To determine the rate of the given gas-phase reaction, we should follow a step-by-step approach using the provided rate law expression and given concentrations.
1. Identify the Rate Law Expression:
The rate law for the reaction [tex]\(2 NO + 2 H_2 \rightarrow N_2 + 2 H_2O\)[/tex] is given by:
[tex]\[
\text{rate} = 0.14 \, \text{L}^2 / (\text{mol}^2 \cdot \text{s}) \cdot [NO]^2 \cdot [H_2]
\][/tex]
2. Substitute the Given Concentrations:
The concentrations of the reactants are provided:
[tex]\[
[NO] = 0.95 \, \text{M}
\][/tex]
[tex]\[
[H_2] = 0.45 \, \text{M}
\][/tex]
3. Calculate the Rate:
Substitute the given concentrations into the rate law expression:
[tex]\[
\text{rate} = 0.14 \, \text{L}^2 / (\text{mol}^2 \cdot \text{s}) \cdot (0.95 \, \text{M})^2 \cdot (0.45 \, \text{M})
\][/tex]
4. Calculate [tex]\((0.95 \, \text{M})^2\)[/tex]:
[tex]\[
(0.95 \, \text{M})^2 = 0.9025 \, \text{M}^2
\][/tex]
5. Multiply by [tex]\(0.45 \, \text{M}\)[/tex]:
[tex]\[
0.9025 \, \text{M}^2 \times 0.45 \, \text{M} = 0.406125 \, \text{M}^3
\][/tex]
6. Multiply by the Rate Constant [tex]\(0.14 \, \text{L}^2 / (\text{mol}^2 \cdot \text{s})\)[/tex]:
[tex]\[
0.14 \, \text{L}^2 / (\text{mol}^2 \cdot \text{s}) \times 0.406125 \, \text{M}^3 = 0.0568575 \, \text{mol} / (\text{L} \cdot \text{s})
\][/tex]
Thus, the calculated rate of the reaction is approximately:
[tex]\[
0.057 \, \text{mol} / (\text{L} \cdot \text{s})
\][/tex]
From the given options, the expected rate is:
[tex]\[
0.057 \, \text{mol} / (\text{L} \cdot \text{s})
\][/tex]
Hence, the correct answer is:
[tex]\[
\boxed{0.057 \, \text{mol} / (\text{L} \cdot \text{s})}
\][/tex]
