Consider the first-order decomposition of cyclobutane at $438^{\circ} \mathrm{C}$ at constant volume: $\mathrm{C}_4 \mathrm{H}_8(g) \rightarrow 2 \mathrm{C}_2 \mathrm{H}_4(g)$ a. Express the rate of the reaction in terms of the change in total pressure as a function of time. b. The rate constant for the reaction is $2.48 \times 10^{-4} \mathrm{~s}^{-1}$. What is the half-life? c. After initiation of the reaction, how long will it take for the initial pressure of $\mathrm{C}_4 \mathrm{H}_8$ to drop to $90 \%$ of its initial value?

What is meant by a diffusion-controlled reaction?

A convenient source of gamma rays for radiation chemistry research is ${ }_k^{60} \mathrm{Co}$, which undergoes the following decay process: ${ }_{27}^{60} \mathrm{Co} \stackrel{k}{\rightarrow}{ }_{28}^{60} \mathrm{Ni}+\beta^{-}+\gamma$. The half-life of ${ }^{60} \mathrm{Co}$ is $1.9 \times 10^3$ days. a. What is the rate constant for the decay process? b. How long will it take for a sample of ${ }^{60} \mathrm{Co}$ to decay to half of its original concentration?

What is a transition state? How is the concept of a transition state used in activated complex theory?

One issue confronting the use of ${ }^{14} \mathrm{C}$ decay (halflife of 5760 years) to date materials is that of obtaining a standard. One approach to this issue is found in the field of dendrochronology or using tree rings to determine age. Using this approach, tree materials dating back 10,000 years have been identified. Assuming you had a sample of such a tree in which the number of decay events was $15.3$ decays per minute before decomposition, what would the decays per minute be in the present day?

In a temperature-jump experiment, why does a change in temperature result in a corresponding change in equilibrium?

You are performing an experiment using ${ }^3 \mathrm{H}$ (halflife $=4.5 \times 10^3$ days) labeled phenylalanine in which the five aromatic hydrogens are labeled. To perform the experiment, the initial activity cannot be lower than $10 \%$ of the initial activity when the sample was received. How long after receiving the sample can you wait before performing the experiment?

What is the kinetic definition of equilibrium?

The half-life of ${ }^{238} \mathrm{U}$ is $4.5 \times 10^9$ years. How many disintegrations occur in $1 \mathrm{~min}$ for a $10 \mathrm{mg}$ sample of this element?

A certain reaction is first order, and $540 \mathrm{~s}$ after initiation of the reaction, $32.5 \%$ of the reactant remains. a. What is the rate constant for this reaction? b. At what time after initiation of the reaction will $10 \%$ of the reactant remain?

In a parallel reaction in which two products can be formed from the same reactant, what determines the extent to which one product will be formed over another?

What is the steady-state approximation, and when is this approximation employed?

Consider the schematic reaction A $\stackrel{k}{\rightarrow}$ P. a. If the reaction is one-half order with respect to A, what is the integrated rate law expression for this reaction? b. What plot would you construct to determine the rate constant $k$ for the reaction? c. What would be the half-life for this reaction? Will it depend on initial concentration of the reactant?

You are given the following data for the decomposition of acetaldehyde:

$$\begin{array}{cll}\text { Initial Concentration (M) } & 9.72 \times 10^{-3} & 4.56 \times 10^{-3} \\ \text { Half-Life (s) } & 328 & 685\end{array}$$

Determine the order of the reaction and the rate constant for the reaction.