standard-solution data above, with concentration x on the horizontal axis and blank-corrected absorbance y on the vertical axis, gives the following calibration-curve equation.
y = 0.0760x + 0.0005
| Item | Value | Meaning |
|---|---|---|
| Slope | 0.0760 | Increase in absorbance per 1 mg/L of concentration |
| Intercept | 0.0005 | Corrected absorbance at zero concentration |
| Correlation coefficient R | 0.9999 | Very high linearity |
| Coefficient of determination R2 | 0.9998 | Good as a calibration curve |
| Valid range | 0-10.0 mg/L | Evaluate unknown samples within this range |
When the intercept is close to 0 and R2 is close to 1, the proportional relationship between concentration and absorbance can be judged to hold well.
Example of Calculating an Unknown Sample Concentration
If the measured absorbance of an unknown sample is 0.395 and the blank absorbance is 0.015, the corrected absorbance is as follows.
Corrected absorbance = 0.395 − 0.015 = 0.380
Substitute this value into the calibration-curve equation y = 0.0760x + 0.0005 and solve for concentration x.
0.380 = 0.0760x + 0.0005
x = (0.380 − 0.0005) ÷ 0.0760 = 4.99 mg/L
Therefore, the concentration of the unknown sample is determined to be approximately 5.0 mg/L.
Example Considering the Dilution Factor
If the unknown sample was diluted 10-fold before measurement, the concentration determined from the calibration curve is the concentration after dilution.
The original sample concentration is determined by multiplying by the dilution factor.
| Item | Value | Calculation |
|---|---|---|
| Measured absorbance | 0.395 | Measured value of the unknown sample |
| Blank absorbance | 0.015 | Used for correction |
| Corrected absorbance | 0.380 | 0.395 − 0.015 |
| Concentration determined from the calibration curve | 4.99 mg/L | Concentration after dilution |
| Dilution factor | 10-fold | Diluted 10-fold before measurement |
| Original sample concentration | 49.9 mg/L | 4.99 × 10 |
When dilution is performed, it is necessary to clearly state whether the final reported concentration is before or after dilution.
Example of Multiple Measurements of an Unknown Sample
The following is an example in which the same unknown sample was measured three times to evaluate reproducibility.
| Measurement | Measured Absorbance | Corrected Absorbance | Concentration | Assessment |
|---|---|---|---|---|
| 1st | 0.395 | 0.380 | 4.99 mg/L | Good |
| 2nd | 0.401 | 0.386 | 5.07 mg/L | Good |
| 3rd | 0.392 | 0.377 | 4.95 mg/L | Good |
| Average | 0.396 | 0.381 | 5.00 mg/L | Representative value |
Because the three concentrations were within the range of 4.95-5.07 mg/L and showed little variation, the reproducibility of the measurements is considered relatively good.
Example of Deviation From the Linear Range of the Calibration Curve
When absorbance is too high, it may deviate from the Beer-Lambert law and the calibration curve may become curved.
| Concentration | Ideal Absorbance | Measured Absorbance | Deviation | Direction of Discussion |
|---|---|---|---|---|
| 2.0 mg/L | 0.152 | 0.152 | Small | Linear range |
| 6.0 mg/L | 0.456 | 0.456 | Small | Linear range |
| 10.0 mg/L | 0.760 | 0.761 | Small | Almost linear |
| 15.0 mg/L | 1.140 | 1.060 | Measured lower | Deviation at high absorbance |
| 20.0 mg/L | 1.520 | 1.290 | Much lower | Outside the calibration-curve range |
In a range where absorbance is much greater than 1, measurement error and the influence of stray light tend to become larger, so it is desirable to dilute the sample and measure it within the linear range.
Difference With and Without Blank Correction
If the blank absorbance is not subtracted, the absorbances of all standard solutions and unknown samples appear higher.
| Processing | Calibration-Curve Equation | Unknown-Sample Absorbance | Calculated Concentration | Problem |
|---|---|---|---|---|
| With blank correction | y = 0.0760x + 0.0005 | 0.380 | 4.99 mg/L | Reference |
| Without blank correction | y = 0.0760x + 0.0155 | 0.395 | 4.99 mg/L | Similar if the same blank is included in both standards and unknown sample |
| Only the unknown sample not corrected | y = 0.0760x + 0.0005 | 0.395 | 5.19 mg/L | Concentration is overestimated |
| Only standard solutions not corrected | Intercept becomes large | 0.380 | May be underestimated | Inconsistent processing |
If the correction method is not consistent between the standard solutions and the unknown sample, an error occurs in the concentration calculation.
