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The reaction NO(g)+O3(g)NO2(g)+O2(g)\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 O3.\mathrm { O } _ { 3 . } (The [O3]\left[ \mathrm { O } _ { 3 } \right] remains effectively constant at 1.0×10141.0 \times 10 ^ { 14 } molecules/cm 3.)^ { 3 } . )

 Time [NO] (ms)  (molecules/cm 3)06.0×108100±15.0×108500±12.4×108700±11.7×1081000±19.9×107\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, [NO][ \mathrm { NO } ] was held constant at 2.0×10142.0 \times 10 ^ { 14 } molecules/cm 3.^ { 3 } . The data for the disappearance of O3\mathrm { O } _ { 3 } were as follows:

 Time [O3](ms) (molecules/cm 3)01.0×101050±18.4×109100±17.0×109200±14.9×109300±13.4×109\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 order with respect to each reactant?

The reaction NO(g)+O3(g)NO2(g)+O2(g)\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 O3.\mathrm { O } _ { 3 . } (The [O3]\left[ \mathrm { O } _ { 3 } \right] remains effectively constant at 1.0×10141.0 \times 10 ^ { 14 } molecules/cm 3.)^ { 3 } . )

 Time [NO] (ms)  (molecules/cm 3)06.0×108100±15.0×108500±12.4×108700±11.7×1081000±19.9×107\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, [NO][ \mathrm { NO } ] was held constant at 2.0×10142.0 \times 10 ^ { 14 } molecules/cm 3.^ { 3 } . The data for the disappearance of O3\mathrm { O } _ { 3 } were as follows:

 Time [O3](ms) (molecules/cm 3)01.0×101050±18.4×109100±17.0×109200±14.9×109300±13.4×109\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?

The reaction NO(g)+O3(g)NO2(g)+O2(g)\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 O3.\mathrm { O } _ { 3 . } (The [O3]\left[ \mathrm { O } _ { 3 } \right] remains effectively constant at 1.0×10141.0 \times 10 ^ { 14 } molecules/cm 3.)^ { 3 } . )

 Time [NO] (ms)  (molecules/cm 3)06.0×108100±15.0×108500±12.4×108700±11.7×1081000±19.9×107\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, [NO][ \mathrm { NO } ] was held constant at 2.0×10142.0 \times 10 ^ { 14 } molecules/cm 3.^ { 3 } . The data for the disappearance of O3\mathrm { O } _ { 3 } were as follows:

 Time [O3](ms) (molecules/cm 3)01.0×101050±18.4×109100±17.0×109200±14.9×109300±13.4×109\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? Rate=k[NO]xRate=k[O3]y.\text {Rate} = k ^ { \prime } [ \mathrm { NO } ] ^ { x } \quad \text {Rate} = k ^ { \prime \prime } \left[ \mathrm { O } _ { 3 } \right] ^ { y }.

Question

The reaction NO(g)+O3(g)NO2(g)+O2(g)\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 O3.\mathrm { O } _ { 3 . } (The [O3]\left[ \mathrm { O } _ { 3 } \right] remains effectively constant at 1.0×10141.0 \times 10 ^ { 14 } molecules/cm 3.)^ { 3 } . )

 Time [NO] (ms)  (molecules/cm 3)06.0×108100±15.0×108500±12.4×108700±11.7×1081000±19.9×107\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, [NO][ \mathrm { NO } ] was held constant at 2.0×10142.0 \times 10 ^ { 14 } molecules/cm 3.^ { 3 } . The data for the disappearance of O3\mathrm { O } _ { 3 } were as follows:

 Time [O3](ms) (molecules/cm 3)01.0×101050±18.4×109100±17.0×109200±14.9×109300±13.4×109\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? Rate=k[NO]x[O3]y.\text {Rate} = k [ \mathrm { NO } ] ^ { x } [ \mathrm { O } _ { 3 } ] ^ { y }.

Solution

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We can determine value for k from the first experiment knowing that k=1.82 s1\text{k}' = 1.82 \ \text{s}^{-1}.

k=k[O3]=1.82 s11×1014 molecules cm3\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}}

k=1.82×1014 cm3 molecules1 s1\boxed{\text{k} = 1.82 \times 10^{-14} \ \text{cm}^3 \ \text{molecules}^{-1} \ \text{s}^{-1}}

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