Calculate the `EMF` of a Daniel cell when the concentartion of `ZnSO_(4)` and `CuSO_(4)` are `0.001M` and `0.1M` respectively. The standard potential of the cell is `1.1V`.

Explanation

To calculate the EMF of a Daniel cell with given concentrations of ZnSO₄ and CuSO₄, we can use the Nernst equation. Here’s a step-by-step solution:

### Step 1: Identify the Given Data
- Concentration of Zn²⁺ (from ZnSO₄) = 0.001 M
- Concentration of Cu²⁺ (from CuSO₄) = 0.1 M
- Standard cell potential (E°cell) = 1.1 V

### Step 2: Write the Nernst Equation
The Nernst equation is given by:
\[ E_{cell} = E^{\circ}_{cell} - \frac{0.0591}{n} \log \left( \frac{[Zn^{2+}]}{[Cu^{2+}]} \right) \]
where:
- \( E_{cell} \) is the cell potential (EMF).
- \( E^{\circ}_{cell} \) is the standard cell potential.
- \( n \) is the number of moles of electrons transferred in the reaction.

### Step 3: Determine the Number of Electrons Transferred
In the Daniel cell reaction:
\[ Zn \rightarrow Zn^{2+} + 2e^{-} \]
\[ Cu^{2+} + 2e^{-} \rightarrow Cu \]
The number of electrons (n) transferred is 2.

### Step 4: Substitute the Values into the Nernst Equation
Now we can substitute the known values into the Nernst equation:
\[ E_{cell} = 1.1 - \frac{0.0591}{2} \log \left( \frac{0.001}{0.1} \right) \]

### Step 5: Calculate the Logarithmic Term
Calculate the logarithmic term:
\[ \frac{0.001}{0.1} = 0.01 \]
\[ \log(0.01) = -2 \]

### Step 6: Substitute the Logarithmic Value into the Equation
Now substitute this back into the equation:
\[ E_{cell} = 1.1 - \frac{0.0591}{2} \times (-2) \]
\[ E_{cell} = 1.1 + 0.0591 \]
\[ E_{cell} = 1.1 + 0.0591 = 1.1591 \, V \]

### Step 7: Final Answer
Thus, the EMF of the Daniel cell is approximately:
\[ E_{cell} \approx 1.16 \, V \]

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