Example of a Calibration Curve With an Outlier
If only one standard solution deviates greatly from the straight line, there may have been an error in preparation or measurement.
| Concentration | Expected Absorbance | Measured Absorbance | Assessment | Possible Cause |
|---|---|---|---|---|
| 2.0 mg/L | 0.152 | 0.152 | Good | – |
| 4.0 mg/L | 0.304 | 0.304 | Good | – |
| 6.0 mg/L | 0.456 | 0.530 | Possible outlier | Error in standard-solution preparation, dirty cell, air bubble |
| 8.0 mg/L | 0.608 | 0.608 | Good | – |
| 10.0 mg/L | 0.760 | 0.761 | Good | – |
When excluding an outlier, a reasonable explanation such as an error in preparation or measurement must be provided rather than simply removing the value because it is inconvenient.
Example of Comparing Calibration Curves
The calibration-curve equation and correlation coefficient change depending on whether the outlier is included or excluded.
| Condition | Calibration-Curve Equation | R2 | Unknown-Sample Concentration | Assessment |
|---|---|---|---|---|
| Including outlier | y = 0.0758x + 0.018 | 0.982 | 4.78 mg/L | Linearity decreases |
| Excluding outlier | y = 0.0760x + 0.0005 | 0.9998 | 4.99 mg/L | Good linearity |
| Using only the low-concentration side | y = 0.0762x − 0.001 | 0.9995 | 4.98 mg/L | Appropriate if the unknown sample is within the range |
| Using through the high-concentration side | y = 0.0710x + 0.025 | 0.965 | 5.00 mg/L | Attention required for nonlinearity at high concentrations |
A calibration curve should be evaluated not only by R2, but also by checking whether each point follows the straight line and whether the absorbance of the unknown sample lies within the range of the standard solutions.
When the Unknown Sample Is Outside the Calibration-Curve Range
If the absorbance of the unknown sample exceeds the range of the standard solutions, determining the concentration by extrapolation may result in a large error.
| Condition of Unknown Sample | Absorbance | Calibration-Curve Range | Action | Direction of Discussion |
|---|---|---|---|---|
| Within range | 0.380 | 0.000-0.761 | Calculate directly | High reliability |
| Slightly high | 0.850 | 0.000-0.761 | Dilute and remeasure | Avoid extrapolation |
| Very high | 1.300 | 0.000-0.761 | Dilute substantially | May be outside the linear range |
| Very low | 0.010 | 0.000-0.761 | Concentrate or use higher-sensitivity conditions | Large influence of noise |
As a basic rule, an unknown sample should be diluted or concentrated so that its measured value falls within the range of the calibration curve prepared from the standard solutions.
Example of Relative Error and Recovery
Measuring a check sample of known concentration makes it possible to evaluate the validity of the calibration curve.
| Check Sample | Known Concentration | Measured Concentration | Relative Error | Recovery |
|---|---|---|---|---|
| Low concentration | 3.00 mg/L | 2.94 mg/L | −2.0% | 98.0% |
| Medium concentration | 5.00 mg/L | 5.03 mg/L | +0.6% | 100.6% |
| High concentration | 9.00 mg/L | 8.82 mg/L | −2.0% | 98.0% |
When recovery is close to 100%, the calibration curve and measurement procedure can be considered generally appropriate.
