Discussion Examples for Current Efficiency | Difference Between Theoretical Deposition Amount and Measured Value

What Is Current Efficiency?

Current efficiency is a value representing the proportion of the electric charge passed through the system that was actually used for the intended electrode reaction.
For example, in copper plating and electrolytic refining of copper, the intended reaction is the reaction in which Cu2+ accepts electrons and is deposited as metallic copper, Cu.
If all of the electric charge passed through the system is used for this reaction, the current efficiency approaches 100%.

However, in actual experiments, the amount predicted theoretically may not be obtained because of side reactions such as hydrogen evolution, loss of deposits, electrode-surface condition, fluctuations in current, and other factors.
Therefore, current efficiency is an important indicator for evaluating how closely electrolysis proceeded according to the intended reaction.

Current efficiency = Measured deposition amount ÷ Theoretical deposition amount × 100

Main Items to Include in the Results

In experiments discussing current efficiency, organize the type of electrolyte, electrode materials, current, voltage, electrolysis time, electrode masses before and after electrolysis, measured deposition amount, theoretical deposition amount, current efficiency, and other information.
The current value and electrolysis time are particularly necessary for calculating the theoretical deposition amount.

Main Items to Include in the Results

• Type of experiment
• Type of electrolyte
• Type of metal deposited
• Electrode material
• Electrode area
• Current
• Voltage
• Electrolysis time
• Electrode mass before electrolysis
• Electrode mass after electrolysis
• Measured deposition amount
• Theoretical deposition amount calculated from Faraday’s law
• Current efficiency
• Condition of the deposit
• Presence or absence of side reactions
• Causes of error and points for improvement

Reference Experimental Values and Calculation Examples for Current Efficiency and Theoretical Deposition Amount

Here, using a copper-plating experiment as an example, the process of determining the theoretical deposition amount from the electric charge passed through the system and calculating the current efficiency by comparison with the actual deposition amount is organized.

In electrolysis and plating, a metal is deposited on an electrode in proportion to the electric charge passed through the system.
However, in practice, the theoretical and measured values may not agree because of side reactions, electrode-surface condition, solution concentration, current density, and errors during washing and drying.

Reference Experimental Conditions

Example Measurement Results

The following is an example in which the amount of copper deposited was measured while the current and electrolysis time were varied.
The theoretical deposition amount is the value calculated under the assumption that all of the electric charge passed through the system was used for copper deposition.

Example Calculation of Electric Charge

Electric charge is determined from the product of current and electrolysis time.

Electric charge Q = Current I × Time t

For sample B, the current is 0.20 A and the electrolysis time is 600 s, so the electric charge is calculated as follows.

Q = 0.20 A × 600 s = 120 C

Therefore, 120 C of electric charge was passed through sample B.

Example Calculation of Theoretical Deposition Amount

The copper-deposition reaction is a reaction in which Cu2+ accepts two electrons and becomes copper.
Therefore, 2 mol of electrons are required to deposit 1 mol of copper.

Cu2+ + 2e− → Cu

The theoretical deposition amount can be determined using the following equation.

Theoretical deposition amount m = Q × M ÷ (n × F)

Here, Q is the electric charge, M is the molar mass of copper, n is the number of electrons involved in the reaction, and F is the Faraday constant.
For sample B, Q = 120 C, M = 63.5 g/mol, n = 2, and F = 96500 C/mol.

m = 120 × 63.5 ÷ (2 × 96500)

m = 7620 ÷ 193000 = 0.0395 g

Therefore, the theoretical deposition amount for sample B is 0.0395 g.

Example Calculation of Current Efficiency

Current efficiency expresses as a percentage how much was actually deposited relative to the amount that should theoretically have been deposited.

Current efficiency (%) = Measured deposition amount ÷ Theoretical deposition amount × 100

For sample B, the theoretical deposition amount is 0.0395 g and the measured deposition amount is 0.0369 g.

Current efficiency = 0.0369 ÷ 0.0395 × 100 = 93.4%

From this result, approximately 93.4% of the electric charge passed through the system was considered to have been effectively used for copper deposition.

Example Calculation of the Difference Between the Theoretical and Measured Values

By examining the difference between the theoretical deposition amount and measured deposition amount, it is possible to consider whether part of the electric charge was used for reactions other than the intended reaction.

