Chapter 11

Express the rate of the reaction $$2 \mathrm{C}_{2} \mathrm{H}_{6}(g)+7 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)$$ in terms of (a) \(\Delta\left[\mathrm{C}_{2} \mathrm{H}_{6}\right]\) (b) \(\Delta\left[\mathrm{CO}_{2}\right]\)

Express the rate of the reaction $$2 \mathrm{~N}_{2} \mathrm{H}_{4}(l)+\mathrm{N}_{2} \mathrm{O}_{4}(l) \longrightarrow 3 \mathrm{~N}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)$$ in terms of (a) \(\Delta\left[\mathrm{N}_{2} \mathrm{O}_{4}\right]\) (b) \(\Delta\left[\mathrm{N}_{2}\right]\)

Consider the following hypothetical reaction: $$\mathrm{X}(g) \longrightarrow \mathrm{Y}(g)$$ A 200.0-mL flask is filled with \(0.120\) moles of \(\mathrm{X}\). The disappearance of \(\mathrm{X}\) is monitored at timed intervals. Assume that temperature and volume are kept constant. The data obtained are shown in the table below. $$\begin{array}{lccccc}\hline \text { Time }(\min ) & 0 & 20 & 40 & 60 & 80 \\\ \text { moles of } \mathrm{X} & 0.120 & 0.103 & 0.085 & 0.071 & 0.066 \\ \hline\end{array}$$ (a) Make a similar table for the appearance of Y. (b) Calculate the average disappearance of \(\mathrm{X}\) in \(\mathrm{M} / \mathrm{s}\) in the first two twenty-minute intervals. (c) What is the average rate of appearance of \(\mathrm{Y}\) between the 20 - and 60-minute intervals?

Consider the combustion of ethane: $$\mathrm{C}_{2} \mathrm{H}_{6}(g)+7 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)$$ If the ethane is burning at the rate of \(0.20 \mathrm{~mol} / \mathrm{L} \cdot \mathrm{s}\), at what rates are \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) being produced?

For the reaction $$5 \mathrm{Br}^{-}(a q)+\mathrm{BrO}_{3}^{-}(a q)+6 \mathrm{H}^{+}(a q) \longrightarrow 3 \mathrm{Br}_{2}(a q)+3 \mathrm{H}_{2} \mathrm{O}$$ it was found that at a particular instant bromine was being formed at the rate of \(0.039 \mathrm{~mol} / \mathrm{L} \cdot \mathrm{s}\). At that instant, at what rate is (a) water being formed? (b) bromide ion being oxidized? (c) \(\mathrm{H}^{+}\) being consumed?

Nitrosyl chloride (NOCl) decomposes to nitrogen oxide and chlorine gases. (a) Write a balanced equation using smallest whole-number coefficients for the decomposition. (b) Write an expression for the reaction rate in terms of \(\Delta[\mathrm{NOCl}] .\) (c) The concentration of NOCl drops from \(0.580 M\) to \(0.238 M\) in \(8.00 \mathrm{~min}\). Calculate the average rate of reaction over this time interval.

Ammonia is produced by the reaction between nitrogen and hydro- gen gases. (a) Write a balanced equation using smallest whole-number coefficients for the reaction. (b) Write an expression for the rate of reaction in terms of \(\Delta\left[\mathrm{NH}_{3}\right]\). (c) The concentration of ammonia increases from \(0.257 \mathrm{M}\) to \(0.815 \mathrm{M}\) in \(15.0 \mathrm{~min} .\) Calculate the average rate of reaction over this time interval.

Experimental data are listed for the hypothetical reaction $$\mathrm{A}+\mathrm{B} \longrightarrow \mathrm{C}+\mathrm{D}$$ $$\begin{array}{lcccccc}\hline \text { Time (s) } & 0 & 10 & 20 & 30 & 40 & 50 \\\\{[\mathrm{~A}]} & 0.32 & 0.24 & 0.20 & 0.16 & 0.14 & 0.12 \\ \hline\end{array}$$ (a) Plot these data as in Figure \(11.2\). (b) Draw a tangent to the curve to find the instantaneous rate at \(30 \mathrm{~s}\). (c) Find the average rate over the 10 to \(40 \mathrm{~s}\) interval. (d) Compare the instantaneous rate at \(30 \mathrm{~s}\) with the average rate over the thirty-second interval.