Main Sources of Error
| Source of Error | Effect on Absorbance | Effect on Concentration Calculation | Improvement |
|---|---|---|---|
| Error in standard-solution preparation | Slope or points of the calibration curve shift | Affects all unknown-sample concentrations | Use pipettes and volumetric flasks accurately |
| Insufficient blank correction | Absorbance appears high | Concentration may be overestimated | Measure an appropriate blank |
| Dirty or scratched cell | Absorbance becomes unstable | Variation increases | Clean the cell and measure in the same orientation |
| Air bubbles | Light is scattered | Absorbance may appear high | Remove air bubbles before measurement |
| Turbidity or precipitate | Appears high because of scattering | Concentration tends to be overestimated | Filter, centrifuge, or review the conditions |
| Incorrect wavelength setting | Absorbance may become low | Sensitivity decreases | Measure at the absorption maximum |
| Outside the calibration-curve range | Deviates from linearity | Extrapolation causes large errors | Dilute and measure within the range |
Example of How to Write the Results
Standard solutions were prepared over the concentration range of 0-10.0 mg/L and their absorbances were measured.
A calibration curve was prepared using absorbance values after subtracting the blank absorbance of 0.015, and the linear equation y = 0.0760x + 0.0005 was obtained.
The coefficient of determination R2 was 0.9998, indicating a good linear relationship between concentration and absorbance within the range of the standard solutions.
The measured absorbance of the unknown sample was 0.395, and the absorbance after blank correction was 0.380.
Substituting this value into the calibration-curve equation gave an unknown sample concentration of 4.99 mg/L.
If the unknown sample had been diluted 10-fold before measurement, the original sample concentration would be 4.99 × 10 = 49.9 mg/L.
When the same unknown sample was measured three times, the calculated concentrations were 4.95-5.07 mg/L, and no large variation was observed.
Therefore, the reproducibility of the absorbance measurements is considered relatively good.
However, a sample with high absorbance outside the calibration-curve range must be diluted before being remeasured.
Points to Connect to the Discussion
In discussing absorbance and calibration curves, it is important not only to prepare a calibration-curve equation and determine the concentration, but also to explain linearity, blank correction, the range of the unknown sample, outliers, dilution factor, and measurement errors in relation to one another.
- Was a calibration curve prepared from the concentrations and absorbances of the standard solutions?
- Were absorbance values after blank correction used?
- Can the slope, intercept, and R2 of the calibration-curve equation be interpreted?
- Can the unknown sample concentration be calculated by substituting its absorbance into the calibration-curve equation?
- Can the original sample concentration be determined by considering the dilution factor?
- Was it confirmed that the absorbance of the unknown sample lies within the calibration-curve range?
- Can the reason for deviation from linearity on the high-concentration side be explained?
- If an outlier is excluded, can the reason be explained rationally?
- Can standard-solution preparation, cell contamination, air bubbles, turbidity, and wavelength setting be discussed as sources of error?
Example Discussion Text
In this experiment, the absorbances of standard solutions were measured to prepare a calibration curve, and the concentration of an unknown sample was determined.
When a calibration curve was prepared using absorbance values after blank correction, the linear equation y = 0.0760x + 0.0005 was obtained.
The coefficient of determination R2 was 0.9998, suggesting that within the range of 0-10.0 mg/L, absorbance and concentration were approximately proportional in accordance with the Beer-Lambert law.
The corrected absorbance of the unknown sample was 0.380, and substitution into the calibration-curve equation gave a concentration of 4.99 mg/L.
Because this absorbance was within the range of the standard solutions, the concentration was determined by interpolation rather than extrapolation and is therefore considered relatively reliable.
If the sample had been diluted before measurement, the value obtained from the calibration curve would represent the concentration after dilution, so the dilution factor would need to be applied to determine the original sample concentration.
Although the calibration curve showed good linearity, absorbance may become too high on the high-concentration side and deviate from linearity.
This is because the proportional relationship between absorbance and concentration may no longer hold completely due to the effects of stray light, detector response, solution turbidity, intermolecular interactions, and other factors.
Therefore, if the absorbance of the unknown sample exceeds the range of the standard solutions, the sample must be diluted and remeasured.
Possible sources of error include errors in standard-solution preparation, insufficient blank correction, contamination or air bubbles in the cell, deviation of the measurement wavelength, and turbidity of the sample.
In particular, errors in standard-solution preparation affect the slope of the entire calibration curve and therefore directly affect calculation of the unknown sample concentration.
In addition, air bubbles and turbidity may scatter light and make the absorbance appear higher than the actual value.
Therefore, accurate quantitative analysis requires careful preparation of standard solutions, blank measurement, handling of the cell, and confirmation of the measurement range.
