Following are two first order reaction with their half times given at `25^(@)C`.
`A overset(t_(1//2) = 30 min)rarr` Products
`B overset(t_(1//2)=40 min)rarr` Products
The temperature coefficients of their reactions rates are `3` and `2`, respectively, beween `25^(@)C` and `35^(@)C`. IF the above two resctions are carried out taking `0.4 M` of each reactant but at different temperatures: `25^(@)C` for the first order reaction and `35^(@)C` for the second order reaction, find the ratio of the concentrations of `A` and `B` after an hour.

Explanation

To solve the problem, we need to analyze the two first-order reactions and their respective half-lives at different temperatures. We will calculate the concentrations of reactants A and B after one hour (60 minutes) and then find the ratio of these concentrations.

### Step-by-Step Solution:

1. **Identify the half-lives and initial concentrations:**
- For reaction A: \( t_{1/2} = 30 \) minutes, initial concentration \( [A]_0 = 0.4 \, M \)
- For reaction B: \( t_{1/2} = 40 \) minutes, initial concentration \( [B]_0 = 0.4 \, M \)

2. **Calculate the number of half-lives for each reaction in 60 minutes:**
- For A:
\[ \text{Number of half-lives} = \frac{60 \, \text{minutes}}{30 \, \text{minutes}} = 2 \]
- For B:
\[ \text{Number of half-lives} = \frac{60 \, \text{minutes}}{40 \, \text{minutes}} = 1.5 \]

3. **Calculate the concentration of A after 60 minutes:**
- After 2 half-lives:
\[ [A] = [A]_0 \times \left(\frac{1}{2}\right)^2 = 0.4 \, M \times \frac{1}{4} = 0.1 \, M \]

4. **Calculate the concentration of B after 60 minutes:**
- After 1.5 half-lives:
\[ [B] = [B]_0 \times \left(\frac{1}{2}\right)^{1.5} = 0.4 \, M \times \frac{1}{\sqrt{2} \times 2} = 0.4 \, M \times \frac{1}{2\sqrt{2}} \approx 0.4 \, M \times 0.3536 \approx 0.1414 \, M \]

5. **Calculate the ratio of concentrations of A and B:**
\[ \text{Ratio} = \frac{[A]}{[B]} = \frac{0.1 \, M}{0.1414 \, M} \approx 0.707 \approx \frac{1}{\sqrt{2}} \approx \frac{2}{2.828} \approx 2:3 \]

### Final Answer:
The ratio of the concentrations of A and B after one hour is approximately \( 2:3 \).