Experimental data are listed for the hypothetical reaction $$\mathrm{x} \longrightarrow \mathrm{Y}+\mathrm{Z}$$ $$\begin{array}{lcccccc}\hline \text { Time (s) } & 0 & 10 & 20 & 30 & 40 & 50 \\\ {[\mathrm{X}]} & 0.0038 & 0.0028 & 0.0021 & 0.0016 & 0.0012 & 0.00087 \\\\\hline\end{array}$$ (a) Plot these data as in Figure \(11.2 .\) (b) Draw a tangent to the curve to find the instantaneous rate at \(40 \mathrm{~s}\). (c) Find the average rate over the 10 to 50 s interval. (d) Compare the instantaneous rate at \(40 \mathrm{~s}\) with the average rate over the \(40-\mathrm{s}\) interval.

A reaction has two reactants \(\mathrm{A}\) and \(\mathrm{B}\). What is the order with respect to each reactant and the overall order of the reaction described by each of the following rate expressions? (a) rate \(=k_{1}[\mathrm{~A}]^{3}\) (b) rate \(=k_{2}[\mathrm{~A}] \times[\mathrm{B}]\) (c) rate \(=k_{3}[\mathrm{~A}] \times[\mathrm{B}]^{2}\) (d) rate \(=k_{4}[\mathrm{~B}]\)

A reaction has two reactants \(\mathrm{X}\) and \(\mathrm{Y}\). What is the order with respect to each reactant and the overall order of the reaction described by the following rate expressions? (a) rate \(=k_{1}[\mathrm{X}]^{2} \times[\mathrm{Y}]\) (b) rate \(=k_{2}[\mathrm{X}]\) (c) rate \(=k_{3}[\mathrm{X}]^{2} \times[\mathrm{Y}]^{2}\) (d) rate \(=k_{4}\)

The decomposition of nitrogen dioxide is a second-order reaction. At \(550 \mathrm{~K}\), a \(0.250 M\) sample decomposes at the rate of \(1.17 \mathrm{~mol} / \mathrm{L} \cdot \mathrm{min} .\) (a) Write the rate expression. (b) What is the rate constant at \(550 \mathrm{~K}\) ? (c) What is the rate of decomposition when \(\left[\mathrm{NO}_{2}\right]=0.800 \mathrm{M?}\)

The decomposition of ammonia on tungsten at \(1100^{\circ} \mathrm{C}\) is zero- order with a rate constant of \(2.5 \times 10^{-4} \mathrm{~mol} / \mathrm{L} \cdot \mathrm{min} .\) (a) Write the rate expression. (b) Calculate the rate when \(\left[\mathrm{NH}_{3}\right]=0.075 M\). (c) At what concentration of ammonia is the rate equal to the rate constant?

The reaction $$\mathrm{NO}(g)+\frac{1}{2} \mathrm{Br}_{2}(g) \longrightarrow \mathrm{NOBr}(g)$$ is second-order in nitrogen oxide and first-order in bromine. The rate of the reaction is \(1.6 \times 10^{-8} \mathrm{~mol} / \mathrm{L} \cdot \mathrm{min}\) when the nitrogen oxide concentration is \(0.020 \mathrm{M}\) and the bromine concentration is \(0.030 \mathrm{M}\). (a) What is the value of \(k\) ? (b) At what concentration of bromine is the rate \(3.5 \times 10^{-7} \mathrm{~mol} / \mathrm{L} \cdot \min\) and \([\mathrm{NO}]=0.043 \mathrm{M} ?\) (c) At what concentration of nitrogen oxide is the rate \(2.0 \times\) \(10^{-6} \mathrm{~mol} / \mathrm{L} \cdot \mathrm{min}\) and the bromine concentration one fourth of the nitrogen oxide concentration?