Summary
In quantitative analysis using absorbance, a calibration curve is prepared from standard solutions and the concentration of an unknown sample is determined by applying its absorbance to the curve.
When the calibration curve has high linearity and the unknown sample lies within the range of the standard solutions, the reliability of the concentration calculation increases.
This reference example covered absorbance of standard solutions, blank correction, calibration-curve equations, unknown sample concentration, dilution factors, repeated measurements, the linear range, outliers, recovery, and sources of error.
In a report, it is useful to discuss not only the concentration calculation, but also the validity of the calibration curve and the effects of the measurement conditions.
What Is a Calibration Curve?
A calibration curve is a graph showing the relationship between the concentrations and absorbances of standard solutions of known concentrations.
In spectrophotometry, the absorbance of an unknown sample is measured and its concentration is determined by applying that value to the calibration curve.
In a calibration curve, concentration is commonly placed on the horizontal axis and absorbance on the vertical axis.
When the Beer-Lambert law holds within the measurement range, the points are approximately aligned along a straight line.
The higher this linearity, the easier it is to use the calibration curve to estimate an unknown concentration.
Example Discussion:
When the concentrations and absorbances of the standard solutions were plotted, the measurement points were generally aligned along a straight line.
This suggests that a proportional relationship between absorbance and concentration was established within the concentration range used in this experiment.
Therefore, it is considered appropriate to use this calibration curve to determine the concentration of the unknown sample.
How to Read the Calibration-Curve Equation
When a calibration curve is fitted with a straight line, an equation such as the following is obtained.
y = ax + b
Here, y is absorbance, x is concentration, a is the slope, and b is the intercept.
By substituting the absorbance of the unknown sample for y and solving for x, the concentration of the unknown sample can be determined.
x = (y − b) ÷ a
Calculation Example:
Calibration-curve equation: y = 0.125x + 0.003
Absorbance of unknown sample: y = 0.503
x = (0.503 − 0.003) ÷ 0.125 = 4.00
However, if the unknown sample was diluted before measurement, it is necessary to multiply the concentration obtained from the calibration curve by the dilution factor to determine the original sample concentration.
How to Interpret the Correlation Coefficient and Coefficient of Determination
The correlation coefficient and coefficient of determination may be used as indicators for evaluating the linearity of a calibration curve.
The correlation coefficient indicates how linear the relationship between concentration and absorbance is.
The coefficient of determination indicates how well the regression line explains the measured data.
The closer these values are to 1, the closer the measurement points are to a straight line and the higher the linearity of the calibration curve is considered to be.
However, high correlation or determination coefficients do not necessarily mean that all measurements are correct.
It is also necessary to check the measurement range, blank correction, outliers, and whether the unknown sample lies within the calibration-curve range.
| Condition | Possible Interpretation |
|---|---|
| Correlation coefficient close to 1 | High linearity between concentration and absorbance |
| Low correlation coefficient | Variation in measured values, preparation errors, or an inappropriate measurement range may be present |
| Only one point deviates greatly | An error in preparing or measuring that standard solution may have occurred |
| Curve bends on the high-concentration side | The measurement may be outside the range where the Beer-Lambert law holds |
Example Discussion:
The correlation coefficient of the calibration curve was close to 1, indicating high linearity between the concentrations and absorbances of the standard solutions.
From this, calculation of concentration using the calibration curve is considered appropriate within the measured concentration range.
However, even when the correlation coefficient is high, the accuracy of concentration estimation may decrease if the absorbance of the unknown sample lies outside the range of the calibration curve.
How to Determine an Unknown Concentration
The concentration of an unknown sample is determined by substituting the measured absorbance into the calibration-curve equation.
If the calibration-curve equation is y = ax + b, substitute the absorbance of the unknown sample for y and solve for x.
If the unknown sample was diluted before measurement, the value obtained from the calibration curve is the concentration after dilution.
To determine the original sample concentration, the dilution factor must be applied.
Calculation Example Including Dilution:
Concentration of the diluted unknown sample obtained from the calibration curve: 2.50 mg/L
Dilution factor: 10-fold
Original sample concentration: 2.50 × 10 = 25.0 mg/L
Example Discussion:
The concentration of the unknown sample was determined by substituting its absorbance into the calibration-curve equation.
