Question

Which of the following is true for a spontaneous galvanic cell?

• A. \(E^\circ_{cell}0,\ Q_c>K_c\)
• B. \(E^\circ_{cell}=0,\ \Delta G^\circ=0,\ Q_c=K_c\)
• C. \(E^\circ_{cell}<0,\ \Delta G^\circ<0,\ Q_c<K_c\)
• D. \(E^\circ_{cell}>0,\ \Delta G^\circ<0,\ Q_c<K_c\)

Hint:

For electrochemical cells, remember the shortcut: \[ E^\circ_{cell}>0 \Rightarrow \text{Spontaneous reaction} \] \[ E^\circ_{cell}=0 \Rightarrow \text{Equilibrium} \] \[ E^\circ_{cell}<0 \Rightarrow \text{Non-spontaneous reaction} \]

Answer 1

The Correct Option is D

To solve the question of which statement is true for a spontaneous galvanic cell, we need to understand how galvanic cells function and what characterizes spontaneity in electrochemical reactions:

1. \(E^\circ_{cell}\): This is the standard cell potential. For a galvanic cell, which operates spontaneously, the cell potential must be positive. Thus, \(E^\circ_{cell} > 0\) is expected for spontaneous reactions.
2. \(\Delta G^\circ\): This is the change in Gibbs free energy at standard conditions. For a process to be spontaneous, the Gibbs free energy change must be negative, so \(\Delta G^\circ < 0\).
3. \(Q_c\) and \(K_c\): \(Q_c\) is the reaction quotient, and \(K_c\) is the equilibrium constant. For a reaction to proceed spontaneously in the forward direction, the reaction quotient should be less than the equilibrium constant, so \(Q_c < K_c\).

By understanding these conditions, we can evaluate the given options:

\(E^\circ_{cell} > 0, \Delta G^\circ < 0, Q_c < K_c\)

This option matches the characteristics of a spontaneous reaction in a galvanic cell. Therefore, this is the correct answer.

\(E^\circ_{cell} < 0, \Delta G^\circ < 0, Q_c < K_c\)

This option incorrectly states that the cell potential is negative, which is not possible for a spontaneous galvanic cell.

\(E^\circ_{cell} = 0, \Delta G^\circ = 0, Q_c = K_c\)

This condition represents a system at equilibrium, not a spontaneous process.

\(E^\circ_{cell} < 0, Q_c > K_c\)

This describes a non-spontaneous process, as it suggests the cell potential is negative, and the reaction quotient is greater than the equilibrium constant.

Hence, the correct answer for a spontaneous galvanic cell is:

\(E^\circ_{cell} > 0, \Delta G^\circ < 0, Q_c < K_c\)