The reaction $$\mathrm{ICl}(g)+\frac{1}{2} \mathrm{H}_{2}(g) \longrightarrow \frac{1}{2} \mathrm{I}_{2}(g)+\mathrm{HCl}(g)$$ is first-order in both reactants. The rate of the reaction is \(4.89 \times 10^{-5} \mathrm{~mol} / \mathrm{L} \cdot \mathrm{s}\) when the ICl concentration is \(0.100 M\) and that of the hydrogen gas is \(0.030 \mathrm{M}\) (a) What is the value of \(k\) ? (b) At what concentration of hydrogen is the rate \(5.00 \times 10^{-4} \mathrm{~mol} / \mathrm{L} \cdot \mathrm{s}\) and \([\mathrm{ICl}]=0.233 \mathrm{M?}\) (c) At what concentration of iodine chloride is the rate \(0.0934 \mathrm{~mol} / \mathrm{L} \cdot \mathrm{s}\) if the hydrogen concentration is three times that of ICl?

For a reaction involving the decomposition of \(\mathrm{Y}\), the following data are obtained: $$\begin{array}{lllll}\hline \text { Rate }(\mathrm{mol} / \mathrm{L} \cdot \min ) & 0.288 & 0.245 & 0.202 & 0.158 \\ {[\mathrm{Y}]} & 0.200 & 0.170 & 0.140 & 0.110 \\ \hline\end{array}$$ (a) Determine the order of the reaction. (b) Write the rate expression for the decomposition of Y. (c) Calculate \(k\) for the experiment above.

WEB When boron trifluoride reacts with ammonia, the following \(T\) reaction occurs: for $$\mathrm{BF}_{3}(g)+\mathrm{NH}_{3}(g) \longrightarrow \mathrm{BF}_{3} \mathrm{NH}_{3}(g)$$ The following data are obtained at a particular temperature: $$\begin{array}{cccc}\hline \text { Expt. } & {\left[\mathrm{BF}_{3}\right]} & {\left[\mathrm{NH}_{3}\right]} & \text { Initial Rate }(\mathrm{mol} / \mathrm{L} \cdot \mathrm{s}) \\\\\hline 1 & 0.100 & 0.100 & 0.0341 \\ 2 & 0.200 & 0.233 & 0.159 \\ 3 & 0.200 & 0.0750 & 0.0512 \\ 4 & 0.300 & 0.100 & 0.102 \\\\\hline\end{array}$$

Hydrogen bromide is a highly reactive and corrosive gas used mainly as a catalyst for organic reactions. It is produced by reacting hydrogen and bromine gases together. $$\mathrm{H}_{2}(g)+\mathrm{Br}_{2}(g) \longrightarrow 2 \mathrm{HBr}(g)$$ The rate is followed by measuring the intensity of the orange color of the bromine gas. The following data are obtained: $$\begin{array}{cccc}\hline \text { Expt. } & {\left[\mathrm{H}_{2}\right]} & {\left[\mathrm{Br}_{2}\right]} & \text { Initial Rate }(\mathrm{mol} / \mathrm{L} \cdot \mathrm{s}) \\ \hline 1 & 0.100 & 0.100 & 4.74 \times 10^{-3} \\ 2 & 0.100 & 0.200 & 6.71 \times 10^{-3} \\ 3 & 0.250 & 0.200 & 1.68 \times 10^{-2} \\ \hline\end{array}$$(a) What is the order of the reaction with respect to hydrogen, bromine, and overall? (b) Write the rate expression for the reaction. (c) Calculate \(k\) for the reaction. What are the units for \(k ?\) (d) When \(\left[\mathrm{H}_{2}\right]=0.455 \mathrm{M}\) and \(\left[\mathrm{Br}_{2}\right]=0.215 M\), what is the rate of the reaction?

