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 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?

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?

The disaccharide lactose can be decomposed into its constituent sugars galactose and glucose. This decomposition can be accomplished through acid-based hydrolysis or by the enzyme lactase. Lactose intolerance in humans is due to the lack of lactase production by cells in the small intestine. However, the stomach is an acidic environment; therefore, one might expect lactose hydrolysis to still be an efficient process. The following data were obtained on the rate of lactose decomposition as a function of acid and lactose concentration. Using this information, determine the rate law expression for the acid-based hydrolysis of lactose.

The first-order thermal decomposition of chlorocyclohexane is as follows: $\mathrm{C}_6 \mathrm{H}_{11} \mathrm{Cl}(g) \rightarrow$ $\mathrm{C}_6 \mathrm{H}_{10}(g)+\mathrm{HCl}(g)$. For a constant volume system the following total pressures were measured as a function of time:

a. Derive the following relationship for a first-order reaction: $P\left(t_2\right)-P\left(t_1\right)=\left(P\left(t_{\infty}\right)-P\left(t_0\right)\right) e^{-k t_1}\left(1-e^{-k\left(t_2-t_1\right)}\right)$. In this relation, $P\left(t_1\right)$ and $P\left(t_2\right)$ are the pressures at two specific times; $\mathrm{P}\left(t_0\right)$ is the initial pressure when the reaction is initiated, $P\left(t_{\infty}\right)$ is the pressure at the completion of the reaction, and $k$ is the rate constant for the reaction. To derive this relationship do the following: i. Given the first-order dependence of the reaction, write the expression for the pressure of chlorocyclohexane at a specific time $t_1$. ii. Write the expression for the pressure at another time $t_2$, which is equal to $t_1+\Delta$ where delta is a fixed quantity of time. iii. Write expressions for $P\left(t_{\infty}\right)-P\left(t_1\right)$ and $P\left(t_{\infty}\right)-P\left(t_2\right)$. iv. Subtract the two expressions from part (iii). b. Using the natural log of the relationship from part (a) and the data provided in the table given earlier in this problem, determine the rate constant for the decomposition of chlorocyclohexane. (Hint: Transform the data in the table by defining $t_2-t_1$ to be a constant value, for example, $9 \mathrm{~s}$.)

Thermal neutrons, thermal protons, and thermal electrons all have the same kinetic energy of about 0.04 eV. Rank the speeds of these particles in descending order (greatest speed first).

How is the loss of ozone from Earth’s atmosphere related to cancer?

The reaction rate as a function of initial reactant pressures was investigated for the reaction $2 \mathrm{NO}(g)+$ $2 \mathrm{H}_2(g) \rightarrow \mathrm{N}_2(g)+2 \mathrm{H}_2 \mathrm{O}(g)$, and the following data were obtained: What is the rate law expression for this reaction?

A proposed two-step mechanism for the destruction of ozone in the upper atmosphere is What is the overall balanced equation for the ozone destruction reaction?

For the following rate expressions, state the order of the reaction with respect to each species, the total order of the reaction, and the units of the rate constant $k$ : a. $R=k[\mathrm{ClO}][\mathrm{BrO}]$ b. $R=k[\mathrm{NO}]^2\left[\mathrm{O}_2\right]$ c. $R=k \frac{[\mathrm{HI}]^2\left[\mathrm{O}_2\right]}{\left[\mathrm{H}^{+}\right]^{1 / 2}}$

What is the overall reaction order?

What is the overall reaction order?

For the following rate expressions, state the order of the reaction with respect to each species, the total order of the reaction, and the units of the rate constant $k$ : a. $R=k[\mathrm{ClO}][\mathrm{BrO}]$ b. $R=k[\mathrm{NO}]^2\left[\mathrm{O}_2\right]$ c. $R=k \frac{[\mathrm{HI}]^2\left[\mathrm{O}_2\right]}{\left[\mathrm{H}^{+}\right]^{1 / 2}}$

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?