For the reaction : `2A + B rarr C + D`, measurement of the rate of the reaction at varying concentrations are given below:
`{:("Trial No.",[A],[B],"Rate in mol L"^(-1)s^(-1)),(1,0.010,0.010,2.5),(2,0.010,0.020,5.0),(3,0.030,0.020,45.0):}`
The overall order of the reaction is :

Options

A. 3
B. 2
C. 1
D. 0

Explanation

To determine the overall order of the reaction given the data from the trials, we will follow these steps:

### Step 1: Write the Rate Law Expression
The general form of the rate law for the reaction \(2A + B \rightarrow C + D\) can be expressed as:
\[ \text{Rate} = k [A]^x [B]^y \]
where \(x\) is the order with respect to reactant \(A\) and \(y\) is the order with respect to reactant \(B\).

### Step 2: Analyze the Data from the Trials
We have the following data from the trials:

- **Trial 1**: \([A] = 0.010\), \([B] = 0.010\), Rate = 2.5
- **Trial 2**: \([A] = 0.010\), \([B] = 0.020\), Rate = 5.0
- **Trial 3**: \([A] = 0.030\), \([B] = 0.020\), Rate = 45.0

### Step 3: Determine the Order with Respect to \(B\) (Using Trials 1 and 2)
Compare Trial 1 and Trial 2 where the concentration of \(A\) remains constant:
\[ \frac{\text{Rate}_2}{\text{Rate}_1} = \frac{k [A]^{x} [B]_2^{y}}{k [A]^{x} [B]_1^{y}} = \frac{5.0}{2.5} \]
Substituting the values:
\[ \frac{5.0}{2.5} = \frac{[0.020]^y}{[0.010]^y} \Rightarrow 2 = \left(\frac{0.020}{0.010}\right)^y = 2^y \]
This simplifies to:
\[ 2 = 2^y \Rightarrow y = 1 \]

### Step 4: Determine the Order with Respect to \(A\) (Using Trials 2 and 3)
Now, compare Trial 2 and Trial 3 where the concentration of \(B\) remains constant:
\[ \frac{\text{Rate}_3}{\text{Rate}_2} = \frac{k [A]_3^{x} [B]^{y}}{k [A]_2^{x} [B]^{y}} = \frac{45.0}{5.0} \]
Substituting the values:
\[ \frac{45.0}{5.0} = \frac{[0.030]^x}{[0.010]^x} \Rightarrow 9 = \left(\frac{0.030}{0.010}\right)^x = 3^x \]
This simplifies to:
\[ 9 = 3^x \Rightarrow x = 2 \]

### Step 5: Calculate the Overall Order
The overall order of the reaction is the sum of the individual orders:
\[ \text{Overall Order} = x + y = 2 + 1 = 3 \]

### Conclusion
The overall order of the reaction is **3**.

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