To calculate the value of the rate constant $ k $, we can use the rate law expression for the reaction. The general form of the rate law is:

$$ \text{Rate} = k \cdot [\text{N}_2]^m \cdot [\text{O}_3]^n $$

Given the rate of the reaction and the concentrations of the reactants, we can solve for $ k $. Here are the steps:

1. **Identify the given values:**
- Rate = 32.0 M/s
- $[\text{N}_2] = 0.11 \text{ M}$
- $[\text{O}_3] = 0.51 \text{ M}$

2. **Assume the reaction order:**
For simplicity, let's assume the reaction is first order with respect to both $\text{N}_2$ and $\text{O}_3$. This means $ m = 1 $ and $ n = 1 $.

3. **Write the rate law expression:**
$$ \text{Rate} = k \cdot [\text{N}_2] \cdot [\text{O}_3] $$

4. **Substitute the given values into the rate law expression:**
$$ 32.0 \text{ M/s} = k \cdot (0.11 \text{ M}) \cdot (0.51 \text{ M}) $$

5. **Solve for $ k $:**
$$ k = \frac{32.0 \text{ M/s}}{(0.11 \text{ M}) \cdot (0.51 \text{ M})} $$
$$ k = \frac{32.0}{0.0561} $$
$$ k \approx 570.4 \text{ M}^{-1} \text{s}^{-1} $$

6. **Round the answer to 2 significant digits:**
$$ k \approx 570 \text{ M}^{-1} \text{s}^{-1} $$

Therefore, the value of the rate constant $ k $ is approximately $ 570 \text{ M}^{-1} \text{s}^{-1} $.

Question

To calculate the value of the rate constant $ k $, we can use the rate law expression for the reaction. The general form of the rate law is:

$$ \text{Rate} = k \cdot [\text{N}_2]^m \cdot [\text{O}_3]^n $$

Given the rate of the reaction and the concentrations of the reactants, we can solve for $ k $. Here are the steps:

1. **Identify the given values:**
   - Rate = 32.0 M/s
   - $[\text{N}_2] = 0.11 \text{ M}$
   - $[\text{O}_3] = 0.51 \text{ M}$

2. **Assume the reaction order:** 
   For simplicity, let's assume the reaction is first order with respect to both $\text{N}_2$ and $\text{O}_3$. This means $ m = 1 $ and $ n = 1 $.

3. **Write the rate law expression:**
   $$ \text{Rate} = k \cdot [\text{N}_2] \cdot [\text{O}_3] $$

4. **Substitute the given values into the rate law expression:**
   $$ 32.0 \text{ M/s} = k \cdot (0.11 \text{ M}) \cdot (0.51 \text{ M}) $$

5. **Solve for $ k $:**
   $$ k = \frac{32.0 \text{ M/s}}{(0.11 \text{ M}) \cdot (0.51 \text{ M})} $$
   $$ k = \frac{32.0}{0.0561} $$
   $$ k \approx 570.4 \text{ M}^{-1} \text{s}^{-1} $$

6. **Round the answer to 2 significant digits:**
   $$ k \approx 570 \text{ M}^{-1} \text{s}^{-1} $$

Therefore, the value of the rate constant $ k $ is approximately $ 570 \text{ M}^{-1} \text{s}^{-1} $.

Knowee AI · Accepted Answer