The following data are for the system $$\mathrm{A}(g) \rightleftharpoons 2 \mathrm{~B}(g)$$ $$\begin{array}{ccccccc}\hline \text { Time (s) } & 0 & 20 & 40 & 60 & 80 & 100 \\ P_{\mathrm{A}} \text { (atm) } & 1.00 & 0.83 & 0.72 & 0.65 & 0.62 & 0.62 \\ P_{\mathrm{B}} \text { (atm) } & 0.00 & 0.34 & 0.56 & 0.70 & 0.76 & 0.76 \\ \hline\end{array}$$ Prepare a graph of \(P_{\Lambda}\) and \(P_{\mathrm{B}}\) versus time and use it to answer the following questions: (a) Estimate \(P_{\mathrm{A}}\) and \(P_{\mathrm{g}}\) after \(30 \mathrm{~s}\). (b) Estimate \(P_{\mathrm{A}}\) after \(150 \mathrm{~s}\). (c) Estimate \(P_{\mathrm{B}}\) when \(P_{\mathrm{A}}=0.700 \mathrm{~atm}\).

Chemical kinetics is the branch of chemistry that deals with the speeds or rates at which chemical reactions occur. Understanding kinetics allows chemists to determine how different conditions, such as concentration and temperature, affect the speed of a reaction. This is crucial for controlling processes in industries and in conducting laboratory experiments.

At its core, a chemical reaction transforms reactants into products, and kinetics analyzes the factors that influence this transformation over time. For instance, a rapid reaction, such as a combustion explosion, happens in a split second, while a slow one, like rusting iron, can take years. By examining changes in concentrations of reactants and products or, as in our textbook case, pressures of gaseous species, reaction rates can be determined.

The rate of a chemical reaction indicates how fast reactants are converted into products over time. It's measured by the change in concentration of reactants or products per unit time. In cases involving gases, as seen in the textbook exercise, changes in pressure are often more accessible to measure and can serve as a proxy for concentration changes. This is particularly true under the assumption that the volume of the system is constant and the temperature remains the same, allowing us to use the ideal gas law for conversions if necessary.

In the given exercise, the reaction rate could be approximated by observing the changes in pressures of gas A and B. Initially, the pressure of A decreases while that of B increases, reflective of reactant consumption and product formation. As the reaction progresses towards equilibrium, these changes in pressure will slow down and eventually stop, indicating the reaction rate has decreased to zero.

A pressure vs time graph is an insightful way to visualize the changes in gases' pressures during a chemical reaction. From such a graph, not only can the reaction rates be inferred by examining the slope of the lines, but it also provides information regarding when the system reaches chemical equilibrium — a state where the pressures of gases no longer change significantly.

In our exercise, plotting the pressures of A and B over time allows us to estimate values at intermediate times (like at 30 seconds) and predict future behaviors (like at 150 seconds). The flat region of the graph where the pressures stabilize indicates that chemical equilibrium has been established. Such graphs are invaluable for interpreting kinetic data and are much easier to understand than simply looking at a table of numbers, as they provide a visual representation of the dynamics of the reaction.