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? $\text {Rate} = k [ \mathrm { NO } ] ^ { x } [ \mathrm { O } _ { 3 } ] ^ { y }.$

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 obtained from each set of experiments? $\text {Rate} = k ^ { \prime } [ \mathrm { NO } ] ^ { x } \quad \text {Rate} = k ^ { \prime \prime } \left[ \mathrm { O } _ { 3 } \right] ^ { y }.$

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 overall rate law?