The temperature of 15 ml of a strong acid increases by `2^(@)C` when 15 ml of a strong base is added to it. If 5 ml of each are mixed, temperature should increase by

Options

A. `0.6^(@)C`
B. `0.3 ^(@)C`
C. `2^(@)C`
D. `6^(@)C`

Answer

To solve the problem, we need to understand the concept of enthalpy of neutralization and how it relates to the temperature change when mixing a strong acid and a strong base.

### Step-by-Step Solution:

1. **Identify the Given Information**:
- When 15 ml of a strong acid is mixed with 15 ml of a strong base, the temperature increases by 2°C.

2. **Understand the Enthalpy of Neutralization**:
- The enthalpy of neutralization for strong acids and strong bases is approximately constant at about -57.1 kJ/mol. This means that the heat released during the neutralization reaction does not depend on the volume of the solutions, as long as they are strong acids and bases.

3. **Determine the Temperature Change for 5 ml Each**:
- Since the temperature change is independent of the volume of the acid and base, we can conclude that if 15 ml of acid and 15 ml of base cause a temperature increase of 2°C, then mixing 5 ml of acid with 5 ml of base will also cause a temperature increase of the same proportion.

4. **Calculate the Proportional Temperature Increase**:
- The ratio of the volumes is 5 ml to 15 ml, which is 1/3. Therefore, the temperature increase when mixing 5 ml of each will be:
\[ \text{Temperature Increase} = \frac{1}{3} \times 2°C = \frac{2}{3}°C \approx 0.67°C \]

5. **Final Conclusion**:
- The temperature should increase by approximately 0.67°C when 5 ml of strong acid is mixed with 5 ml of strong base.