In data given below.
`{:(,[A],[B],"rate"),(,mol//L,mol//L,mol L ^(-1)s^(-1)),(a., 0.02,1.2,3.0xx10^(-3)),(b.,0.04,2.4,6.0xx10^(-3)):}`
The reaction may be

Options

A. First order
B. Second order
C. Pseudo second order
D. Second order w.r.t. A

Answer

To determine the order of the reaction based on the provided data, we will follow these steps:

### Step 1: Write the Rate Law Expression
The rate of a reaction can generally be expressed as:
\[ \text{Rate} = k [A]^x [B]^y \]
where:
- \( k \) is the rate constant,
- \( [A] \) is the concentration of reactant A,
- \( [B] \) is the concentration of reactant B,
- \( x \) is the order with respect to A,
- \( y \) is the order with respect to B.

### Step 2: Substitute the Given Data into the Rate Law
From the data provided:
- For reaction a: \( [A] = 0.02 \, \text{mol/L}, [B] = 1.2 \, \text{mol/L}, \text{Rate} = 3.0 \times 10^{-3} \, \text{mol L}^{-1} \text{s}^{-1} \)
- For reaction b: \( [A] = 0.04 \, \text{mol/L}, [B] = 2.4 \, \text{mol/L}, \text{Rate} = 6.0 \times 10^{-3} \, \text{mol L}^{-1} \text{s}^{-1} \)

We can write two equations based on the rate law:
1. For reaction a:
\[ 3.0 \times 10^{-3} = k (0.02)^x (1.2)^y \] (Equation 1)

2. For reaction b:
\[ 6.0 \times 10^{-3} = k (0.04)^x (2.4)^y \] (Equation 2)

### Step 3: Divide the Two Equations
To eliminate \( k \), we can divide Equation 2 by Equation 1:
\[ \frac{6.0 \times 10^{-3}}{3.0 \times 10^{-3}} = \frac{k (0.04)^x (2.4)^y}{k (0.02)^x (1.2)^y} \]
This simplifies to:
\[ 2 = \frac{(0.04)^x (2.4)^y}{(0.02)^x (1.2)^y} \]

### Step 4: Simplify the Expression
Now we can simplify the right side:
\[ 2 = \frac{(0.04)^x}{(0.02)^x} \cdot \frac{(2.4)^y}{(1.2)^y} \]
This can be rewritten as:
\[ 2 = 2^x \cdot 2^y \]
where \( \frac{0.04}{0.02} = 2 \) and \( \frac{2.4}{1.2} = 2 \).

### Step 5: Combine the Exponents
Since the bases are the same, we can equate the exponents:
\[ 2 = 2^{x+y} \implies x + y = 1 \]

### Step 6: Determine the Order of the Reaction
The sum \( x + y = 1 \) indicates that the overall order of the reaction is first order. This means the reaction is first order with respect to the total concentration of reactants.

### Conclusion
Based on the calculations, the order of the reaction is **first order**.

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