Difference = Theoretical deposition amount − Measured deposition amount

For sample B, the value is determined as follows.

Difference = 0.0395 − 0.0369 = 0.0026 g

This difference may have resulted from some of the electric charge not being used for copper deposition, loss of the deposited material, or losses during washing and drying.

Trend When the Current Is Changed

The results are compared when the electrolysis time is fixed at 600 s and the current is changed.
As the current increases, the electric charge and theoretical deposition amount also increase.

In this reference example, increasing the current increases the deposition amount, but the current efficiency decreases slightly.
This is because at high current, depletion of concentration near the electrode surface, side reactions such as hydrogen evolution, and formation of coarse deposits become more likely.

Trend When the Electrolysis Time Is Changed

The results are compared when the current is fixed at 0.20 A and the electrolysis time is changed.
As the electrolysis time increases, the electric charge and theoretical deposition amount increase.

In this reference example, when the electrolysis time was changed at the same current, the current efficiencies were almost the same.
This was considered to result from current density and electrode-surface condition having a stronger effect on current efficiency than differences in electrolysis time.

Example of Efficiency Reduction Caused by Side Reactions

In electrolysis, side reactions such as hydrogen evolution may occur in addition to the intended metal deposition.
When electric charge is used for side reactions, the measured deposition amount becomes smaller than the theoretical deposition amount and the current efficiency decreases.

Example of How to Write the Results

Electrolysis was performed using an aqueous copper-ion solution and the amount of copper deposited was measured.
When a current of 0.20 A was passed for 600 s, the electric charge was 120 C.
The theoretical deposition amount calculated using Faraday’s law was 0.0395 g, while the measured deposition amount was 0.0369 g.
Therefore, the current efficiency was calculated to be 93.4%.

When the current was increased from 0.10 A to 0.30 A, both the theoretical and measured deposition amounts increased.
On the other hand, the current efficiency decreased from 95.4% to 90.9%.
From this result, side reactions other than copper deposition or deterioration of the deposit condition were considered to have become more likely under high-current conditions.

Points for Connecting the Results to the Discussion

In a discussion of current efficiency, it is important to show the difference between the theoretical and measured deposition amounts and then specifically explain why that difference occurred.

• Was the electric charge correctly calculated from the current and time?
• Was the fact that the number of electrons is 2 in the copper-deposition reaction reflected in the calculation?
• Was the difference between the theoretical and measured deposition amounts shown quantitatively?
• Can the reason why the current efficiency was below 100% be explained?
• Could side reactions or coarsening of the deposit have occurred under high-current conditions?
• Could insufficient washing or drying have caused the measured value to be overestimated?
• Could loss of the deposit or contamination of the electrode surface have caused the measured value to be smaller?

Example Discussion

In this experiment, the theoretical deposition amount in the electrolytic deposition of copper was determined from the electric charge passed through the system and compared with the measured deposition amount to calculate the current efficiency.
Under the condition where a current of 0.20 A was passed for 600 s, the electric charge was 120 C, the theoretical deposition amount was 0.0395 g, and the measured deposition amount was 0.0369 g.
The current efficiency was 93.4%, and the measured value was smaller than the theoretical value.

One possible reason why the measured deposition amount was smaller than the theoretical deposition amount is that part of the electric charge passed through the system was used for reactions other than copper deposition.
Particularly under high-current conditions, side reactions such as hydrogen evolution are more likely to occur at the electrode surface, so the amount of electric charge used for copper deposition may have decreased.
In addition, if the supply of copper ions cannot keep up with the electrode reaction, the deposit may become coarse and more likely to fall off.

When the current was increased, both the theoretical and measured deposition amounts increased, but the current efficiency decreased slightly.
This was considered to result from the greater reaction amount per unit time at higher current, while the copper-ion concentration near the electrode more readily decreased, making side reactions and nonuniform deposition more likely.
Therefore, to deposit metal efficiently, it is necessary to appropriately control the current density, stirring, solution concentration, and electrode-surface condition.

