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.
