The unit of rate constant depends upon the

Options

A. molecularity of the reaction
B. activation energy of the reaction
C. order of the reaction
D. temperature of the reaction

Explanation

To determine the unit of the rate constant (k) for a chemical reaction, we need to consider the order of the reaction and the relationship between the rate of the reaction and the concentrations of the reactants. Here’s a step-by-step solution:

### Step 1: Understand the Reaction
Assume a general reaction of the form:
\[ xA + yB \rightarrow \text{Products} \]
where \( x \) and \( y \) are the stoichiometric coefficients of the reactants A and B.

### Step 2: Write the Rate Law
The rate of the reaction can be expressed as:
\[ \text{Rate} = k [A]^x [B]^y \]
where:
- \( k \) is the rate constant,
- \( [A] \) is the concentration of reactant A,
- \( [B] \) is the concentration of reactant B.

### Step 3: Define the Units of Rate
The unit of rate is typically expressed in terms of concentration per time. In SI units, this is:
\[ \text{Rate} = \text{mol L}^{-1} \text{s}^{-1} \]
This means that the rate of reaction is measured in moles per liter per second.

### Step 4: Define the Units of Concentration
The concentration of a substance is measured in moles per liter:
\[ [A] = \text{mol L}^{-1} \]
\[ [B] = \text{mol L}^{-1} \]

### Step 5: Substitute Units into the Rate Law
Substituting the units into the rate law gives:
\[ \text{Rate} = k [A]^x [B]^y \]
\[ \text{mol L}^{-1} \text{s}^{-1} = k (\text{mol L}^{-1})^x (\text{mol L}^{-1})^y \]

### Step 6: Simplify the Expression
This can be simplified to:
\[ \text{mol L}^{-1} \text{s}^{-1} = k \cdot \text{mol}^x \cdot \text{mol}^y \cdot \text{L}^{-x} \cdot \text{L}^{-y} \]
\[ = k \cdot \text{mol}^{x+y} \cdot \text{L}^{-(x+y)} \]

### Step 7: Rearrange to Solve for k
Now, we can rearrange to find the unit of \( k \):
\[ k = \frac{\text{mol L}^{-1} \text{s}^{-1}}{\text{mol}^{x+y} \cdot \text{L}^{-(x+y)}} \]
\[ = \text{mol}^{1 - (x+y)} \cdot \text{L}^{(x+y) - 1} \cdot \text{s}^{-1} \]

### Step 8: Conclusion
Thus, the unit of the rate constant \( k \) depends on the order of the reaction, which is given by \( x + y \). Therefore, the final unit of \( k \) can be expressed as:
\[ k = \text{mol}^{1 - (x+y)} \cdot \text{L}^{(x+y) - 1} \cdot \text{s}^{-1} \]