Diethylhydrazine reacts with iodine according to the following equation: $$\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2}(\mathrm{NH})_{2}(l)+\mathrm{I}_{2}(a q) \longrightarrow\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2} \mathrm{~N}_{2}(l)+2 \mathrm{HI}(a q)$$ The rate of the reaction is followed by monitoring the disappearance of the purple color due to iodine. The following data are obtained at a certain temperature. $$ \begin{array}{cccc} \hline \text { Expt. } & {\left[\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2}(\mathrm{NH})_{2}\right]} & {\left[\mathrm{I}_{2}\right]} & \text { Initial Rate }(\mathrm{mol} / \mathrm{L} \cdot \mathrm{h}) \\ \hline 1 & 0.150 & 0.250 & 1.08 \times 10^{-4} \\ 2 & 0.150 & 0.3620 & 1.56 \times 10^{-4} \\ 3 & 0.200 & 0.400 & 2.30 \times 10^{-4} \\ 4 & 0.300 & 0.400 & 3.44 \times 10^{-4} \\ \hline\end{array}$$ (a) What is the order of the reaction with respect to diethylhydrazine, iodine, and overall? (b) Write the rate expression for the reaction. (c) Calculate \(k\) for the reaction. (d) What must \(\left[\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2}(\mathrm{NH})_{2}\right]\) be so that the rate of the reaction is \(5.00 \times 10^{-4} \mathrm{~mol} / \mathrm{L} \cdot \mathrm{h}\) when \(\left[\mathrm{I}_{2}\right]=0.500 ?\)

The equation for the iodination of acetone in acidic solution is $$\mathrm{CH}_{3} \mathrm{COCH}_{3}(a q)+\mathrm{I}_{2}(a q) \longrightarrow \mathrm{CH}_{3} \mathrm{COCH}_{2} \mathrm{I}(a q)+\mathrm{H}^{+}(a q)+\mathrm{I}^{-}(a q)$$ The rate of the reaction is found to be dependent not only on the concentration of the reactants but also on the hydrogen ion concentration. Hence the rate expression of this reaction is $$\text { rate }=k\left[\mathrm{CH}_{3} \mathrm{COCH}_{3}\right]^{m}\left[\mathrm{I}_{2}\right]^{n}\left[\mathrm{H}^{+}\right]^{p}$$ The rate is obtained by following the disappearance of iodine using starch as an indicator. The following data are obtained: $$ \begin{array}{cccc} \hline\left[\mathrm{CH}_{3} \mathrm{COCH}_{3}\right] & \left.\mathrm{[H}^{+}\right] & {\left[\mathrm{I}_{2}\right]} & \text { Initial Rate }(\mathrm{mol} / \mathrm{L} \cdot \mathrm{s}) \\ \hline 0.80 & 0.20 & 0.001 & 4.2 \times 10^{-6} \\ 1.6 & 0.20 & 0.001 & 8.2 \times 10^{-6} \\ 0.80 & 0.40 & 0.001 & 8.7 \times 10^{-6} \\ 0.80 & 0.20 & 0.0005 & 4.3 \times 10^{-6} \\ \hline\end{array}$$ (a) What is the order of the reaction with respect to each reactant? (b) Write the rate expression for the reaction. (c) Calculate \(k\). (d) What is the rate of the reaction when \(\left[\mathrm{H}^{+}\right]=0.933 M\) and \(\left[\mathrm{CH}_{3} \mathrm{COCH}_{3}\right]=3\left[\mathrm{H}^{+}\right]=10\left[\mathrm{I}^{-}\right] ?\)