On the other hand, under conditions where the measured deposition amount was close to the theoretical value, most of the current was considered to have been used for copper deposition.
However, the measured value may contain errors caused by residual electrolyte or salts due to insufficient washing, residual water due to insufficient drying, or mass loss caused by detachment of the deposit.
Therefore, to accurately evaluate current efficiency, it is important to keep the washing, drying, and weighing procedures after deposition consistent.

Summary

In a current-efficiency experiment, the electric charge is determined from the current and time, and the theoretical deposition amount is calculated using Faraday’s law.
The proportion of electric charge used for the intended reaction can then be evaluated by comparing the measured deposition amount with the theoretical deposition amount.

In this reference example, increasing the current increased the amount deposited, but the current efficiency decreased slightly.
In a report, after presenting the theoretical deposition amount, measured deposition amount, and current efficiency, it is useful to discuss side reactions, condition of the deposit, and errors in washing, drying, and weighing in relation to one another.

Faraday’s Law and Theoretical Deposition Amount

According to Faraday’s law, the amount of substance reacting during electrolysis is proportional to the electric charge passed through the system.
The electric charge Q is determined from the product of current I and electrolysis time t.
The electric charge carried by 1 mol of electrons is the Faraday constant F, approximately 96500 C/mol.

A fixed number of electrons is required for a metal ion to be deposited as a metal.
For example, 2 mol of electrons are required for Cu2+ to be deposited as Cu.
One mole of electrons is required for Ag+ to be deposited as Ag.
By using this number of electrons, the theoretical deposition amount can be calculated.

Q = I × t

Amount of electrons = Q ÷ F

F ≒ 96500 C/mol

Concept of Calculating the Theoretical Deposition Amount

To determine the theoretical deposition amount, first calculate the electric charge passed through the system.
Next, divide that electric charge by the Faraday constant to calculate the amount of electrons.
Then, use the electrode-reaction equation to confirm the number of electrons required to deposit 1 mol of the metal and convert this to the amount of metal.
Finally, multiply by the molar mass of the metal to convert it to mass.

For copper deposition, for example, Cu2+ + 2e- → Cu, so 2 mol of electrons are required to deposit 1 mol of copper.
Therefore, dividing the amount of electrons by 2 gives the theoretical amount of copper deposited.
This calculation is the basis for determining current efficiency.

Cu2+ + 2e- → Cu

Theoretical amount of Cu = Amount of electrons ÷ 2

Theoretical mass of Cu = Theoretical amount of Cu × Molar mass of Cu

How to Determine the Measured Deposition Amount

In many cases, the measured deposition amount is determined from the difference in cathode mass before and after electrolysis.
The cathode before electrolysis is washed and dried before its mass is measured, and after electrolysis it is washed and dried again while taking care not to lose the deposit.
The difference is the amount of metal actually deposited.

However, the measured deposition amount is strongly affected by the measurement procedure.
If water or electrolyte remains because of insufficient drying, the measured deposition amount becomes larger.
Conversely, if the deposit peels off during washing or drying, the measured deposition amount becomes smaller.
Therefore, the reliability of the measured value depends on how the electrode is handled.

Measured deposition amount = Cathode mass after electrolysis − Cathode mass before electrolysis

Why the Theoretical and Measured Values Do Not Agree

The theoretical deposition amount is calculated under the assumption that all of the electric charge passed through the system is used for the intended metal-deposition reaction.
However, in an actual experiment, not all of the electric charge is necessarily used for the intended reaction.
Side reactions such as hydrogen evolution may occur, the deposit may peel off, or the current may fluctuate, causing a difference between the measured and theoretical values.

Deviations may also arise from the mass-measurement procedure.
If water or electrolyte remains on the electrode, the measured value becomes larger, while loss of the deposit makes it smaller.
Therefore, the difference between the theoretical and measured values must be discussed from both the efficiency of the reaction itself and the measurement procedure.

When Current Efficiency Is Below 100%

When current efficiency is below 100%, the measured deposition amount is smaller than the theoretical deposition amount.
Possible major causes include side reactions such as hydrogen evolution, loss of deposits, overrecording of current, overrecording of electrolysis time, insufficient metal-ion concentration, and contamination of the electrode surface.

Particularly when hydrogen evolution occurs, part of the electric charge is used for H2 formation rather than reduction of metal ions.
Therefore, less metal is deposited than theoretically expected.
If many bubbles were observed on the electrode surface, the possibility of a side reaction should be discussed.

