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 can follow these steps:

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

### Step 2: Substitute the Given Data
We have two sets of data:
1. For the first data set:
- \( [A] = 0.02 \, \text{mol/L} \)
- \( [B] = 1.2 \, \text{mol/L} \)
- Rate = \( 3.0 \times 10^{-3} \, \text{mol L}^{-1}s^{-1} \)

Substituting into the rate law:
\[ 3.0 \times 10^{-3} = k(0.02)^x(1.2)^y \tag{1} \]

2. For the second data set:
- \( [A] = 0.04 \, \text{mol/L} \)
- \( [B] = 2.4 \, \text{mol/L} \)
- Rate = \( 6.0 \times 10^{-3} \, \text{mol L}^{-1}s^{-1} \)

Substituting into the rate law:
\[ 6.0 \times 10^{-3} = k(0.04)^x(2.4)^y \tag{2} \]

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

### Step 4: Simplify the Equation
Rearranging gives:
\[ \frac{1}{2} = \left(\frac{0.02}{0.04}\right)^x \left(\frac{1.2}{2.4}\right)^y \]
This simplifies to:
\[ \frac{1}{2} = \left(\frac{1}{2}\right)^x \left(\frac{1}{2}\right)^y \]
Thus:
\[ \frac{1}{2} = \left(\frac{1}{2}\right)^{x+y} \]

### Step 5: Solve for \( x + y \)
From the equation:
\[ 1 = x + y \]

### Step 6: Analyze Possible Reaction Orders
Now we need to analyze the possible values for \( x \) and \( y \):
- If \( x = 1 \) and \( y = 0 \), the reaction is first order with respect to A.
- If \( x = 0 \) and \( y = 1 \), the reaction is first order with respect to B.
- If \( x = 2 \) and \( y = -1 \), it would imply a second order, which is not possible.

### Conclusion
The reaction can be either first order with respect to A or first order with respect to B. Therefore, the overall order of the reaction is 1.

### Final Answer
The reaction is first order.

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