During the working of a galvanic cell and with the passage of time.

Options

A. spontaneity of the cell reaction decreases, `E_(Cell)` decreases
B. reaction quotient `Q` decreases, `E_(cell)` increases
C. reaction quotient Q increases, `E_(cell)` decreases
D. at equilibrium `Q=K_(c),E_(cell)=0`

Explanation

To solve the question regarding the behavior of a galvanic cell over time, we will analyze each of the provided options based on the principles of electrochemistry, particularly the Nernst equation.

### Step-by-Step Solution:

1. **Understanding the Galvanic Cell**:
A galvanic cell converts chemical energy into electrical energy through spontaneous redox reactions. Over time, as the reaction proceeds, the concentrations of reactants and products change.

**Hint**: Recall that a galvanic cell operates based on the spontaneity of the redox reaction.

2. **Nernst Equation**:
The Nernst equation is given by:
\[ E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{RT}{nF} \ln Q \]
where:
- \(E_{\text{cell}}\) is the cell potential,
- \(E^\circ_{\text{cell}}\) is the standard cell potential,
- \(R\) is the universal gas constant,
- \(T\) is the temperature in Kelvin,
- \(n\) is the number of moles of electrons transferred,
- \(F\) is Faraday's constant,
- \(Q\) is the reaction quotient.

**Hint**: Familiarize yourself with the components of the Nernst equation and how they relate to the cell potential.

3. **Behavior of Reaction Quotient (Q)**:
As the reaction proceeds, the concentration of products increases and the concentration of reactants decreases, leading to an increase in the reaction quotient \(Q\).

**Hint**: Remember that \(Q\) reflects the ratio of products to reactants at any point in time.

4. **Effect on Cell Potential (E_cell)**:
As \(Q\) increases, the term \(-\frac{RT}{nF} \ln Q\) becomes more negative, which means that \(E_{\text{cell}}\) decreases over time.

**Hint**: Consider how logarithmic functions behave as their arguments increase.

5. **Equilibrium Condition**:
At equilibrium, \(Q\) becomes equal to the equilibrium constant \(K_c\), and at this point, \(E_{\text{cell}} = 0\). This indicates that the cell can no longer do work.

**Hint**: Equilibrium signifies a balance where the forward and reverse reactions occur at the same rate.

6. **Evaluating the Options**:
- **Option 1**: "Spontaneity of the cell reaction decreases and E_cell decreases." - This is correct as spontaneity decreases as the cell approaches equilibrium.
- **Option 2**: "Reaction quotient Q decreases E_cell increases." - This is incorrect because \(Q\) actually increases with time.
- **Option 3**: "Reaction quotient Q increases E_cell decreases." - This is correct as explained.
- **Option 4**: "At equilibrium Q is equal to K_c E_cell is equal to zero." - This is also correct.

7. **Conclusion**:
The correct options are 1, 3, and 4.

### Final Answer:
The correct options are 1, 3, and 4.