Consider the reaction $$\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{3+}(a q)+\mathrm{SCN}^{-}(a q) \longrightarrow \mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5} \mathrm{SCN}^{2+}(a q)+\mathrm{H}_{2} \mathrm{O}$$ The following data were obtained: $$\begin{array}{ccc}\hline\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}{\underline{\phantom{xx}}}^{3+}\right] & {\left[\mathrm{SCN}^{-}\right]} & \text {Initial Rate }(\mathrm{mol} /\mathrm{L} \cdot \mathrm{min}) \\ \hline 0.025 & 0.060 & 6.5 \times 10^{-4} \\\0.025 & 0.077 & 8.4 \times 10^{-4} \\\0.042 & 0.077 & 1.4 \times 10^{-3} \\ 0.042 & 0.100 & 1.8 \times 10^{-3} \\\\\hline\end{array}$$ (a) Write the rate expression for the reaction. (b) Calculate \(k\). (c) What is the rate of the reaction when \(15 \mathrm{mg}\) of \(\mathrm{KSCN}\) is added to \(1.50 \mathrm{~L}\) of a solution \(0.0500 \mathrm{M}\) in \(\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}{\underline{\phantom{xx}}}^{3+}\) ?

Nitrosyl bromide (NOBr) decomposes to nitrogen oxide and bromine. Use the following data to determine the order of the decomposition reaction of nitrosyl bromide. $$\begin{array}{cccccc}\hline \text { Time (s) } & 0 & 6 & 12 & 18 & 24 \\ \text { [NOBr] } & 0.0286 & 0.0253 & 0.0229 & 0.0208 & 0.0190 \\\\\hline\end{array}$$

Hypofluorous acid, HOF, is extremely unstable at room temperature. The following data apply to the decomposition of HOF to \(\mathrm{HF}\) and \(\mathrm{O}_{2}\) gases at a certain temperature. $$\begin{array}{cl}\hline \text { Time (min) } & \text { [HOF] } \\\\\hline 1.00 & 0.607 \\\2.00 & 0.223 \\\3.00 & 0.0821 \\\4.00 & 0.0302 \\\5.00 & 0.0111 \\\\\hline \end{array}$$ (a) By plotting the data, show that the reaction is first-order. (b) From the graph, determine \(k\). (c) Using \(k\), find the time it takes to decrease the concentration to \(0.100 \mathrm{M}\) (d) Calculate the rate of the reaction when [HOF] \(=0.0500 M\).

The first-order rate constant for the decomposition of a certain hormone in water at \(25^{\circ} \mathrm{C}\) is \(3.42 \times 10^{-4}\) day \(^{-1}\). (a) If a \(0.0200 \mathrm{M}\) solution of the hormone is stored at \(25^{\circ} \mathrm{C}\) for two months, what will its concentration be at the end of that period? (b) How long will it take for the concentration of the solution to drop from \(0.0200 M\) to \(0.00350 \mathrm{M} ?\) (c) What is the half-life of the hormone?

In the first-order decomposition of acetone at \(500^{\circ} \mathrm{C}\), $$\mathrm{CH}_{3}-\mathrm{CO}-\mathrm{CH}_{3}(g) \longrightarrow \text { products }$$ it is found that the concentration is \(0.0300 \mathrm{M}\) after \(200 \mathrm{~min}\) and \(0.0200 \mathrm{M}\) after 400 min. Calculate the following. (a) the rate constant (b) the half-life (c) the initial concentration

The decomposition of dimethyl ether \(\left(\mathrm{CH}_{3} \mathrm{OCH}_{3}\right)\) to methane, carbon monoxide, and hydrogen gases is found to be first-order. At \(500^{\circ} \mathrm{C}\), a \(150.0\) -mg 35 sample of dimethyl ether is reduced to \(43.2 \mathrm{mg}\) after three quarters of an hour. Calculate (a) the rate constant. (b) the half-life at \(500^{\circ} \mathrm{C}\). (c) how long it will take to decompose \(95 \%\) of the dimethyl ether.

The first-order rate constant for the decomposition of a certain drug at \(25^{\circ} \mathrm{C}\) is \(0.215 \mathrm{month}^{-1}\) (a) If \(10.0 \mathrm{~g}\) of the drug is stored at \(25^{\circ} \mathrm{C}\) for one year, how many grams of the drug will remain at the end of the year? (b) What is the half-life of the drug? (c) How long will it take to decompose \(65 \%\) of the drug?

