For a reaction `A+2Brarr2C`, the following data were obtained . Initial concentration
`{:(,[A],[B],"Rate"(moll^(-1)min^(-1))),(i.,1.0,1.0,0.15),(ii,2.0,1.0,0.30),(iii.,3.0,1.0,0.45),(iv.,1.0,2.0,0.15),(v.,1.0,3.0,0.15):}`
The rate law for this reaction

Options

A. `R=k[A][B]^0`
B. `R=k[A][B]^2`
C. `R=k[A][B]`
D. `R=k[A]^2[B]`

Answer

To determine the rate law for the reaction \( A + 2B \rightarrow 2C \) based on the provided data, we will follow these steps:

### Step 1: Write the General Rate Law
The general rate law can be expressed as:
\[ \text{Rate} = k[A]^m[B]^n \]
where \( k \) is the rate constant, \( m \) is the order with respect to \( A \), and \( n \) is the order with respect to \( B \).

### Step 2: Analyze the Data
We have the following experimental data:

| Experiment | [A] (mol/L) | [B] (mol/L) | Rate (mol/L/min) |
|------------|-------------|-------------|-------------------|
| (i) | 1.0 | 1.0 | 0.15 |
| (ii) | 2.0 | 1.0 | 0.30 |
| (iii) | 3.0 | 1.0 | 0.45 |
| (iv) | 1.0 | 2.0 | 0.15 |
| (v) | 1.0 | 3.0 | 0.15 |

### Step 3: Determine the Order with Respect to A
Compare experiments (i) and (ii):
- From (i): \([A] = 1.0\), \([B] = 1.0\), Rate = 0.15
- From (ii): \([A] = 2.0\), \([B] = 1.0\), Rate = 0.30

The concentration of \( A \) doubles while \( B \) remains constant, and the rate also doubles:
\[ \frac{0.30}{0.15} = 2 = \left(\frac{2.0}{1.0}\right)^m \]
This implies:
\[ 2 = 2^m \implies m = 1 \]

### Step 4: Determine the Order with Respect to B
Now compare experiments (i) and (iv):
- From (i): \([A] = 1.0\), \([B] = 1.0\), Rate = 0.15
- From (iv): \([A] = 1.0\), \([B] = 2.0\), Rate = 0.15

The concentration of \( B \) doubles while \( A \) remains constant, and the rate does not change:
\[ \frac{0.15}{0.15} = 1 = \left(\frac{2.0}{1.0}\right)^n \]
This implies:
\[ 1 = 2^n \implies n = 0 \]

### Step 5: Write the Final Rate Law
Now that we have determined \( m = 1 \) and \( n = 0 \), we can write the rate law as:
\[ \text{Rate} = k[A]^1[B]^0 = k[A] \]

### Conclusion
The rate law for the reaction \( A + 2B \rightarrow 2C \) is:
\[ \text{Rate} = k[A] \]