The rate of the reaction is proportional to the concentration of the reactant. Hydrogenation of ethene results in the formation of ethane. The rate constant, k for the reaction was found to be `2.5xx10^(-15)s^(-1)`. The concentration of the reactant reduces to one-third of the initial concentration in 5 minutes.
Q. The rate law equation is:

Options

A. Rate=k`[C_(2)H_(6)]`
B. Rate=k`[C_(2)H_(4)]^(2)`
C. Rate=`k[C_(2)H_(4)]`
D. Rate=`k[C_(2)H_(4)]^(2)`

Explanation

To solve the question, we need to derive the rate law equation based on the information provided. Here’s a step-by-step solution:

### Step 1: Understand the Reaction
The question states that the rate of the reaction is proportional to the concentration of the reactant. The reaction involves the hydrogenation of ethene (C2H4) to form ethane (C2H6).

### Step 2: Identify the Order of the Reaction
Since the rate of the reaction is directly proportional to the concentration of the reactant, we can conclude that this is a first-order reaction. In a first-order reaction, the rate can be expressed as:
\[ \text{Rate} = k [\text{C2H4}]^1 \]
where \( k \) is the rate constant.

### Step 3: Write the Rate Law Equation
From the information above, we can write the rate law equation as:
\[ \text{Rate} = k [\text{C2H4}] \]
This indicates that the rate of the reaction depends linearly on the concentration of ethene.

### Step 4: Substitute the Value of k
The rate constant \( k \) is given as \( 2.5 \times 10^{-15} \, \text{s}^{-1} \). However, since the question asks for the rate law equation, we will keep \( k \) in the equation without substituting its value:
\[ \text{Rate} = 2.5 \times 10^{-15} [\text{C2H4}] \]

### Final Rate Law Equation
Thus, the final rate law equation for the reaction is:
\[ \text{Rate} = 2.5 \times 10^{-15} [\text{C2H4}] \]