Assertion: `Ni//Ni^(2+)(1.0M)||Au^(3+)(1.0M)|Au`, for this cell emf is 1.75V if `E_(Au^(3+)//Au)^(o)=1.50` and `E_(Ni^(2+)//Ni)^(o)=0.25V`
Reason: Emf of the cell `=E_("cathode")^(o)-E_("anode")^(o)`

Options

A. if both assertion and reason are true and the reason is the correct explanation of the assertion.
B. If both assertion and reason are true but reason is not the correct explanation of the assertion.
C. If assertion is true but reason is false
D. If the assertion and reason both are false.

Explanation

To solve the problem, we need to calculate the EMF of the given electrochemical cell and verify the assertion and reason provided.

### Step-by-Step Solution:

1. **Identify the Components of the Cell:**
The cell is represented as:
\[ \text{Ni} | \text{Ni}^{2+} (1.0M) || \text{Au}^{3+} (1.0M) | \text{Au} \]
Here, Ni is the anode and Au is the cathode.

2. **Write the Standard Reduction Potentials:**
We are given:
- \( E^\circ_{\text{Au}^{3+}/\text{Au}} = 1.50 \, \text{V} \) (cathode)
- \( E^\circ_{\text{Ni}^{2+}/\text{Ni}} = 0.25 \, \text{V} \) (anode)

3. **Determine the EMF of the Cell:**
The formula for the EMF of the cell is:
\[ E_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}} \]
Substituting the values:
\[ E_{\text{cell}} = E^\circ_{\text{Au}^{3+}/\text{Au}} - E^\circ_{\text{Ni}^{2+}/\text{Ni}} \]
\[ E_{\text{cell}} = 1.50 \, \text{V} - 0.25 \, \text{V} \]
\[ E_{\text{cell}} = 1.50 + 0.25 = 1.75 \, \text{V} \]

4. **Conclusion:**
The calculated EMF of the cell is \( 1.75 \, \text{V} \), which matches the assertion. Therefore, both the assertion and the reason are correct.

### Final Answer:
The assertion is true, and the reason is true. The reason correctly explains the assertion.