Electrolysis of Cadmium: What mass of cadmium metal is produced when an electric current of 4.0 Amps passes through a dilute aqueous solution of cadmium chloride for 3.0 minutes?

Answer 1

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To determine the mass of cadmium metal produced during the electrolysis of cadmium chloride, you can use Faraday's laws of electrolysis. The equation that relates the mass of a substance produced during electrolysis to the electric current and time is given by:

\[ \text{Mass (g)} = \frac{\text{Current (A)} \times \text{Time (s)}}{\text{Faraday's Constant (C/mol)}} \times \frac{\text{Molar Mass (g/mol)}}{\text{Number of Electrons Transferred}} \]

Here's how you can calculate it:

1. Identify the balanced chemical equation for the electrolysis of cadmium chloride to determine the number of electrons transferred.

2. Find the molar mass of cadmium (Cd) from the periodic table.

3. Faraday's constant is approximately \( 96,485 \, \text{C/mol} \).

4. Plug in the values into the equation.

Remember to convert the time from minutes to seconds.

If the chemical equation for the electrolysis of cadmium chloride is, for example:

\[ \text{Cd}^{2+} + 2e^- \rightarrow \text{Cd} \]

Then, the number of electrons transferred (\(n\)) is 2.

Assuming the molar mass of cadmium is 112.41 g/mol, and the current is 4.0 Amps for 3.0 minutes, the calculation would be:

\[ \text{Mass (g)} = \frac{(4.0 \, \text{A} \times 3.0 \, \text{min} \times 60 \, \text{s/min})}{96485 \, \text{C/mol}} \times \frac{112.41 \, \text{g/mol}}{2} \]

After performing this calculation, you'll find the mass of cadmium metal produced during the electrolysis is 0.42g

Answer 2

To obtain solid cadmium (Cd) from a solution of cadmium chloride (CdCl₂), we have to convert Cd²⁺(aq) to Cd(s) as shown below:

Cd²⁺(aq) + 2e- ==> Cd(s)

Thus each mole of Cd²⁺ will require 2 moles of electrons (e-)

How many mols of electrons can be transferred by 4 amps running for 3 minutes?

4.0 amps of current is equal to 4.0 coulombs/sec

3.0 minutes x 60 sec / min = 180 sec

Thus, total number of coulombs (C) provided = 180 sec x 4.0 C/sec = 720 C

Convert this value to moles of electrons using the Faraday constant:

720 C x 1 mol e- / 96485 C = 7.46x10^-3 mols e-

Finally, use the fact that each mol of Cd²⁺ needs 2 mols of electrons. Thus...

mols of Cd(s) produced = 7.46x10^-3 mols e- x 1 mol Cd / 2 mols e- = 3.73x10^-3 mols Cd(s)

Convert this to mass using the atomic mass of Cd (112 g / mol):

3.73x10^-3 mols Cd(s) x 112 g / mol = 0.42 g Cd (Answer)