Because the unknown sample had been diluted before measurement, the concentration obtained from the calibration curve was the concentration after dilution.
Therefore, the dilution factor must be taken into account when determining the original sample concentration.
Whether the Unknown Sample Lies Within the Calibration-Curve Range
It is desirable for the absorbance of the unknown sample to lie within the range of the calibration curve prepared from the standard solutions.
If a concentration is determined using a value outside the range of the calibration curve, extrapolation is required and the reliability of the estimate decreases.
If the absorbance of the unknown sample is too high, the sample may be diluted and remeasured.
Conversely, if the absorbance is too low, the effects of measurement sensitivity and the blank become relatively large, making errors more noticeable.
Example Discussion:
The absorbance of the unknown sample was within the range of the calibration curve prepared from the standard solutions.
Therefore, it is considered appropriate to determine the unknown concentration using the calibration curve.
On the other hand, if the absorbance of the unknown sample were outside the calibration-curve range, concentration estimation would require extrapolation and the reliability would decrease, so the sample would need to be appropriately diluted and remeasured.
Meaning of Blank Measurement
In spectrophotometry, a blank is measured to correct for absorption by components other than the sample, the solvent, and the cell.
A solution that does not contain the target component is often used as the blank.
If blank correction is not appropriate, absorption by the solvent and reagents is included in the absorbance of the sample, preventing accurate determination of the concentration.
By setting the zero reference using the blank, the absorbance caused by the target component can be measured more accurately.
Example Discussion:
Blank measurement is performed to correct for absorption by the solvent, reagents, and cell.
If blank correction was insufficient, absorption from sources other than the target component would also be included in the measured value, and the absorbance could become larger than the actual value.
As a result, errors could occur in the calibration curve and the concentration of the unknown sample.
Selection of the Measurement Wavelength
In spectrophotometry, measurements are made at a wavelength strongly absorbed by the target substance.
Usually, selecting a wavelength near the absorption maximum makes the change in absorbance relative to concentration larger and allows measurements with high sensitivity.
If the measurement wavelength is inappropriate, absorbance may become small and differences in concentration may not be reflected clearly.
In addition, if a wavelength absorbed by another component is selected, interference may affect the result.
Example Discussion:
It is important to select a measurement wavelength at which the target component shows strong absorption.
Measuring at an appropriate wavelength increases the change in absorbance relative to changes in concentration and increases the sensitivity of the calibration curve.
On the other hand, if the measurement wavelength is inappropriate, absorbance may become small or absorption by other components may affect the result, causing errors in concentration calculations.
Errors Caused by Cell Contamination and Air Bubbles
In absorbance measurements, the condition of the cell greatly affects the results.
If fingerprints or water droplets are present on the outside of the cell, light may be scattered or absorbed, causing the absorbance to become larger than the actual value.
Air bubbles inside the cell may also interfere with the optical path and cause deviations in measured values.
Example Discussion:
Possible reasons the absorbance became larger than expected include contamination or water droplets on the cell surface and air bubbles inside the cell.
If these are present, light is scattered or blocked and effects other than absorption by the target component are included in the measured value.
As a result, the absorbance may become larger than the actual value and the concentration determined from the calibration curve may be overestimated.
Effects of Cell Orientation and Optical Path Length
Because absorbance is proportional to optical path length, it is important to perform measurements under the same conditions.
Cells with the same optical path length are normally used, but if the orientation or type of cell changes or the cell is not correctly positioned, differences may occur in measured values.
Example Discussion:
Because absorbance is proportional to optical path length, it is desirable to use the same cell in the same orientation during measurement.
If the orientation or placement of the cell differs between measurements, the path of light may change and variation may occur in absorbance.
Therefore, handling of the cell is considered to affect the linearity of the calibration curve and the accuracy of the unknown concentration.
Errors in Standard-Solution Preparation
The accuracy of a calibration curve depends on the concentrations of the standard solutions being accurate.
If, during preparation of a standard solution, the liquid level exceeds the calibration mark of a volumetric flask, the volume delivered by a pipette is incorrect, or mixing is insufficient, the entire calibration curve is affected.