The decomposition of phosphine, \(\mathrm{PH}_{3}\), to \(\mathrm{P}_{4}(g)\) and \(\mathrm{H}_{2}(g)\) is firstorder. Its rate constant at a certain temperature is \(1.1 \mathrm{~min}^{-1}\). (a) What is its half-life in seconds? (b) What percentage of phosphine is decomposed after \(1.25 \mathrm{~min}\) ? (c) How long will it take to decompose one fifth of the phosphine?

The decomposition of ethane, \(\mathrm{C}_{2} \mathrm{H}_{6}\), is a first-order reaction. It is found that it takes 212 s to decompose \(0.00839 \mathrm{M} \mathrm{C}_{2} \mathrm{H}_{6}\) to \(0.00768 \mathrm{M}\). (a) What is the rate constant for the reaction? (b) What is the rate of decomposition (in \(\mathrm{mol} / \mathrm{L} \cdot \mathrm{h}\) ) when \(\left[\mathrm{C}_{2} \mathrm{H}_{6}\right]=\) \(0.00422 \mathrm{M} ?\) (c) How long (in minutes) will it take to decompose \(\mathrm{C}_{2} \mathrm{H}_{6}\) so that \(27 \%\) remains? (d) What percentage of \(\mathrm{C}_{2} \mathrm{H}_{6}\) is decomposed after \(22 \mathrm{~min}\) ?

Dinitrogen pentoxide gas decomposes to form nitrogen dioxide and oxygen. The reaction is first-order and has a rate constant of \(0.247 \mathrm{~h}^{-1}\) at \(25^{\circ} \mathrm{C}\). If a 2.50-L flask originally contains \(\mathrm{N}_{2} \mathrm{O}_{5}\) at a pressure of \(756 \mathrm{~mm} \mathrm{Hg}\) at \(25^{\circ} \mathrm{C}\), then how many moles of \(\mathrm{O}_{2}\) are formed after 135 minutes? (Hint: First write a balanced equation for the decomposition.)

Sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) hydrolyzes into glucose and fructose. The hydrolysis is a first-order reaction. The half-life for the hydrolysis of sucrose is \(64.2\) min at \(25^{\circ} \mathrm{C}\). How many grams of sucrose in \(1.25 \mathrm{~L}\) of a \(0.389 \mathrm{M}\) solution are hydrolyzed in \(1.73\) hours?

Copper-64 is one of the metals used to study brain activity. Its decay constant is \(0.0546 \mathrm{~h}^{-1}\). If a solution containing \(5.00 \mathrm{mg}\) of \(\mathrm{Cu}-64\) is used, how many milligrams of Cu-64 remain after eight hours?

Iodine-131 is used to treat tumors in the thyroid. Its first-order half-life is \(8.1\) days. If a patient is given a sample containing \(5.00 \mathrm{mg}\) of \(\mathrm{I}-131\), how long will it take for \(25 \%\) of the isotope to remain in her system?

Argon- 41 is used to measure the rate of gas flow. It has a decay constant of \(6.3 \times 10^{-3} \mathrm{~min}^{-1}\). (a) What is its half-life? (b) How long will it take before only \(1.00 \%\) of the original amount of Ar- 41 is left?

A sample of sodium-24 chloride contains \(0.050 \mathrm{mg}\) of \(\mathrm{Na}-24\) to study the sodium balance of an animal. After \(24.9 \mathrm{~h}, 0.016 \mathrm{mg}\) of \(\mathrm{Na}-24\) is left. What is the half- life of \(\mathrm{Na}-24 ?\)

The decomposition of \(\mathrm{Y}\) is a zero-order reaction. Its half-life at \(25^{\circ} \mathrm{C}\) and \(0.188 M\) is 315 minutes. (a) What is the rate constant for the decomposition of Y? (b) How long will it take to decompose a \(0.219 \mathrm{M}\) solution of \(\mathrm{Y}\) ? (c) What is the rate of the decomposition of \(0.188 \mathrm{M}\) at \(25^{\circ} \mathrm{C}\) ? (d) Does the rate change when the concentration of \(\mathrm{Y}\) is increased to \(0.289 \mathrm{M}\) ? If so, what is the new rate?

