Which of the following is correct

Options

A. `log.K_2/K_1=E_a/2.303[(DeltaT)/(T_1T_2)]`
B. For zero order `t_(1//2)` is inversely proportional to initial concentration
C. Catalyst decreases the activation energy
D. All of these

Answer

To solve the question regarding which statement is correct, we will analyze the provided options based on the principles of chemical kinetics, specifically focusing on the Arrhenius equation and the effects of catalysts.

### Step-by-Step Solution:

1. **Understanding the Arrhenius Equation**:
The Arrhenius equation is given by:
\[ k = A e^{-\frac{E_a}{RT}} \]
where \( k \) is the rate constant, \( A \) is the pre-exponential factor, \( E_a \) is the activation energy, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin.

2. **Comparing Rate Constants at Different Temperatures**:
When comparing the rate constants \( k_1 \) and \( k_2 \) at two different temperatures \( T_1 \) and \( T_2 \), we can derive the following relationship:
\[ \log \frac{k_2}{k_1} = \frac{E_a}{2.303R} \left(\frac{1}{T_1} - \frac{1}{T_2}\right) \]
This shows how the rate constants change with temperature and activation energy.

3. **Analyzing the Options**:
We need to evaluate the given options to determine which one is correct. The options likely include statements about the relationship between activation energy, temperature, and the effect of catalysts.

4. **Understanding the Role of Catalysts**:
Catalysts are substances that increase the rate of a reaction by lowering the activation energy \( E_a \). This means that in the presence of a catalyst, the activation energy \( E_a' \) is less than the original activation energy \( E_a \):
\[ E_a' < E_a \]
This is a key point that we need to verify against the options.

5. **Identifying the Correct Statement**:
After evaluating the statements, we find that the only correct statement is that "a catalyst decreases the activation energy." Other statements regarding the relationship between half-life and concentration or incorrect forms of the Arrhenius equation are not valid.

### Conclusion:
The correct answer to the question is that a catalyst decreases the activation energy, thereby increasing the rate of the reaction.