In particular, if the concentration of a standard solution is incorrect, the slope and intercept of the calibration curve may shift, and the concentration of the unknown sample may also be calculated incorrectly.
Example Discussion:
One possible reason the measurement points of the calibration curve deviated from the straight line is an error in preparation of the standard solutions.
If dilution exceeded the calibration mark of a volumetric flask, the actual concentration of that standard solution would be lower than intended.
In addition, if mixing was insufficient, the sampled solution would not have a uniform concentration and variation could occur in absorbance.
Errors Caused by Dilution Procedures
When unknown samples or standard solutions are diluted before measurement, errors in the dilution procedure affect the results.
Errors in aligning the calibration marks of pipettes and volumetric flasks or insufficient mixing may cause the actual dilution factor to differ from the intended value.
Example Discussion:
One possible reason the concentration of the unknown sample differed from the expected value is an error in the dilution procedure.
If the volume collected with the pipette or the final volume adjusted with the volumetric flask was inaccurate, the actual dilution factor would differ from the calculated value.
As a result, even after correcting the concentration obtained from the calibration curve using the dilution factor, an error could remain in the original sample concentration.
Why the High-Concentration Side Deviates From the Straight Line
Absorbance and concentration are not always completely proportional over all concentration ranges.
At high concentrations, the Beer-Lambert law may no longer hold because of intermolecular interactions, stray light, measurement limits of the instrument, and other effects.
If measurement points on the high-concentration side deviate from the calibration curve, that concentration range may not be suitable for quantitative analysis.
In this case, it is desirable to dilute the standard solutions or unknown samples and measure them within a range where linearity is maintained.
Example Discussion:
One possible reason the measurement points on the high-concentration side deviated from the regression line is that the concentration exceeded the range in which the Beer-Lambert law holds.
If the concentration is too high, the proportional relationship between absorbance and concentration may break down and the linearity of the calibration curve may decrease.
Therefore, if the absorbance of the unknown sample is too high, the sample must be appropriately diluted and measured within the range of the calibration curve.
Why Errors Appear Larger at Low Concentrations
On the low-concentration side, absorbance is small, so slight measurement errors and deviations in blank correction may have a large effect on the result.
When absorbance is extremely small, the difference in absorbance corresponding to differences in concentration also becomes small, increasing the uncertainty of concentration estimation.
Example Discussion:
At low concentrations, absorbance is small, so the relative effects of cell contamination, deviations in blank correction, and instrument-reading errors become larger.
Therefore, measurement points for low-concentration standard solutions are more likely to deviate from the regression line, and uncertainty is also more likely to arise in estimating the concentration of an unknown sample.
Discussion When There Is an Outlier
If only some points in a calibration curve deviate greatly from the straight line, an error in preparing or measuring that standard solution may have occurred.
However, when excluding an outlier, it is necessary to explain a clear reason rather than removing the point simply because it is inconvenient.
Example Discussion:
One possible reason some measurement points deviated greatly from the regression line is that a concentration error occurred during preparation of that standard solution.
In addition, an air bubble inside the cell or contamination on the cell surface may have caused the absorbance to be measured higher than the actual value.
When excluding an outlier, the decision must be based on a specific operational error or observed fact confirmed during measurement.
Discussion When the Correlation Coefficient Is Low
If the correlation coefficient or coefficient of determination is low, a sufficient linear relationship between the standard-solution concentration and absorbance may not have been obtained.
Possible causes include errors in standard-solution preparation, inappropriate measurement wavelength, cell contamination, variation in measured values, and an excessively wide concentration range.
Example Discussion:
Possible reasons the correlation coefficient of the calibration curve was low include errors in preparation of the standard solutions and operational errors during absorbance measurement.
If the concentrations of the standard solutions were inaccurate, the correspondence between concentration and absorbance would break down, making the measurement points more likely to deviate from the straight line.
In addition, contamination or air bubbles in the cell could also cause variation in absorbance and reduce the linearity of the calibration curve.
When the Absorbance of the Unknown Sample Is Too High
If the absorbance of the unknown sample is higher than the maximum value of the calibration curve, directly extrapolating the calibration curve to determine the concentration reduces reliability.
