Chapter 11

What are the units for each of the following if the concentrations are expressed in moles per liter and the time in seconds? a. rate of a chemical reaction b. rate constant for a zero-order rate law c. rate constant for a first-order rate law d. rate constant for a second-order rate law e. rate constant for a third-order rate law

The rate law for the reaction $${\mathrm{Cl}}_2(g)+{\mathrm{CHCl}}_3(g)⟶\mathrm{HCl}(g)+{\mathrm{CCl}}_4(g)$$ is $$\text{ Rate }=k{\left[{\mathrm{Cl}}_2\right]}^{1/2}\left[{\mathrm{CHCl}}_3\right]$$ What are the units for $k$, assuming time in seconds and concentration in mol/L?

A certain reaction has the following general form: $$\text{ aA }⟶\mathrm{bB}$$ At a particular temperature and $[\mathrm{A}{]}_0=2.00\times {10}^{-2}\mathrm{M},$concentration versus time data were collected for this reaction, and a plot of $\ln [\mathrm{A}]$ versus time resulted in a straight line with a slope value of $-2.97\times {10}^{-2}{\min }^{-1}$a. Determine the rate law, the integrated rate law, and the value of the rate constant for this reaction. b. Calculate the half-life for this reaction. c. How much time is required for the concentration of A to decrease to $2.50\times {10}^{-3}\mathrm{M}?$

A certain reaction has the following general form: $$\mathrm{aA}⟶\mathrm{bB}$$ At a particular temperature and $[\mathrm{A}{]}_0=2.80\times {10}^{-3}\mathrm{M},$concentration versus time data were collected for this reaction, and a plot of $1/[\mathrm{A}]$ versus time resulted in a straight line with a slope value of $+3.60\times {10}^{-2}\mathrm{L}/\mathrm{mol}\cdot \mathrm{s}$ a. Determine the rate law, the integrated rate law, and the value of the rate constant for this reaction. b. Calculate the half-life for this reaction. c. How much time is required for the concentration of A to decrease to $7.00\times {10}^{-4}\mathrm{M}?$

The decomposition of ethanol $\left({\mathrm{C}}_2{\mathrm{H}}_5\mathrm{OH}\right)$ on an alumina $\left({\mathrm{Al}}_2{\mathrm{O}}_3\right)$ surface$${\mathrm{C}}_2{\mathrm{H}}_5\mathrm{OH}(g)⟶{\mathrm{C}}_2{\mathrm{H}}_4(g)+{\mathrm{H}}_2\mathrm{O}(g)$$was studied at 600 K. Concentration versus time data were collected for this reaction, and a plot of $[\mathrm{A}]$ versus time resulted in a straight line with a slope of $-4.00\times {10}^{-5}\mathrm{mol}/\mathrm{L}\cdot \mathrm{s}$ a. Determine the rate law, the integrated rate law, and the value of the rate constant for this reaction. b. If the initial concentration of ${\mathrm{C}}_2{\mathrm{H}}_5\mathrm{OH}$ was $1.25\times {10}^{-2}$ $M,$ calculate the half-life for this reaction. c. How much time is required for all the $1.25\times {10}^{-2}M$ ${\mathrm{C}}_2{\mathrm{H}}_5\mathrm{OH}$ to decompose?

The reaction $$A⟶B+C$$ is known to be zero order in A and to have a rate constant of $5.0\times {10}^{-2}\mathrm{mol}/\mathrm{L}\cdot \mathrm{s}$ at ${25}^{\circ }\mathrm{C}.$ An experiment was run at ${25}^{\circ }\mathrm{C}$ where $[\mathrm{A}{]}_0=1.0\times {10}^{-3}\mathrm{M}$ a. Write the integrated rate law for this reaction. b. Calculate the half-life for the reaction. c. Calculate the concentration of $\mathrm{B}$ after $5.0\times {10}^{-3}\mathrm{s}$ has elapsed assuming $[\mathrm{B}{]}_0=0$

The decomposition of hydrogen iodide on finely divided gold at ${150}^{\circ }\mathrm{C}$ is zero order with respect to HI. The rate defined below is constant at $1.20\times {10}^{-4}\mathrm{mol}/\mathrm{L}\cdot \mathrm{s}$ $$\begin{array}{c}2\mathrm{HI}(g)\stackrel{\mathrm{Au}}{⟶}{\mathrm{H}}_2(g)+{\mathrm{I}}_2(g)\\ \text{ Rate }=-\frac{\mathrm{\Delta }[\mathrm{HI}]}{\mathrm{\Delta }t}=k=1.20\times {10}^{-4}\mathrm{mol}/\mathrm{L}\cdot \mathrm{s}\end{array}$$ a. If the initial HI concentration was 0.250 mol/L, calculate the concentration of HI at 25 minutes after the start of the reaction. b. How long will it take for all of the $0.250\mathrm{M}$ HI to decompose?

A certain first-order reaction is $45.0\mathrm{\%}$ complete in 65 s. What are the values of the rate constant and the half-life for this process?

A first-order reaction is $75.0\mathrm{\%}$ complete in $320.$ s. a. What are the first and second half-lives for this reaction? b. How long does it take for $90.0\mathrm{\%}$ completion?

The rate law for the decomposition of phosphine $\left({\mathrm{PH}}_3\right)$ is $$\text{ Rate }=-\frac{\mathrm{\Delta }\left[{\mathrm{PH}}_3\right]}{\mathrm{\Delta }t}=k\left[{\mathrm{PH}}_3\right]$$ It takes $120.$ s for $1.00M$ PH ${}_3$ to decrease to 0.250 M. How much time is required for $2.00\mathrm{M}{\mathrm{PH}}_3$ to decrease to a concentration of $0.350\mathrm{M}?$