When Current Efficiency Exceeds 100%

When current efficiency exceeds 100%, the measured deposition amount is larger than the theoretical deposition amount.
It is unnatural for the measured amount to greatly exceed the theoretical value based only on the intended reaction.
Therefore, insufficient drying, electrolyte adhesion, insufficient washing, adhesion of impurities, weighing errors, and similar factors should be suspected.

For example, if the electrode is weighed while water or electrolyte remains on the surface after electrolysis, the mass becomes larger by that amount and the measured deposition amount is overestimated.
In addition, if precipitates or impurities other than the deposited material adhere to the electrode, the apparent mass increase may become larger.

Side Reactions Caused by Hydrogen Evolution

During electrolysis or plating, hydrogen evolution may occur at the cathode at the same time as reduction of metal ions.
In acidic solutions, H+ may be reduced to produce H2, while in neutral or basic solutions, water may be reduced to produce H2.
These reactions compete with the intended metal deposition.

When hydrogen evolution occurs, electrons are used for H+ or H2O rather than metal ions, so the measured metal-deposition amount becomes smaller than the theoretical value.
In addition, if the generated bubbles adhere to the electrode surface, metal ions cannot easily approach those areas, which may cause nonuniform deposition and reduced adhesion.

2H+ + 2e- → H2

2H2O + 2e- → H2 + 2OH-

Effect of Loss of Deposits

If metal deposits peel off from the electrode surface, the measured deposition amount becomes smaller than the amount actually deposited.
When the deposit adheres in a powdery, dendritic, or coarse form, it becomes more likely to fall off during washing, drying, or handling.
Such peeling is more likely when the current density is too high or the substrate pretreatment is insufficient.

Because the amount of metal remaining on the electrode is used as the measured value in the current-efficiency calculation, the lost portion is not included.
Therefore, loss of the deposit causes the current efficiency to be underestimated.
If metal powder is observed in the electrolyte or at the bottom of the container after the experiment, loss of deposits should be included in the discussion.

Effect of Insufficient Drying

If the electrode is weighed without being sufficiently dried after electrolysis, water and electrolyte remain attached to it.
In this case, mass other than that of the deposited metal is included, so the measured deposition amount becomes larger.
This is a representative cause when the current efficiency exceeds 100%.

Water tends to remain particularly when the electrode surface is rough or the deposit is porous.
To avoid insufficient drying, the electrode must be appropriately washed and sufficiently dried before weighing.
However, rubbing too strongly or heating excessively may cause the deposit to peel off.

Effect of Current Fluctuations

The theoretical deposition amount is determined from the current and electrolysis time.
Therefore, if the current fluctuates during the experiment but only the initial or final current value is used, an error occurs in the calculation of the electric charge passed through the system.
If the current is recorded as larger than the actual value, the theoretical deposition amount becomes larger and the current efficiency is calculated as lower.

Conversely, if the current is underestimated, the theoretical deposition amount becomes smaller and the current efficiency is calculated as higher.
Causes of unstable current include bubbles on the electrode surface, changes in electrolyte concentration, changes in the distance between the electrodes, and poor electrical contact.
It is desirable to record the current at regular intervals during the experiment.

Error in Electrolysis Time

Electrolysis time also directly affects the theoretical deposition amount.
If a longer time than the actual electrolysis time is recorded, the theoretical deposition amount becomes larger and the current efficiency is calculated as lower.
Conversely, if the electrolysis time is recorded as shorter, the theoretical deposition amount becomes smaller and the current efficiency is calculated as higher.

It is important to accurately manage the time when the power supply is turned on and off.
In addition, if time was required for the current to stabilize even though the power supply was on, or if poor contact occurred during electrolysis, the actual electric charge passed through the system may differ from the simple product of current and time.

Effect of Electrode-Surface Condition

Because electrolysis occurs at the electrode surface, the surface condition affects the deposition amount and current efficiency.
If the electrode is dirty, covered with an oxide film, contaminated with oil, or covered with bubbles, reduction of metal ions becomes difficult to proceed uniformly.
As a result, the deposition amount may decrease or the deposit may become more likely to peel off.