The decomposition of \(\mathrm{A}\) at \(85^{\circ} \mathrm{C}\) is a zero-order reaction. It takes 35 minutes to decompose \(37 \%\) of an initial mass of \(282 \mathrm{mg}\). (a) What is \(k\) at \(85^{\circ} \mathrm{C}\) ? (b) What is the half-life of \(282 \mathrm{mg}\) at \(85^{\circ} \mathrm{C}\) ? (c) What is the rate of decomposition for \(282 \mathrm{mg}\) at \(85^{\circ} \mathrm{C} ?\) (d) If one starts with \(464 \mathrm{mg}\), what is the rate of its decomposition at \(85^{\circ} \mathrm{C} ?\)

For the zero-order decomposition of HI on a gold surface $$\mathrm{HI}(g) \stackrel{\mathrm{Au}}{\longrightarrow} \frac{1}{2} \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{I}_{2}(g)$$ it takes \(16.0 \mathrm{~s}\) for the pressure of HI to drop from \(1.00\) atm to \(0.200 \mathrm{~atm}\). (a) What is the rate constant for the reaction? (b) How long will it take for the pressure to drop from \(0.150 \mathrm{~atm}\) to \(0.0432\) atm? (c) What is the half-life of \(\mathrm{HI}\) at a pressure of \(0.500 \mathrm{~atm}\) ?

For the zero-order decomposition of ammonia on tungsten $$\mathrm{NH}_{3}(\mathrm{~g}) \stackrel{\mathrm{w}}{\longrightarrow} \frac{1}{2} \mathrm{~N}_{2}(g)+\frac{3}{2} \mathrm{H}_{2}(g)$$ the rate constant is \(2.08 \times 10^{-4} \mathrm{~mol} / \mathrm{L} \cdot \mathrm{s}\). (a) What is the half-life of a \(0.250 \mathrm{M}\) solution of ammonia? (b) How long will it take for the concentration of ammonia to drop from \(1.25 M\) to \(0.388 M ?\)

The following gas-phase reaction is second-order. $$2 \mathrm{C}_{2} \mathrm{H}_{4}(g) \longrightarrow \mathrm{C}_{4} \mathrm{H}_{8}(g)$$ Its half-life is \(1.51\) min when \(\left[\mathrm{C}_{2} \mathrm{H}_{4}\right]\) is \(0.250 \mathrm{M}\) (a) What is \(k\) for the reaction? (b) How long will it take to go from \(0.187 M\) to \(0.0915 \mathrm{M}\) ? (c) What is the rate of the reaction when \(\left[\mathrm{C}_{2} \mathrm{H}_{4}\right]\) is \(0.335 \mathrm{M} ?\)

Ammonium cyanate, \(\mathrm{NH}_{4} \mathrm{NCO}\), in water rearranges to produce urea, a common fertilizer, \(\left(\mathrm{NH}_{2}\right)_{2} \mathrm{CO}\) : $$\mathrm{NH}_{4} \mathrm{NCO}(a q) \longrightarrow\left(\mathrm{NH}_{2}\right)_{2} \mathrm{CO}(a q)$$ The rearrangement is a second-order reaction. It takes \(11.6 \mathrm{~h}\) for the concentration of \(\mathrm{NH}_{4} \mathrm{NCO}\) to go from \(0.250 \mathrm{M}\) to \(0.0841 \mathrm{M}\). (a) What is \(k\) for the reaction? (b) What is the half-life of the reaction when \(\mathrm{NH}_{4} \mathrm{NCO}\) is \(0.100 \mathrm{M}\) ? (c) How long will it take to rearrange \(39 \%\) of a \(0.450 \mathrm{M}\) solution? (d) How fast is a \(0.839 \mathrm{M}\) solution being changed to urea?

