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?

It has been suggested that the surface melting of ice plays a role in enabling speed skaters to achieve peak performance. Carry out the following calculation to test this hypothesis. At $1$ $\mathrm{atm}$ pressure, ice melts at $273.15 \mathrm{~K}$, $\Delta H_{\text {fusion }}=6010 . \mathrm{J} \mathrm{mol}^{-1}$, the density of ice is $920 \mathrm{~kg} \mathrm{~m}^{-3}$, and the density of liquid water is $997 . \mathrm{kg} \mathrm{m}^{-3}$. a. What pressure is required to lower the melting temperature by $4.0^{\circ} \mathrm{C}$ ? b. Assume that the width of the skate in contact with the ice has been reduced by sharpening to $19 \times 10^{-3} \mathrm{~cm}$, and that the length of the contact area is $18 \mathrm{~cm}$. If a skater of mass $78 \mathrm{~kg}$ is balanced on one skate, what pressure is exerted at the interface of the skate and the ice? c. What is the melting point of ice under this pressure? d. If the temperature of the ice is $-4.0^{\circ} \mathrm{C}$, do you expect melting of the ice at the ice-skate interface to occur?

A reasonable approximation to the vapor pressure krypton is given by $\log _{10}(P /$ Torr $)=b-0.05223(a / T)$. For solid krypton, $a=10,065$ and $b=7.1770$. For liquid krypton, $a=9377.0$ and $b=6.92387$. Use these formulas estimate the triple point temperature and pressure and also the enthalpies of vaporization, fusion, and sublimation of krypton.

To understand how elementary steps make up a mechanism and how the rate law for an elementary step can be determined. Very often, a reaction does not tell us the whole story. For instance, the reaction NO$_2$(g)+CO(g)→NO(g)+CO$_2$(g) does not involve a collision between an NO$_2$  molecule and a CO  molecule. Based on experimental data at moderate temperatures, this reaction is thought to occur in the following two steps: Each individual step is called an elementary step. Together, these elementary steps are called the reaction mechanism. Overall, the resulting reaction is NO$_2$(g)+CO(g)→NO(g)+CO$_2$(g). Notice that in the elementary steps, NO$_3$ appears both as a product and then as a reactant; therefore it cancels out of the final chemical equation. NO3  is called a reaction intermediate. Also, notice that 2 molecules of  NO$_2$  appear in the reactants of the first step and 1 molecule of NO$_2$  appears as the product of the second step. The net effect leaves only 1 molecule of  NO$_2$  as a reactant in the net equation. Molecularity is the proper term for "how the molecules collide" in a reaction. For example, step 1 is bimolecular because it involves the collision of two molecules. Step 2 is also bimolecular for the same reason. Unimolecular reactions involve only one molecule in the reactants. Though rare, collisions among three molecules can occur. Such a reaction would be called termolecular.

What is the overall reaction?

What is the rate law for step 1 of this reaction?

What is the rate law for step 2 of this reaction?

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?

Which of the enthalpies of combustion in Table $9.2$ the table are also standard enthalpies of formation?

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?

It has been suggested that the surface melting of ice plays a role in enabling speed skaters to achieve peak performance. Carry out the following calculation to test this be hypothesis. At $1 \mathrm{~atm}$ pressure, ice melts at $273.15 \mathrm{~K}, of$\Delta H_${\text {fusion }}$=6010.\ $\mathrm{J}$\ $\mathrm{mol}$^{-1}$, the density of ice is$920.\ $\mathrm{kg}$\ $\mathrm{m}$^{-3}$, and the density of liquid water is$997.\ $\mathrm{kg}$\ $\mathrm{m}$^{-3}$. a. What pressure is required to lower the melting temperature by$4.0^${\circ}$ $\mathrm{C} ? b. Assume that the width of the skate in contact with the ice has been reduced by sharpening to$19 \times 10^{-3} $\mathrm{~cm}, and that the length of the contact area is$18\ cm$. If a skater of mass$78\ kg$is balanced on one skate, what pressure is exerted at the interface of the skate and the ice? c. What is the melting point of ice under this pressure? d. If the temperature of the ice is$-40^\circ C$, do you expect melting of the ice at the ice-skate interface to occur?

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?