If the surface condition is poor, the theoretical amount may not be deposited even when the same electric charge is passed through the system, and the current efficiency may decrease.
It is important to wash the electrode before the experiment and polish it when necessary.
In addition, if bubbles adhere during electrolysis, the effective electrode area becomes smaller.

Effect of Current Density

Current density is the current flowing per unit area of the electrode.
If the current density is too high, reduction of metal ions proceeds rapidly at the electrode surface and the supply of ions may not be able to keep up.
As a result, the deposit becomes coarse, powdery, or dendritic and is more likely to peel off.

In addition, side reactions such as hydrogen evolution are more likely to occur at high current density, so current efficiency may decrease.
On the other hand, if the current density is too low, the deposition rate is slow and a sufficient mass change may not be obtained within the experimental time.
Setting an appropriate current density is important for obtaining results close to the theoretical value.

Effect of Metal-Ion Concentration

If the concentration of metal ions in the electrolyte is too low, the supply of metal ions to the cathode surface may become insufficient and metal deposition may not proceed efficiently.
In this case, part of the electric charge passed through the system is more likely to be used for side reactions such as hydrogen evolution, and the current efficiency decreases.

In addition, as metal ions continue to be consumed during electrolysis, their concentration near the cathode decreases.
If stirring is insufficient, a concentration gradient may form near the electrode surface and deposition may become nonuniform.
Metal-ion concentration and mass transfer are important when considering current efficiency.

Effect of the Anode Material

In plating and electrolytic refining, changes in metal-ion concentration differ depending on the anode material.
When the same metal as the metal being deposited is used as the anode, the metal is oxidized at the anode and dissolves into the solution as metal ions, replenishing the metal ions consumed at the cathode.
Therefore, the metal-ion concentration is more easily maintained.

On the other hand, when an inert anode is used, the anode does not replenish metal ions, so the metal-ion concentration may decrease as metal is deposited at the cathode.
This may change the deposition rate and current efficiency.
When discussing current efficiency, it is also necessary to confirm whether the anode participated in the reaction.

Effect of Insufficient Stirring

If stirring is insufficient, metal ions are consumed at the cathode surface and their concentration near the electrode decreases.
As a result, the supply of metal ions cannot keep up and the intended deposition reaction becomes difficult to proceed.
In this case, side reactions such as hydrogen evolution may increase and the current efficiency may decrease.

Moderate stirring has the effect of supplying metal ions to the cathode surface and reducing concentration nonuniformity.
However, if stirring is too strong, the deposit may peel off or the surface may become nonuniform.
Stirring conditions must be kept constant to obtain reproducible results.

Causes of Error in Current Efficiency

Causes of error in current efficiency include side reactions, loss of deposits, insufficient drying, electrolyte adhesion, fluctuations in current, errors in electrolysis time, differences in electrode area, nonuniform current density, insufficient metal-ion concentration, contamination of electrode surfaces, and weighing errors.
Because current efficiency is determined from the ratio of the theoretical and measured values, it is important to separately consider which value contains the error.

Errors on the theoretical-deposition side include mistakes in recording the current or electrolysis time, errors in determining the number of electrons, and unit-conversion errors.
Errors on the measured-deposition side include mass measurement, drying, loss of deposits, and electrolyte adhesion.
Classifying the errors in this way makes the discussion more specific.

When the Results Can Be Considered Good

A current-efficiency experiment can be considered to have produced good results when the current is stable, the electrolysis time is accurately controlled, the intended metal is uniformly deposited on the electrode surface, and the measured value is close to the theoretical deposition amount.
In addition, if the deposit does not peel off and the mass can be accurately measured after drying, the reliability of the measured value is high.

The current efficiency does not need to agree exactly with 100%.
In experiments, some deviation occurs because of side reactions and measurement errors.
What is important is that the obtained value lies within a reasonable range and that the reason for the deviation can be explained chemically.

Example Discussions When the Experiment Did Not Go Well

When the current efficiency deviates greatly, first determine whether it is too low or exceeds 100%.
If it is low, consider side reactions, loss of deposits, and fluctuations in current.
If it exceeds 100%, consider insufficient drying, electrolyte adhesion, and weighing errors.
It is important to organize the possible causes according to the direction of the deviation.