The rate constant for the second-order reaction $$\mathrm{NOBr}(g) \longrightarrow \mathrm{NO}(g)+\frac{1}{2} \mathrm{Br}_{2}(g)$$ is \(48 \mathrm{~L} / \mathrm{mol} \cdot \mathrm{min}\) at a certain temperature. How long will it take to decompose \(90.0 \%\) of a \(0.0200 \mathrm{M}\) solution of nitrosyl bromide?

The decomposition of nitrosyl chloride $$\mathrm{NOCl}(g) \longrightarrow \mathrm{NO}(g)+\frac{1}{2} \mathrm{Cl}_{2}(g)$$ is a second-order reaction. If it takes \(0.20 \mathrm{~min}\) to decompose \(15 \%\) of a \(0.300 \mathrm{M}\) solution of nitrosyl chloride, what is \(k\) for the reaction?

If the activation energy of a reaction is \(4.86 \mathrm{~kJ}\), then what is the percent increase in the rate constant of a reaction when the temperature is increased from \(45^{\circ}\) to \(75^{\circ} \mathrm{C}\) ?

Consider the following hypothetical reaction: $$\mathrm{A}+\mathrm{B} \longrightarrow \mathrm{C}+\mathrm{D} \quad \Delta H=-125 \mathrm{~kJ}$$ Draw a reaction-energy diagram for the reaction if its activation energy is \(37 \mathrm{~kJ} .\)

For the reaction $$\mathrm{X}+\mathrm{Y} \longrightarrow \mathrm{R}+\mathrm{Z} \quad \Delta H=+295 \mathrm{~kJ},$$ draw a reaction-energy diagram for the reaction if its activation energy is \(378 \mathrm{~kJ} .\)

The uncoiling of deoxyribonucleic acid (DNA) is a first-order reaction. Its activation energy is \(420 \mathrm{~kJ}\). At \(37^{\circ} \mathrm{C}\), the rate constant is \(4.90 \times 10^{-4} \mathrm{~min}^{-1}\). (a) What is the half-life of the uncoiling at \(37^{\circ} \mathrm{C}\) (normal body temperature)? (b) What is the half-life of the uncoiling if the organism has a temperature of \(40^{\circ} \mathrm{C}\left(\approx 104^{\circ} \mathrm{F}\right)\) ? (c) By what factor does the rate of uncoiling increase (per \({ }^{\circ} \mathrm{C}\) ) over this temperature interval?

Cold-blooded animals decrease their body temperature in cold weather to match that of their environment. The activation energy of a certain reaction in a cold-blooded animal is \(65 \mathrm{~kJ} / \mathrm{mol} .\) By what percentage is the rate of the reaction decreased if the body temperature of the animal drops from \(35^{\circ} \mathrm{C}\) to \(22^{\circ} \mathrm{C} ?\)

The activation energy for the reaction involved in the souring of raw milk is \(75 \mathrm{~kJ}\). Milk will sour in about eight hours at \(21^{\circ} \mathrm{C}\left(70^{\circ} \mathrm{F}=\right.\) room temperature). How long will raw milk last in a refrigerator maintained at \(5^{\circ} \mathrm{C}\) ? Assume the rate constant to be inversely related to souring time.

The chirping rate of a cricket \(\mathrm{X}\), in chirps per minute near room temperature, is $$\mathrm{X}=7.2 t-32$$ where \(t\) is the temperature in \({ }^{\circ} \mathrm{C}\). (a) Calculate the chirping rates at \(25^{\circ} \mathrm{C}\) and \(35^{\circ} \mathrm{C}\). (b) Use your answers in (a) to estimate the activation energy for the chirping. (c) What is the percentage increase for a \(10^{\circ} \mathrm{C}\) rise in temperature?