Consider the following equation for an electrochemical cell reaction. Which of the following changes in condition will increase the cell voltage ?
`H_(2)(g)+PbCl_(2)(s)toPb(s)+2HCl(aq)`
(I) addition of concentrated `HClO_(4)` solution
`{:(II)"Increase the pressure of "H_(2)(g) (III)"increase the amount of " Pb(s)}`

Options

A. III
B. I and II
C. II and III
D. II

Answer

To determine which changes in conditions will increase the cell voltage for the electrochemical reaction:

\[ H_2(g) + PbCl_2(s) \rightarrow Pb(s) + 2HCl(aq) \]

we will analyze each condition step by step using the Nernst equation.

### Step 1: Understanding the Reaction
The reaction involves hydrogen gas reacting with lead(II) chloride to produce solid lead and hydrochloric acid. The relevant species in the Nernst equation will be the concentration of \( H^+ \) ions and the partial pressure of \( H_2 \).

### Step 2: Applying the Nernst Equation
The Nernst equation is given by:

\[ E_{cell} = E^0_{cell} - \frac{0.0591}{n} \log \left( \frac{[Products]}{[Reactants]} \right) \]

In this case, the products are \( Pb(s) \) and \( HCl(aq) \), and the reactants are \( H_2(g) \) and \( PbCl_2(s) \).

### Step 3: Analyzing Each Condition

**Condition I: Addition of Concentrated \( HClO_4 \) Solution**
- Adding \( HClO_4 \) increases the concentration of \( H^+ \) ions in the solution.
- According to the Nernst equation, an increase in \( [H^+] \) will increase the value of the logarithmic term, which is subtracted from \( E^0_{cell} \).
- Therefore, this will **decrease** the cell voltage.

**Condition II: Increase the Pressure of \( H_2(g) \)**
- Increasing the pressure of \( H_2 \) effectively increases its concentration.
- In the Nernst equation, an increase in the partial pressure of \( H_2 \) will decrease the value of the logarithmic term because it appears in the denominator.
- Thus, this will **increase** the cell voltage.

**Condition III: Increase the Amount of \( Pb(s) \)**
- The concentration of pure solids does not affect the cell potential since they are considered to have an activity of 1.
- Therefore, increasing the amount of \( Pb(s) \) will **not affect** the cell voltage.

### Conclusion
From the analysis, only the second condition (increasing the pressure of \( H_2(g) \)) will increase the cell voltage.

### Final Answer
The correct answer is **Condition II: Increase the pressure of \( H_2(g) \)**.

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