How to Write Points for Improvement

In a discussion of current efficiency, writing not only the causes of error but also points for improvement makes the report easier to organize.
Points for improvement can be organized according to current control, electrode handling, handling of the deposit, mass measurement, and calculations.

Improvements to Current and Electrolysis Conditions

• Keep the current constant
• Record the current at regular intervals
• Measure the electrolysis time accurately
• Avoid excessively high current density
• Keep the distance between the electrodes constant
• Check for poor electrical contact

Improvements to the Electrodes and Deposits

• Wash the electrode surfaces
• Polish the electrodes when necessary
• Handle the electrodes carefully so that the deposits do not peel off
• Review the conditions if many bubbles are observed
• Maintain an appropriate metal-ion concentration
• Stir gently when necessary

Improvements to Mass Measurement and Calculations

• Dry under the same conditions before and after electrolysis
• Thoroughly wash away the electrolyte
• Weigh without leaving residual water
• Use the electronic balance correctly
• Correctly determine the number of electrons from the electrode-reaction equation
• Confirm the units of current, time, and the Faraday constant
• Perform multiple measurements and calculate the average value

Difference Between a Superficial Discussion and a Good Discussion

In a discussion of current efficiency, simply writing that “the value differed from the theoretical value” or “the efficiency was low” results in a superficial discussion.
A good discussion relates the theoretical deposition amount, measured deposition amount, side reactions, measurement errors, and electrode condition.

Examples of Expressions That Can Be Used in Reports

The following expressions can be used when writing the results and discussion of current efficiency.
Adjust the necessary parts according to your own experimental results.

• Current efficiency is the ratio of the measured deposition amount to the theoretical deposition amount.
• According to Faraday’s law, the amount deposited is proportional to the electric charge passed through the system.
• The theoretical deposition amount is determined from the current, electrolysis time, number of electrons, and molar mass of the metal.
• The measured deposition amount is determined from the difference in electrode mass before and after electrolysis.
• When current efficiency is low, side reactions or loss of deposits may be considered.
• When hydrogen evolution occurs, part of the electric charge is not used for deposition of the intended metal.
• If the deposit peels off, the measured deposition amount becomes smaller.
• Insufficient drying or electrolyte adhesion leads to overestimation of the measured deposition amount.
• Fluctuations in current lead to errors in calculating the theoretical deposition amount.
• To increase current efficiency, conditions are required that suppress side reactions and allow the deposit to adhere stably.

Points to Check When Discussing Current Efficiency

Checking the following points before writing the report makes the discussion easier to write.

• Is the definition of current efficiency written?
• Is Faraday’s law explained?
• Is the electric charge determined from the current and electrolysis time?
• Is the required number of electrons confirmed from the electrode-reaction equation?
• Is the calculation process for the theoretical deposition amount shown?
• Is the method for determining the measured deposition amount described?
• Are the reasons for low current efficiency discussed?
• Are the possible causes considered if the value exceeds 100%?
• Are the effects of side reactions and hydrogen evolution explained?
• Are loss of deposits and insufficient drying considered?
• Are errors in current and electrolysis time considered?
• Do the points for improvement correspond to the causes of error?

Summary

Current efficiency is an indicator showing how much of the electric charge passed through the system was used for the intended electrode reaction.
By using Faraday’s law, the theoretical deposition amount can be determined from the current and electrolysis time.
Current efficiency can be calculated by comparing the measured deposition amount with the theoretical deposition amount.

When current efficiency is below 100%, possible causes include side reactions such as hydrogen evolution, loss of deposits, insufficient metal-ion concentration, and fluctuations in current.
On the other hand, when current efficiency exceeds 100%, overestimation of the measured value caused by insufficient drying, electrolyte adhesion, adhesion of impurities, weighing errors, and other factors should be suspected.

In a report, rather than simply writing that “the value differed from the theoretical value,” organize and discuss Faraday’s law, theoretical deposition amount, measured deposition amount, current efficiency, side reactions, loss of deposits, insufficient drying, fluctuations in current, causes of error, and points for improvement.
Current efficiency is an important indicator for determining how closely electrolysis or plating proceeded according to the intended reaction.