In this case, the basic procedure is to appropriately dilute the unknown sample so that its absorbance falls within the range of the calibration curve and then measure it again.
Example Discussion:
If the absorbance of the unknown sample exceeded the range of the calibration curve, the concentration would have to be estimated outside the calibration curve and reliability would decrease.
Therefore, the unknown sample must be appropriately diluted and remeasured so that its absorbance lies within the calibration-curve range.
The concentration obtained after dilution is then multiplied by the dilution factor to determine the original sample concentration.
When the Absorbance of the Unknown Sample Is Too Low
If the absorbance of the unknown sample is extremely small, the relative influence of blank correction and instrument-reading errors becomes large.
Therefore, the accuracy of concentration estimation may decrease.
Example Discussion:
If the absorbance of the unknown sample is extremely small, even a slight deviation in blank correction or instrument-reading error greatly affects the concentration calculation.
Therefore, for samples with low absorbance, the uncertainty of the measured value becomes larger and the reliability of the calculated unknown concentration may decrease.
Discussion When Measurements Are Repeated
When absorbance is measured multiple times, reproducibility can be evaluated from the variation in the measured values.
If similar absorbance values are obtained for the same sample, the reproducibility of the measurement is considered relatively high.
On the other hand, if the variation is large, the condition of the cell, insufficient mixing of the sample, and stability of the instrument should be checked.
Example Discussion:
When the same unknown sample was measured multiple times, the absorbance values were similar.
This suggests that the reproducibility of the measurements was relatively high.
On the other hand, possible reasons a difference from the theoretical value remained in the concentration determined from the calibration curve include errors in preparation of the standard solutions and deviations in blank correction.
When the Result Can Be Considered Good
A good result in spectrophotometry is indicated when the calibration curve shows high linearity, the correlation coefficient is close to 1, and the absorbance of the unknown sample lies within the calibration-curve range.
It is also important that blank correction be performed appropriately and that there be little variation among repeated absorbance measurements.
Example Discussion:
The measurement points of the calibration curve were generally aligned along a straight line, and the correlation coefficient was also close to 1.
This suggests that a good linear relationship was established between the concentrations and absorbances of the standard solutions.
In addition, because the absorbance of the unknown sample was within the calibration-curve range, the reliability of the unknown concentration determined using the calibration curve is considered relatively high.
Example Discussion When the Experiment Did Not Go Well
If the linearity of the calibration curve was poor, the correlation coefficient was low, the absorbance of the unknown sample was outside the range, or the measured values varied, check the preparation of the standard solutions, cell condition, blank, measurement wavelength, and dilution procedure.
Example Discussion:
Some measurement points of the calibration curve deviated from the regression line, reducing the correlation coefficient.
Possible causes include errors in preparation of the standard solutions, contamination of the cell surface, air bubbles inside the cell, and insufficient blank correction.
In addition, if the high-concentration points deviated from the straight line, the concentration may have exceeded the range in which the Beer-Lambert law holds.
How to Write Points for Improvement
In a discussion of spectrophotometry, including points for improvement as well as sources of error makes the report easier to organize.
It is important to write the improvements in correspondence with the actual sources of error considered.
Methods for Improving the Accuracy of the Calibration Curve
- Prepare standard solutions accurately
- Correctly align the calibration marks of volumetric flasks and volumetric pipettes
- Mix the standard solutions thoroughly
- Set an appropriate concentration range
- If there is an outlier, investigate its cause
- Select an appropriate measurement wavelength
Methods for Reducing Errors in Absorbance Measurement
- Measure the blank correctly
- Wipe water droplets and fingerprints from the cell surface
- Avoid air bubbles inside the cell
- Insert the cell into the instrument in the same orientation
- Dilute the unknown sample so that its absorbance falls within the calibration-curve range
- Perform multiple measurements to confirm reproducibility
Example of How to Write Points for Improvement:
To improve the linearity of the calibration curve, it is necessary to prepare the standard solutions accurately and mix each solution thoroughly before measurement.
In addition, contamination and air bubbles on the cell can cause absorbance to become larger, so it is important to check the cell before measurement.
