The energy of activation for a reaction is 50kJ/ mol. Presence of a catalyst lowers the energy of activation by 25%. What will be the effect on rate of reaction at `30^(@)` C- Other things remains same.

Options

A. 142.75
B. 242.75
C. 342.75
D. 442.75

Explanation

To solve the problem, we need to determine the effect of a catalyst on the rate of reaction by calculating the change in the rate constant due to the decrease in activation energy.

### Step-by-Step Solution:

1. **Identify the given values:**
- Activation energy (Ea) = 50 kJ/mol
- Decrease in activation energy due to catalyst = 25%
- Temperature (T) = 30°C = 303 K (after converting to Kelvin)

2. **Calculate the new activation energy (Ea') after the catalyst is added:**
- Decrease in Ea = 25% of 50 kJ/mol
- Decrease in Ea = (25/100) * 50 kJ/mol = 12.5 kJ/mol
- New activation energy (Ea') = 50 kJ/mol - 12.5 kJ/mol = 37.5 kJ/mol

3. **Convert activation energies from kJ/mol to J/mol for calculations:**
- Ea = 50 kJ/mol = 50,000 J/mol
- Ea' = 37.5 kJ/mol = 37,500 J/mol

4. **Use the Arrhenius equation to find the rate constants (k1 and k2):**
- The Arrhenius equation is given by:
\[ k = A e^{-\frac{E_a}{RT}} \]
- For the original activation energy (k1):
\[ k_1 = A e^{-\frac{50,000}{RT}} \]
- For the new activation energy (k2):
\[ k_2 = A e^{-\frac{37,500}{RT}} \]

5. **Calculate the ratio of the rate constants (k2/k1):**
- Dividing the two equations:
\[ \frac{k_2}{k_1} = \frac{A e^{-\frac{37,500}{RT}}}{A e^{-\frac{50,000}{RT}}} \]
- This simplifies to:
\[ \frac{k_2}{k_1} = e^{-\frac{37,500 - 50,000}{RT}} = e^{-\frac{-12,500}{RT}} = e^{\frac{12,500}{RT}} \]

6. **Substitute R (8.314 J/mol·K) and T (303 K) into the equation:**
- Calculate:
\[ \frac{12,500}{R \cdot T} = \frac{12,500}{8.314 \cdot 303} \]
- Calculate the value:
\[ \frac{12,500}{8.314 \cdot 303} \approx 0.5 \]
- Therefore:
\[ \frac{k_2}{k_1} = e^{0.5} \approx 1.6487 \]

7. **Interpret the result:**
- The rate of reaction increases by a factor of approximately 1.6487 due to the presence of the catalyst.

### Conclusion:
The presence of a catalyst increases the rate of reaction by approximately 1.6487 times at 30°C.