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# The reaction $\mathrm { NO } ( g ) + \mathrm { O } _ { 3 } ( g ) \longrightarrow \mathrm { NO } _ { 2 } ( g ) + \mathrm { O } _ { 2 } ( g )$ was studied by performing two experiments. In the first experiment (results shown in following table), the rate of disappearance of NO was followed in a large excess of $\mathrm { O } _ { 3 . }$ (The $\left[ \mathrm { O } _ { 3 } \right]$ remains effectively constant at $1.0 \times 10 ^ { 14 }$ molecules/cm $^ { 3 } . )$$\begin{array} { c c } { \text { Time } } & { [ \mathrm { NO } ] } \\ { \text { (ms) } } & { \text { (molecules/cm } ^ { 3 } ) } \\ \hline { 0 } & { 6.0 \times 10 ^ { 8 } } \\ { 100 \pm 1 } & { 5.0 \times 10 ^ { 8 } } \\ { 500 \pm 1 } & { 2.4 \times 10 ^ { 8 } } \\ { 700 \pm 1 } & { 1.7 \times 10 ^ { 8 } } \\ { 1000 \pm 1 } & { 9.9 \times 10 ^ { 7 } } \end{array}$In the second experiment, $[ \mathrm { NO } ]$ was held constant at $2.0 \times 10 ^ { 14 }$ molecules/cm $^ { 3 } .$ The data for the disappearance of $\mathrm { O } _ { 3 }$ were as follows:$\begin{array} { c c } { \text { Time } } & { \left[ \mathrm { O } _ { 3 } \right] } \\ { ( \mathrm { ms } ) } & { \text { (molecules/cm } ^ { 3 } ) } \\ \hline { 0 } & { 1.0 \times 10 ^ { 10 } } \\ { 50 \pm 1 } & { 8.4 \times 10 ^ { 9 } } \\ { 100 \pm 1 } & { 7.0 \times 10 ^ { 9 } } \\ { 200 \pm 1 } & { 4.9 \times 10 ^ { 9 } } \\ { 300 \pm 1 } & { 3.4 \times 10 ^ { 9 } } \end{array}$What is the value of the rate constant for the overall rate law? $\text {Rate} = k [ \mathrm { NO } ] ^ { x } [ \mathrm { O } _ { 3 } ] ^ { y }.$

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We can determine value for k from the first experiment knowing that $\text{k}' = 1.82 \ \text{s}^{-1}$.

$\text{k} = \dfrac{\text{k}'}{\left[\text{O}_3\right]} = \dfrac{1.82 \ \text{s}^{-1}}{1 \times 10^{14} \ \text{molecules} \ \text{cm}^{-3}}$

$\boxed{\text{k} = 1.82 \times 10^{-14} \ \text{cm}^3 \ \text{molecules}^{-1} \ \text{s}^{-1}}$

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