If the absorbance of the unknown sample lies outside the calibration-curve range, appropriately diluting the sample and remeasuring it can improve the reliability of the concentration estimate.
Difference Between a Superficial Discussion and a Good Discussion
In a discussion of spectrophotometry, simply writing that “a calibration curve was obtained” or “the correlation coefficient was high” results in a superficial discussion.
A persuasive discussion can be produced by relating the linearity of the calibration curve, the correlation coefficient, the range of the unknown sample, and sources of error.
| Superficial Discussion | Good Discussion |
|---|---|
| The calibration curve became linear. | The concentrations and absorbances of the standard solutions showed an approximately linear relationship. This is considered to be because the Beer-Lambert law held within the measured concentration range and absorbance was proportional to concentration. |
| The correlation coefficient was high. | Because the correlation coefficient was close to 1, the linearity of the calibration curve is considered high. However, the reliability of the concentration estimate cannot be adequately judged unless it is also confirmed that the absorbance of the unknown sample lies within the calibration-curve range. |
| The unknown concentration was determined. | The unknown sample concentration was determined by substituting its absorbance into the calibration-curve equation. If the unknown sample was diluted before measurement, the concentration obtained from the calibration curve is the concentration after dilution, so the dilution factor must be considered to determine the original concentration. |
| The value deviated. | Possible reasons the measured value differed from the expected value include errors in preparation of the standard solutions, insufficient blank correction, contamination or air bubbles in the cell, and errors in the dilution factor. |
Examples of Expressions That Can Be Used in Reports
The following expressions can be used when writing the results and discussion of spectrophotometry.
Adjust the necessary parts according to your own experimental results.
- Because absorbance is proportional to concentration, a calibration curve was prepared using standard solutions.
- An approximately linear relationship was observed between the concentrations and absorbances of the standard solutions.
- Because the correlation coefficient was close to 1, the linearity of the calibration curve is considered high.
- The unknown concentration was determined by substituting the absorbance of the unknown sample into the calibration-curve equation.
- Because the unknown sample was diluted before measurement, the dilution factor was taken into account when determining the original concentration.
- Because the absorbance of the unknown sample was within the calibration-curve range, the concentration calculation is considered appropriate.
- One possible reason the high-concentration measurement points deviated from the straight line is that the concentration exceeded the range in which the Beer-Lambert law holds.
- Contamination or air bubbles on the cell surface may have caused the absorbance to be measured larger than the actual value.
- If blank correction was insufficient, absorption from substances other than the target component may have been included in the measured values.
- Errors in preparation of the standard solutions affect the slope and intercept of the calibration curve and can also cause errors in calculating the unknown concentration.
Points to Check When Discussing Spectrophotometry
Checking the following points before writing the report makes the discussion easier to write.
- Was the measurement wavelength appropriate?
- Were the concentrations of the standard solutions prepared accurately?
- Is the calibration curve linear?
- Is the correlation coefficient or coefficient of determination sufficiently high?
- Are there any outliers?
- Is the absorbance of the unknown sample within the calibration-curve range?
- If the unknown sample was diluted, was the dilution factor taken into account?
- Was blank correction performed appropriately?
- Was the cell free of contamination, water droplets, fingerprints, and air bubbles?
- Were the cell orientation and optical path length constant for each measurement?
- Has linearity broken down on the high-concentration or low-concentration side?
- Have the sources of error and points for improvement been written in correspondence with each other?
Summary
Spectrophotometry is an analytical method in which the absorbance of a solution is measured and the concentration of an unknown sample is determined using a calibration curve.
According to the Beer-Lambert law, under constant conditions, a proportional relationship is established between absorbance and concentration.
In a report, it is important to confirm the linearity of the calibration curve, the correlation coefficient, whether the absorbance of the unknown sample lies within the calibration-curve range, and whether the dilution factor has been correctly reflected.
Even when the correlation coefficient is high, if the unknown sample lies outside the range, the reliability of the concentration estimate may decrease.
Possible sources of error include errors in preparation of the standard solutions, insufficient blank correction, contamination or air bubbles in the cell, inappropriate measurement wavelength, and errors in dilution procedures.
In the discussion, specifically explain how these factors affect the absorbance, calibration curve, and unknown concentration.
