Question

A meter reads that a battery is putting out 450 amp in the external circuit of a cell. The cell is involved in the electrolysis of a copper sulfate solution. During the \(30.0 \mathrm{~min}\) that the current was allowed to flow, a total of \(30 \mathrm{~g}\) of copper metal was deposited at the cell's cathode. Was the meter an accurate measurement of current? \((\mathrm{F}=96,500\) coul. \()\)

Short answer

The time given is 30 minutes, which is equal to 1800 seconds. The moles of deposited copper can be calculated as Moles of Cu = \(30 g / (63.5 g/mol)\). Using Faraday's law of electrolysis, the total charge (Q) required to deposit this amount of Cu is Q = \(30 g / (63.5 g/mol) \times 96,500 C/mol \times 2\). The theoretical current (I) can be found by dividing the total charge by time: I = \(Q / 1800 s\). Comparing the theoretical current with the given meter reading of 450 amps, we can determine the accuracy of the meter.

Step-by-step solution

Convert time to seconds

We need to convert the time given in minutes to seconds to use it in our calculations. 30 minutes × 60 seconds/minute = 1800 seconds

Find moles of copper deposited

To find the moles of deposited copper, we should use the molar mass of Copper (Cu), which is 63.5 g/mol. Moles of Cu = mass of Cu / molar mass of Cu Moles of Cu = \(30 g / (63.5 g/mol)\)

Find the total charge transferred (Q)

Using Faraday's law of electrolysis, we can find the total charge (Q) required to deposit this amount of Cu. Total Charge (Q) = Moles of Cu × Faraday's constant (F) × valency of Cu Copper has a valency of +2, so: Q = \(30 g / (63.5 g/mol) \times 96,500 C/mol \times 2\)

Calculate the theoretical current

Now, we will find the theoretical current by dividing the total charge by time in seconds. Theoretical Current (I) = Total Charge (Q) / Time (t) I = \(Q / 1800 s\)

Compare the theoretical current with the given meter reading

Finally, we will compare the theoretical current (I) with the given meter reading (450 amps) to determine if the meter was accurate or not. By following these steps, we can determine the accuracy of the meter and answer the question posed in the exercise.

Key concepts

Copper Sulfate Solution

Copper sulfate solution is a blue liquid that contains copper ions (Cu²⁺) and sulfate ions (SO₄²⁻) dissolved in water. It plays a crucial role in the process of electrolysis, which is a method used to cause a chemical change via electrical current.
During electrolysis, copper sulfate solution breaks down at the electrodes, assisting in the deposition of pure copper metal at the cathode. This indicates that the copper ions in the solution gain electrons and turn into solid copper.
Electrolysis of copper sulfate is often used in industries for refining copper as it helps in purifying copper from its ores. It's important to understand the composition and behavior of this solution when learning about electrochemical processes.

Current Measurement

Current measurement is crucial in electrolysis as it helps determine the amount of substance deposited at the electrodes. Current, measured in amperes (A), is the rate at which charge flows through the circuit.
While measuring current, one must ensure that the instruments are calibrated correctly. This is because incorrect readings can lead to false conclusions about the electrolysis process.
In this exercise, the meter reading was 450 amps. This figure encompasses the amount of charge moving through the circuit, important for determining if the current truly reflects the amount of copper deposited.

Faraday's Law

Faraday's Law of Electrolysis is a fundamental principle that connects the amount of electric charge carried through a circuit with the chemical change it induces at the electrode. The law states that the mass of a substance deposited or dissolved at an electrode is directly proportional to the total electric charge passed through the circuit.
In symbolic terms, Faraday's Law can be expressed as:

• Mass of element = (Equivalent weight of element × Total Charge) / Faraday's Constant (F)

This relationship shows that larger currents will deposit more material over time, assuming the same valency and charge conditions.
Faraday's constant, approximately 96,500 coulombs per mole, represents the charge of one mole of electrons, which is essential in these calculations.

Moles of Copper

Understanding the concept of moles is crucial in determining how much copper gets deposited during electrolysis. A mole is a unit that represents a specific number of particles, often atoms or molecules, in a substance.
To calculate how much copper is deposited, you can use the formula for moles:

• Moles of Copper = Mass of Copper / Molar Mass of Copper

In this exercise, knowing the mass of copper deposited (30 g) and the molar mass (63.5 g/mol) allowed for calculating the moles of copper involved, which further helped in finding out the charge transferred.

Charge Transfer

Charge transfer in the context of electrolysis refers to the movement of charge that causes the deposition of copper on the cathode.
The total charge transferred, denoted as (Q), is calculated by multiplying the moles of copper by Faraday's constant and the valency of copper, which is 2 (due to Cu²⁺ ions).
The process can be represented as:

• Total Charge (Q) = Moles of Copper × Faraday's Constant × Valency of Copper

This calculation reveals the charge necessary to deposit the given amount of copper, serving as an essential part of verifying the meter's accuracy in this exercise.

Theoretical Current Calculation

The theoretical current calculation is a valuable step in verifying the accuracy of the experimental setup. To find the theoretical current, divide the total charge transferred by the time the charge had to flow.
The formula is:

• Theoretical Current (I) = Total Charge (Q) / Time (t)

This calculation gives an estimate of what the current should be under ideal conditions. Comparing this theoretical current to the actual reading, 450 amps in this case, provides insight into how closely the setup aligns to expected conditions and helps assess the measurement instrument's reliability.