A certain reaction has the following general form: aA ⟶bB At a particular temperature and [A]0=2

step 1 Okay, so we are given reaction A to B. And it's given the initial concentration as 2 .80 times 1

A certain reaction has the following general form: aA ⟶bB At...

A certain reaction has the following general form: $$ \mathrm{aA} \longrightarrow \mathrm{bB} $$ At a particular temperature and $[\mathrm{A}]_{0}=2.80 \times 10^{-3} M,$ con- centration 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 $7.00 \times 10^{-4} M ?$

A certain reaction has the following general form:
$$
\mathrm{aA} \longrightarrow \mathrm{bB}
$$
At a particular temperature and $[\mathrm{A}]_{0}=2.80 \times 10^{-3} M,$ con- centration 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 $7.00 \times 10^{-4} M ?$

Key Concepts

Integrated Rate Law

The integrated rate law establishes a mathematical relationship between the concentration of reactants and time. It allows for the determination of reaction kinetics by transforming experimental concentration versus time data into a linear form, which can then be used to extract kinetic parameters. For example, for a second order reaction, the integrated rate law relates the reciprocal of the concentration to time.

Time Calculation for Reaction Progress

Determining the time required for a concentration change during a reaction is a key application of integrated rate laws. It involves rearranging the integrated form to solve for time given initial and final concentrations, along with the rate constant. This approach provides a systematic method for predicting reaction progress over time based on kinetic data.

Half-Life in Second Order Reactions

The half-life of a reaction is the time required for the concentration of a reactant to decrease to half of its initial value. In second order reactions, the half-life is dependent on the initial concentration and is calculated using a formula that inversely relates half-life to both the rate constant and the initial concentration. This contrasts with first order reactions, where the half-life is constant regardless of concentration.

Rate Law

The rate law expresses the relationship between the reaction rate and the concentration of the reactants. It indicates the order of the reaction with respect to each reactant and provides insight into the reaction mechanism. For instance, a reaction where the rate is proportional to the square of a reactant’s concentration is classified as second order with respect to that reactant.

Second Order Kinetics

Second order kinetics refer to reactions where the rate of reaction is directly proportional to the square of the concentration of one reactant or to the product of the concentrations of two reactants. This implies that plotting 1/[reactant] versus time yields a straight line, and the slope of this line is directly related to the rate constant. Understanding second order kinetics is crucial for analyzing reactions that do not follow simple first order behavior.

Rate Constant

The rate constant is a proportionality factor in the rate law that is specific to a given reaction at a particular temperature. It provides quantitative insight into the speed of a reaction. In the context of integrated rate laws, the rate constant can be derived from the slope of the linear plot obtained from experimental data, making it a fundamental parameter in kinetics studies.

Transcript

00:01 Okay, so we are given reaction a to b.

00:04 And it's given the initial concentration as 2 .80 times 10 to nathway motor.

00:09 And then by plotting the 1 over concentration versus time, we serve in a straight line.

00:18 So with this point, 1 over concentration versus time, it will give a straight line.

00:22 And this strict line has a slope 3 .60 times 10 to the power depth 2.

00:29 Okay, so a, we have defined the weight law, integrated weight law, and the value of k.

00:34 And then b, we have to find the half a half a reaction, and also c, we have to find how much time required for the concentration of a, the initial concentration, decrease back to 7 times 10 to a parallel 4.

00:45 Okay, so for a, we have defined the weight law, the integrated weight law, and also the weight constant.

00:52 Okay, so for this case, we have given the information of a plot.

00:57 One over a time.

00:58 So actually, this plot is corresponding or related to the integrative ways law.

01:04 Integrated ways law.

01:06 Okay, when we have a zero -order versus a second order, if we plot the concentration in different way, they will have a strict line.

01:18 And for second order, if we plot one over concentration versus time, if we create a straight line.

01:24 Because the integrated way law state that, if we have a second order, we actually, so 1 over the concentration equals to the equilibrium, weight constant times time, and then we're going to plus 1 over the initial concentration.

01:43 And this is called the integrated weight law.

01:45 Okay, so from here we can see that we have one over concentration and then we have the time, and then we have the one over the initial concentration.

01:55 If you think about that, this is y equals to m8 plus c.

01:59 Is just in the same format.

02:02 Then the weight constant will be our stoop.

02:07 And this is the value of our way constant.

02:10 And the integrated weight law will be the one that i roll over here...

Please give Ace some feedback