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. Find the order of reaction:

Options

A. Zero order
B. First order
C. Second order
D. Fractional order

Explanation

To determine the order of the reaction based on the provided information, we can follow these steps:

### Step 1: Understand the relationship between rate and concentration
The problem states that the rate of the reaction is proportional to the concentration of the reactant. This implies that the reaction follows first-order kinetics, where the rate can be expressed as:
\[ \text{Rate} = k [C_2H_4] \]
where \( k \) is the rate constant and \([C_2H_4]\) is the concentration of ethene.

### Step 2: Analyze the given data
We are given that the concentration of the reactant (ethene, \( C_2H_4 \)) reduces to one-third of its initial concentration in 5 minutes. This means:
\[ [C_2H_4] = \frac{1}{3} [C_2H_4]_0 \]
where \([C_2H_4]_0\) is the initial concentration.

### Step 3: Use the first-order reaction formula
For a first-order reaction, the relationship between concentration and time can be expressed using the following equation:
\[ \ln\left(\frac{[C_2H_4]_0}{[C_2H_4]}\right) = kt \]
Substituting the values we have:
\[ \ln\left(\frac{[C_2H_4]_0}{\frac{1}{3}[C_2H_4]_0}\right) = k \cdot 5 \text{ minutes} \]
This simplifies to:
\[ \ln(3) = k \cdot 5 \text{ minutes} \]

### Step 4: Convert time to seconds
Since the rate constant \( k \) is given in \( s^{-1} \), we need to convert 5 minutes into seconds:
\[ 5 \text{ minutes} = 5 \times 60 = 300 \text{ seconds} \]

### Step 5: Solve for the rate constant \( k \)
Now we can rearrange the equation to solve for \( k \):
\[ k = \frac{\ln(3)}{300} \]

### Step 6: Compare with the given rate constant
The given rate constant \( k \) is \( 2.5 \times 10^{-15} s^{-1} \). Since the unit of \( k \) is \( s^{-1} \), and we have confirmed that the relationship holds true for a first-order reaction, we conclude that the order of the reaction is indeed first order.

### Conclusion
Thus, the order of the reaction is **first order**.

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