The rate constant of a reaction depends on

Explanation

To determine what the rate constant (K) of a reaction depends on, we can analyze the factors that influence it. The rate constant is a crucial parameter in chemical kinetics and is defined by the Arrhenius equation.

### Step-by-Step Solution:

1. **Understanding the Rate Constant (K)**:
The rate constant (K) is a proportionality factor in the rate law of a reaction. The general form of the rate law is given by:
\[ \text{Rate} = K \cdot [A]^n \]
where \([A]\) is the concentration of the reactant and \(n\) is the order of the reaction.

2. **Applying the Arrhenius Equation**:
The Arrhenius equation relates the rate constant to temperature and activation energy:
\[ K = A \cdot e^{-\frac{E_a}{RT}} \]
where:
- \(K\) = rate constant
- \(A\) = pre-exponential factor (frequency factor)
- \(E_a\) = activation energy
- \(R\) = universal gas constant
- \(T\) = temperature (in Kelvin)

3. **Analyzing the Dependence on Temperature**:
From the Arrhenius equation, we can see that the rate constant \(K\) is dependent on temperature (\(T\)). As the temperature increases, the term \(-\frac{E_a}{RT}\) becomes less negative, leading to an increase in \(K\). This implies that:
- Higher temperatures result in a higher rate constant.

4. **Evaluating Other Factors**:
- **Concentration of Reactants**: The rate constant does not depend on the concentration of reactants. It is a characteristic of the reaction at a given temperature.
- **Time of Reaction**: The rate constant is independent of the time duration of the reaction.
- **Extent of Reaction**: The rate constant does not depend on how far the reaction has proceeded.

5. **Conclusion**:
The rate constant \(K\) depends solely on temperature. Therefore, the correct answer is that the rate constant of a reaction depends on temperature.

### Final Answer:
The rate constant of a reaction depends on temperature.