Which is true for the temperature coefficient of a reaction ?

Options

A. ific reaction rate at `25^@C`
B. Rate of the reaction at `100^@C`
C. Ratio of the rate constants at temperature `35^@ C and 25^@C`
D. Ratio of the rate constants at two temperature differing by `1^@C`

Answer

To solve the question regarding the temperature coefficient of a reaction, we need to understand the concept of temperature coefficient and how it relates to the rate of a chemical reaction.

### Step-by-Step Solution:

1. **Definition of Temperature Coefficient**:
The temperature coefficient (often denoted as \( Q_{10} \)) is defined as the factor by which the rate of a reaction increases when the temperature is raised by 10 degrees Celsius.

2. **Understanding the Rate of Reaction**:
If we have a reaction \( A \rightarrow B \), and the temperature coefficient is given as a certain value (e.g., 2), this means that if the temperature is increased by 10 degrees Celsius, the rate of the reaction will double.

3. **Mathematical Expression**:
The temperature coefficient can be mathematically expressed as:
\[ Q_{10} = \frac{\text{Rate at } T_2}{\text{Rate at } T_1} \]
where \( T_2 \) is \( T_1 + 10^\circ C \).

4. **Rate Constants**:
The rate of a reaction is also related to the rate constant \( k \). The relationship can be expressed as:
\[ Q_{10} = \frac{k_{T_2}}{k_{T_1}} \]
Here, \( k_{T_1} \) is the rate constant at the initial temperature \( T_1 \) and \( k_{T_2} \) is the rate constant at the temperature \( T_2 \).

5. **Evaluating Options**:
Now, let's evaluate the options given in the question:
- Option A: "Temperature coefficient is reaction rate at 25 degrees Celsius" - This is incorrect.
- Option B: "Rate of reaction at 100 degrees Celsius" - This is also incorrect.
- Option C: "Ratio of rate constant at temperature 35 and 25 degrees Celsius" - This is incorrect because the temperature difference is not 10 degrees.
- Option D: "Ratio of rate constant at two temperatures differing by 1 degree Celsius" - This is incorrect as well; the standard definition involves a 10-degree difference.

6. **Conclusion**:
Based on the definitions and evaluations, none of the options provided in the question accurately describe the temperature coefficient as it is conventionally understood.