27. For the following reaction:
[tex]\[ C_2H_4(g) + I_2(g) \rightarrow C_2H_4I_2(g) \][/tex]

The rate equation is:
[tex]\[ \text{rate} = k \left[ C_2H_4(g) \right] \left[ I_2(g) \right]^{\frac{3}{2}} \][/tex]

(a) What is the order of reaction with respect to each reactant?

(b) What is the overall order of reaction?



Answer :

Let's solve the given question step-by-step.

### Given:
The reaction is:

[tex]\[ C_2H_4(g) + I_2(g) \rightarrow C_2H_4I_2(g) \][/tex]

The rate equation for this reaction is given as:

[tex]\[ \text{rate} = k \left[ C_2H_4(g) \right] \left[ I_2(g) \right]^{\frac{3}{2}} \][/tex]

### (a) Determine the order of reaction with respect to each reactant:

1. Order with respect to \( C_2H_4(g) \):

In the rate equation, the concentration of \( C_2H_4(g) \) is raised to the power of 1.

[tex]\[ \left[ C_2H_4(g) \right]^1 \][/tex]

Hence, the order of reaction with respect to \( C_2H_4(g) \) is 1.

2. Order with respect to \( I_2(g) \):

In the rate equation, the concentration of \( I_2(g) \) is raised to the power of \( \frac{3}{2} \).

[tex]\[ \left[ I_2(g) \right]^{\frac{3}{2}} \][/tex]

Hence, the order of reaction with respect to \( I_2(g) \) is \( \frac{3}{2} \).

### (b) Determine the overall order of the reaction:

The overall order of a reaction is the sum of the orders with respect to each reactant.

From part (a):
- Order with respect to \( C_2H_4(g) \): 1
- Order with respect to \( I_2(g) \): \( \frac{3}{2} \)

So, the overall order of the reaction is:

[tex]\[ \text{Overall order} = 1 + \frac{3}{2} = \frac{2}{2} + \frac{3}{2} = \frac{5}{2} = 2.5 \][/tex]

### Summary:

(a) The order of the reaction with respect to each reactant:
- Order with respect to \( C_2H_4(g) \) is 1.
- Order with respect to \( I_2(g) \) is \( \frac{3}{2} \).

(b) The overall order of the reaction is 2.5.