The rate of chemical reaction at constant temperature is proportional to:

Options

A. The amount of products formed
B. The product of masses of the reactants
C. The product of the molar concentration of the reactants
D. The mean free path of the reaction

Answer

To determine the relationship between the rate of a chemical reaction at constant temperature and various factors, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Reaction Rate**: The rate of a chemical reaction is generally expressed in terms of the concentrations of the reactants involved in the reaction. For a reaction of the form \( A + B \rightarrow C + D \), the rate can be expressed as:
\[ \text{Rate} = k [A]^m [B]^n \]
where \( k \) is the rate constant, and \( m \) and \( n \) are the orders of the reaction with respect to reactants A and B, respectively.

2. **Constant Temperature Implications**: When the temperature is held constant, the rate constant \( k \) also remains constant. This is because the rate constant is influenced by temperature, as described by the Arrhenius equation:
\[ k = A e^{-\frac{E_a}{RT}} \]
where \( E_a \) is the activation energy, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin.

3. **Dependence on Concentration**: Since \( k \) is constant at a given temperature, the rate of the reaction is directly proportional to the concentrations of the reactants. Therefore, the rate of the reaction can be simplified to:
\[ \text{Rate} \propto [A]^m [B]^n \]
This means that the rate of the reaction depends on the product of the molar concentrations of the reactants.

4. **Evaluating Options**: Now, let's evaluate the provided options:
- **Option 1**: Proportional to the amount of the product formed - Incorrect, as the rate depends on reactants.
- **Option 2**: Proportional to the product of the masses of the reactants - Incorrect, as it depends on concentrations, not masses.
- **Option 3**: Proportional to the product of the molar concentration of the reactants - Correct, as this is how reaction rates are expressed.
- **Option 4**: Proportional to the mean free path of the reaction - Incorrect, as mean free path does not directly affect the rate at constant temperature.

5. **Conclusion**: The correct answer is that the rate of the chemical reaction at constant temperature is proportional to the product of the molar concentrations of the reactants.