Calculate the order of the reaction in A and B :-
`{:(A,,,B,,,Rate),(("mol"//1),,,("mol"//1),,,),(0.05,,,0.05,,,1.2xx10^(-3)),(0.10,,,0.05,,,2.4xx10^(-3)),(0.05,,,0.10,,,1.2xx10^(-3)):}`

Options

A. 1 and 0
B. 1 and 1
C. 0 and 1
D. None of these

Explanation

To calculate the order of the reaction with respect to reactants A and B, we can follow these steps:

### Step 1: Write the rate law expression
The rate law for a reaction can be expressed in the form:
\[ \text{Rate} = k[A]^m[B]^n \]
where:
- \( k \) is the rate constant,
- \( [A] \) is the concentration of reactant A,
- \( [B] \) is the concentration of reactant B,
- \( m \) is the order of the reaction with respect to A,
- \( n \) is the order of the reaction with respect to B.

### Step 2: Analyze the data
We have the following data points:
1. \( [A] = 0.05 \, \text{mol/L}, [B] = 0.05 \, \text{mol/L}, \text{Rate} = 1.2 \times 10^{-3} \)
2. \( [A] = 0.10 \, \text{mol/L}, [B] = 0.05 \, \text{mol/L}, \text{Rate} = 2.4 \times 10^{-3} \)
3. \( [A] = 0.05 \, \text{mol/L}, [B] = 0.10 \, \text{mol/L}, \text{Rate} = 1.2 \times 10^{-3} \)

### Step 3: Determine the order with respect to A
Compare the first two experiments:
- From experiment 1 to experiment 2, the concentration of A doubles (from 0.05 to 0.10), while the concentration of B remains constant.
- The rate also doubles (from \( 1.2 \times 10^{-3} \) to \( 2.4 \times 10^{-3} \)).

Using the rate law:
\[ \frac{\text{Rate}_2}{\text{Rate}_1} = \frac{k[A_2]^m[B_2]^n}{k[A_1]^m[B_1]^n} \]
Substituting the values:
\[ \frac{2.4 \times 10^{-3}}{1.2 \times 10^{-3}} = \frac{[0.10]^m[0.05]^n}{[0.05]^m[0.05]^n} \]
This simplifies to:
\[ 2 = \left(\frac{0.10}{0.05}\right)^m \Rightarrow 2 = 2^m \]
Thus, \( m = 1 \).

### Step 4: Determine the order with respect to B
Now, compare the first and third experiments:
- The concentration of A remains constant (0.05), while the concentration of B doubles (from 0.05 to 0.10).
- The rate remains the same (both are \( 1.2 \times 10^{-3} \)).

Using the rate law:
\[ \frac{\text{Rate}_3}{\text{Rate}_1} = \frac{k[A_3]^m[B_3]^n}{k[A_1]^m[B_1]^n} \]
Substituting the values:
\[ \frac{1.2 \times 10^{-3}}{1.2 \times 10^{-3}} = \frac{[0.05]^m[0.10]^n}{[0.05]^m[0.05]^n} \]
This simplifies to:
\[ 1 = \left(\frac{0.10}{0.05}\right)^n \Rightarrow 1 = 2^n \]
Thus, \( n = 0 \).

### Conclusion
The order of the reaction with respect to A is 1, and with respect to B is 0.

### Final Answer
- Order with respect to A: 1
- Order with respect to B: 0