The reaction SO2 Cl2(g) ⟶SO2(g)+Cl2(g) is first order in SO2 Cl2. Using the following kinetic da

step 1 Problem 47. For a first order reaction, a graph of LNP versus time is linear with slope minus K.

The reaction SO2 Cl2(g) ⟶SO2(g)+Cl2(g) is first order in SO2...

The reaction $$ \mathrm{SO}_{2} \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g) $$ is first order in $\mathrm{SO}_{2} \mathrm{Cl}_{2}$. Using the following kinetic data, determine the magnitude and units of the first order rate constant: $$ \begin{array}{rl} \hline \text { Time (s) } & \text { Pressure } \mathrm{SO}_{2} \mathrm{Cl}_{2} \text { (atm) } \\ \hline 0 & 1.000 \\ 2,500 & 0.947 \\ 5,000 & 0.895 \\ 7,500 & 0.848 \\ 10,000 & 0.803 \\ \hline \end{array} $$

The reaction
$$
\mathrm{SO}_{2} \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g)
$$
is first order in $\mathrm{SO}_{2} \mathrm{Cl}_{2}$. Using the following kinetic data, determine the magnitude and units of the first order rate constant:
$$
\begin{array}{rl}
\hline \text { Time (s) } & \text { Pressure } \mathrm{SO}_{2} \mathrm{Cl}_{2} \text { (atm) } \\
\hline 0 & 1.000 \\
2,500 & 0.947 \\
5,000 & 0.895 \\
7,500 & 0.848 \\
10,000 & 0.803 \\
\hline
\end{array}
$$

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Key Concepts

First Order Reaction Kinetics

In a first order reaction, the rate is directly proportional to the concentration (or, for gases, the pressure) of one reactant. This means that the rate law can be expressed as -d[A]/dt = k[A], where [A] is the concentration and k is the rate constant.

Integrated Rate Law for First Order Reactions

Integrating the first order rate equation leads to the form ln[A] = ln[A?] - kt. This linear relationship allows the determination of the rate constant k by plotting ln[A] (or ln of the gas pressure) versus time, with the slope of the resulting line equal to -k.

Determination of the Rate Constant and Its Units

For a first order reaction, the rate constant k is obtained from the slope of a plot of ln[concentration] versus time. The units of k are reciprocal time (e.g., s?¹), which is consistent with the nature of first order kinetics where the rate decreases exponentially over time.

Using Pressure as a Proxy for Concentration in Gas-Phase Reactions

In gas-phase reactions under conditions of constant temperature and volume, the partial pressure of a gas is proportional to its concentration. Therefore, measured pressures can be used in the integrated rate law in place of concentrations to analyze the reaction kinetics and determine the rate constant.

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