For the reaction $A \rightarrow$ products, successive half-lives are observed to be 10.0, 20.0, and 40.0 min for an experiment in which $[ \mathrm { A } ] _ { 0 } = 0.10\ \mathrm { M } .$ Calculate the concentration of A at the following times. 80.0 min

Solve the following exercise.

For the reaction $\mathrm{A} \rightarrow$ products, successive half-lives are observed to be 10.0, 20.0, and 40.0min for an experiment in which $[\mathrm{A}]_0$ = 0.10 M. Calculate the concentration of $\mathrm{A}$ at the following times.

a. 80.0 min

b. 30.0 min

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

The radioactive isotope $^{32}\mathrm { P }$ decays by first-order kinetics and has a half-life of 14.3 days. How long does it take for 95.0% of a given sample of $^{32}\mathrm { P }$ to decay?

A first-order reaction is 75.0% complete in 320 s. What are the first and second half-lives for this reaction?

Estimate the instantaneous rate of change at the point indicated.

$$y ( t ) = \sqrt { 3 t + 1 };$$

t = 1

Sediment is transported parallel to the shoreline by a _____.

Find the exact value of each expression. $\csc \left[2 \sin ^{-1}\left(-\frac{3}{5}\right)\right]$

You and a coworker have developed a molecule that has shown potential as cobra antivenom (AV). This antivenom works by binding to the venom (V), thereby rendering it nontoxic. This reaction can be desrcibed by the rate law $\mathrm {Rate} = k [ \mathrm { AV } ] ^ { 1 } [ \mathrm { V } ] ^ { 1 }$ You have been given the following data from your coworker: $$ [ \mathrm { V } ] _ { 0 } = 0.20\ \mathrm { M } \\ [ \mathrm { AV } ] _ { 0 } = 1.0 \times 10 ^ { - 4 }\ \mathrm { M } $$ A plot of $\ln [ \mathrm { AV } ]$ versus time gives a straight line with a slope of $- 0.32 \mathrm { s } ^ {-1} .$ What is the value of the rate constant (k) for this reaction?

Consider the following initial rate data for the decomposition of compound AB to give A and B:

$$\lfloor \mathrm { AB } ] _ { 0 } ( \mathrm { mol } / \mathrm { L } ) \quad \quad \text { Initial Rate (mol } \mathrm { L } ^ { - 1 } \mathrm { s } ^ { - 1 } )$$

$$\begin{array} { l l } { 0.200 } &&&&&& { 3.20 \times 10 ^ { - 3 } } \\ { 0.400 } &&&&&& { 1.28 \times 10 ^ { - 2 } } \\ { 0.600 } &&&&&& { 2.88 \times 10 ^ { - 2 } } \end{array}$$

Determine the half-life for the decomposition reaction initially having 1.00 M AB present.

The dimerization of butadiene was studied at 500. K:

$$2 \mathrm { C } _ { 4 } \mathrm { H } _ { 6 } ( \mathrm { g } ) \longrightarrow \mathrm { C } _ { \mathrm { 8 } } \mathrm { H } _ { 12 } ( \mathrm { g } )$$

The following data were obtained, where

$$\text {Rate} = - \frac { d \left[ \mathrm { C } _ { 4 } \mathrm { H } _ { 6 } \right] } { d t }$$

$$\text {Time(s)} \quad \quad \quad \left[ \mathrm { C } _ { 4 } \mathrm { H } _ { 6 } \right] ( \mathrm { mol } / \mathrm { L } )$$

$$\begin{array} { r r } { 195 } \quad \quad \quad \quad \quad { 1.6 \times 10 ^ { - 2 } } \\ { 604 } \quad \quad \quad \quad \quad { 1.5 \times 10 ^ { - 2 } } \\ { 1246 } \quad \quad \quad \quad \quad { 1.3 \times 10 ^ { - 2 } } \\ { 2180 } \quad \quad \quad \quad \quad { 1.1 \times 10 ^ { - 2 } } \\ { 6210 } \quad \quad \quad \quad \quad { 0.68 \times 10 ^ { - 2 } } \end{array}$$

Determine the forms of the integrated rate law, the differential rate law, and the value of the rate constant for this reaction.

Consider the reaction $3 \mathrm { A } + \mathrm { B } + \mathrm { C } \longrightarrow \mathrm { D } + \mathrm { E }$ where the rate law is defined as

$$- \frac { d [ \mathrm { A } ] } { d t } = k [ \mathrm { A } ] ^ { 2 } [ \mathrm { B } ] [ \mathrm { C } ]$$

An experiment is carried out where $[ \mathrm { B } ] _ { 0 } = [ \mathrm { C } ] _ { 0 } = 1.00 \mathrm { M }$ and $[ \mathrm { A } ] _ { 0 } = 1.00 \times 10 ^ { - 4 } \mathrm { M }.$ If after 3.00 minutes $[ A ] = 3.26 \times 10 ^ { - 5 } M ,$ calculate the value of k.

Consider the reaction $3 \mathrm { A } + \mathrm { B } + \mathrm { C } \longrightarrow \mathrm { D } + \mathrm { E }$ where the rate law is defined as $- \frac { d [ \mathrm { A } ] } { d t } = k [ \mathrm { A } ] ^ { 2 } [ \mathrm { B } ] [ \mathrm { C } ].$ An experiment is carried out where $[ \mathrm { B } ] _ { 0 } = [ \mathrm { C } ] _ { 0 } = 1.00\ \mathrm { M }$ and $[ \mathrm { A } ] _ { 0 } = 1.00 \times 10 ^ { - 4 } \mathrm { M }.$ Calculate the half-life for this experiment.

Consider the hypothetical reaction $2 \mathrm { A } + \mathrm { B } \longrightarrow 2 \mathrm { C } + \mathrm { D }$ The following two-step mechanism is proposed for the reaction: $Step \ 1 : A + B \longrightarrow C + X.$ $Step \ 2 : A + X \longrightarrow C + D.$ X is an unstable intermediate. What is the predicted rate law expression if Step 2 is rate determining?