In which of the following cell(s) :E_cell= E°_cell ?

(a) Cu|Cu²⁺(0.01 M) || Ag⁺(0.1 M) |Ag(s)

(b) Pt(H₂) |pH=1||Zn²⁺ (0.01 M) |Zn(s)

(c) Pt(H₂) |pH=1||Zn²⁺ (1 M) |Zn(s)

(d) Pt(H₂) |H⁺=0.01 M||Zn²⁺ (0.01 M) |Zn(s)

To determine in which of the given cells the cell potential (E cell) equals the standard cell potential (E° cell), we need to analyze the conditions of each electrochemical cell. The standard cell potential is measured under standard conditions, which typically include 1 M concentrations of all reactants and products, a temperature of 25°C (298 K), and a pressure of 1 atm for gases. Let's break down each option to see if they meet these criteria.

Analyzing Each Cell

Cell (a): Cu|Cu²⁺ (0.01 M) || Ag⁺ (0.1 M) |Ag(s)

In this cell, we have copper and silver half-cells. The concentration of Cu²⁺ is 0.01 M, which is not standard (1 M), and the concentration of Ag⁺ is 0.1 M, which is also not standard. Since neither half-cell is at standard conditions, E cell will not equal E° cell.

Cell (b): Pt(H₂) | pH=1 || Zn²⁺ (0.01 M) |Zn(s)

Here, we have a hydrogen electrode at pH 1, which corresponds to a hydrogen ion concentration of 0.1 M (since pH = -log[H⁺]). The zinc ion concentration is 0.01 M. Although the hydrogen half-cell is close to standard conditions, the zinc half-cell is not. Therefore, E cell does not equal E° cell.

Cell (c): Pt(H₂) | pH=1 || Zn²⁺ (1 M) |Zn(s)

This cell has the hydrogen half-cell at pH 1 (0.1 M H⁺) and the zinc half-cell at 1 M concentration. The hydrogen half-cell is still not at standard conditions, but the zinc half-cell is. Since one half-cell is not standard, E cell will not equal E° cell.

Cell (d): Pt(H₂) | [H⁺] = 0.01 M || Zn²⁺ (0.01 M) |Zn(s)

In this case, both the hydrogen ion concentration (0.01 M) and the zinc ion concentration (0.01 M) are not at standard conditions. Therefore, E cell will not equal E° cell.

Summary of Findings

After analyzing all the cells, we find that none of the cells meet the criteria for E cell to equal E° cell. Each cell has at least one half-cell that does not conform to standard conditions. Therefore, the answer is that none of the provided cells have E cell equal to E° cell.

Key Takeaways

• Standard conditions require 1 M concentrations for all reactants and products.
• pH affects the concentration of H⁺ ions, which must also be considered.
• Both half-cells must be at standard conditions for E cell to equal E° cell.