Show that for a reaction that obeys the general rate law,...

Show that for a reaction that obeys the general rate law, rate $=k[A]^{n}$ a graph of $\log ($ rate $)$ versus $\log [A]$ should yield a straight line with a slope equal to the order of the reaction. For the reaction in Problem $13.57,$ measure the rate of the reaction at $t=150,300,450,$ and $600 \mathrm{~s}$. Then graph $\log ($ rate $)$ versus $\log \left[\mathrm{SO}_{2} \mathrm{Cl}_{2}\right]$ and determine the order of the reaction with respect to $\mathrm{SO}_{2} \mathrm{Cl}_{2}$.

Show that for a reaction that obeys the general rate law, rate $=k[A]^{n}$ a graph of $\log ($ rate $)$ versus $\log [A]$ should yield a straight line with a slope equal to the order of the reaction. For the reaction in Problem $13.57,$ measure the rate of the reaction at $t=150,300,450,$ and $600 \mathrm{~s}$. Then graph $\log ($ rate $)$ versus $\log \left[\mathrm{SO}_{2} \mathrm{Cl}_{2}\right]$ and
determine the order of the reaction with respect to $\mathrm{SO}_{2} \mathrm{Cl}_{2}$.

Key Concepts

Reaction Rate Law

The reaction rate law expresses the rate of a chemical reaction as a function of the concentration of its reactants raised to a power, with a proportionality constant. In the general form rate = k[A]^n, the exponent n indicates the order of the reaction with respect to the reactant [A] and determines how the rate changes with concentration.

Logarithmic Transformation

Logarithmic transformation involves taking the logarithm of both sides of the rate law equation. This converts the power law relationship into a linear form, making it easier to analyze. Specifically, log(rate) becomes a linear function of log([A]), with the slope of the line corresponding to the reaction order.

Graphical Determination of Reaction Order

By plotting log(rate) versus log([A]), a straight-line graph is obtained if the reaction follows the assumed rate law. The slope of this line is equal to the exponent n, which is the order of the reaction with respect to the given reactant. This graphical method is a powerful tool for experimentally determining the reaction kinetics.

Experimental Data Analysis in Kinetics

Analyzing reaction kinetics often involves measuring reaction rates at various time points or concentrations. By using experimental data to create a log-log plot as described, one can accurately determine the order of the reaction without needing to assume a particular value, thereby validating the kinetic model.

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