Question

A current of $2.0\text{ A}$ is passed for 5 hours through an electrolytic cell containing an aqueous solution of a metal salt, depositing $12.0\text{ g}$ of the metal at the cathode. If the atomic mass of the metal is $193\text{ g mol}^{-1}$, find the oxidation state of the metal ion in the solution. (Take Faraday's constant $F = 96500\text{ C mol}^{-1}$).

• A. \( +1 \)
• B. \( +2 \)
• C. \( +3 \)
• D. \( +6 \)

Hint:

A fast alternative method is: \[ \text{Moles of metal deposited} = \frac{12}{193} \] \[ \text{Moles of electrons passed} = \frac{36000}{96500} \] Then, \[ n = \frac{\text{moles of electrons}}{\text{moles of metal}} \] which again gives: \[ n \approx 6 \]

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
We are asked to determine the oxidation state (valency) of a metal ion in a solution.
We are given the current, duration of electrolysis, mass of metal deposited, and the atomic mass of the metal.
Step 2: Key Formula or Approach:
According to Faraday's First Law of Electrolysis, the mass \(m\) of a metal deposited at the cathode is:
\[ m = \frac{M \cdot I \cdot t}{n \cdot F} \]
where:
- \(m\) is the mass of metal deposited (\(12.0\text{ g}\)).
- \(M\) is the atomic mass of the metal (\(193\text{ g mol}^{-1}\)).
- \(I\) is the current (\(2.0\text{ A}\)).
- \(t\) is the time in seconds.
- \(n\) is the oxidation state (valency) of the metal ion.
- \(F\) is Faraday's constant (\(96500\text{ C mol}^{-1}\)).
Step 3: Detailed Explanation:
1. Convert the electrolysis time from hours into seconds:
\[ t = 5\text{ h} \times 3600\text{ s h}^{-1} = 18000\text{ s} \]
2. Rearrange Faraday's formula to solve for the oxidation state \(n\):
\[ n = \frac{M \cdot I \cdot t}{m \cdot F} \]
3. Substitute the given values into the equation:
\[ n = \frac{193 \times 2.0 \times 18000}{12.0 \times 96500} \]
4. Simplify the numerical calculation:
- Calculate total charge \(Q = I \cdot t = 2.0 \times 18000 = 36000\text{ C}\).
- Substituting this:
\[ n = \frac{193 \times 36000}{12.0 \times 96500} \]
- Recognize that \(96500 / 193 = 500\):
\[ n = \frac{36000}{12.0 \times 500} \]
\[ n = \frac{36000}{6000} = 6 \]
5. Thus, the oxidation state of the metal ion is \(+6\), matching Option (D).
Step 4: Final Answer:
The oxidation state of the metal ion in the solution is \(+6\), which corresponds to Option (D).