Chem113 14.4-14.5

The half-life of a reaction is the time it takes for [A]0 to drop to half its original value. The half-life of a reaction is related to its rate constant. The half-life of a first-order reaction is independent of the initial concentration.

Which of the following statements correctly describe the half-life of a reaction? Select all that apply.

The straight line is obtained by plotting ln[A] versus time. The rate constant for the reaction is related to the slope of the straight line. The slope of the line is negative.

Which of the following statements correctly describe the straight-line plot obtained from concentration and time data for the first-order reaction A → products? Select all that apply.

If [A] is decreased to one-half of its original value and the reaction rate is halved, the reaction is first order with respect to A. If [A] is doubled and the reaction rate increases by a factor of 4, the reaction is second order with respect to A.

Which of the following the statements correctly relate experimental observations with reaction order? Select all that apply. (Assume A is a reactant in all cases.)

What is [A] after y minutes of the reaction? How long will it take to use up x moles per liter of A?

Which question(s) can be answered from an integrated rate law that cannot be answered by other forms of the rate law? Select all that apply.

3.1%

A first-order reaction has a half-life of 4.1 minutes. The percentage of reactant remaining after 20 minutes is approximately equal to ______.

4.6 × 10^21 s {1/[A]t−1/[A]o}/k=t

At 25°C, HI breaks down very slowly to form H2H2 and I2I2. The reaction follows second-order kinetics and k at 25°C is 2.4 × 10−21 L/mol·s2.4 × 10-21 L/mol·s. If 0.0100 mol of HI(g) is placed in a 1.0-L container, how long will it take for the concentration of HI to reach 0.00900 mol/L?

x + y

For the general rate law rate = k[A]x[B]y, the overall reaction order is given by _____.

The reaction is first order with respect to I−. Rate = k[H2O2][I−]

H2O2 (aq) decomposes rapidly in the presence of iodide ion (I−). Select all the statements that correctly interpret the experimental data provided for this reaction.

ln(0.355) = - k(4.90 min) ln[A]t/[A]0 = ln(0.355)

In a particular first-order reaction, [A] drops to 35.5% of its initial value in 4.90 min at 25°C. Select all the options that correctly reflect the steps required to solve for the rate constant, k.

orders, first, order

In the rate law rate = k[A]x[B]y, the exponents x and y are called the reaction ____. If x = 1, the reaction is said to be ____ ____ with respect toe reactant A.

5.29 × 10-2 h-1 t1/2 = 0.693/k; k = 0.693/13.1h = 5.29 × 10-2 h-1

Iodine-123 breaks down in a first-order process with a half-life of 13.1 h. What is the rate constant for this process?

line, slope

Kinetic data are often analyzed graphically. Depending on the reaction order, a function of [A] is plotted versus time to obtain a straight ____ plot. The value of the rate constant is determined from the ____ of the plot. (Note: There is no actual graph given in this question.)

ln[A]t = -kt + ln[A]0 ln[A]t/[A]0 = -kt

Select all the options that correctly reflect the integrated rate law for a first-order reaction.

For a zeroth-order reaction, a plot of [A]t versus time will give a straight line. The rate of a zeroth-order reaction is independent of reactant concentration. The rate constant of a zeroth-order reaction is equal to the reaction rate.

Select all the statements that correctly describe a zeroth-order reaction. The reaction is represented by A → products.

The overall reaction order is 3. The reaction is first order with respect to Mg. The reaction is second order with respect to [O2].

Select all the statements that correctly interpret the experimental data provided for the reaction 2Mg (s) + O2 (g) → MgO (s).

The reactant concentration at any time in the reaction can be determined from the integrated rate law. An integrated rate law includes time as a variable. The value of the reaction constant, k, can be determined using an integrated rate law.

Select all the statements that describe an integrated rate law.

The value of k is 5.00 × 105. The units for k are M-2⋅s-1.

Select the correct value and units for the rate constant, k, for the reaction 4A (g) + 3B (g) → 2C (g), given the data provided. The experimentally determined rate law is rate = k[A]2[B].

t = 0.916/1.94×10−4= 4720 min ln 0.10/.25 = - (1.94 × 10-4)t

The decomposition of N2O to form N2 and O2 is a first-order reaction. The rate constant for the reaction is 1.94 × 10-4 min-1 at 730°C. If [A]0 is 0.25 M, how much time is required for [A] to drop to 0.10 M? Select all the options that correctly reflect the steps required to solve this problem.

k = 2.5 s-1 ⋅ M-1 t1/2 = 2.0 s

The decomposition of NO2 (g) proceeds according to the reaction below: 2NO2 (g) → 2NO (g) + O2 (g) The rate law for this reaction is rate = k[NO2]2. Using the data shown, calculate the value of k, as well as the half-life for the initial concentration given.

t1/2 = 29 min t1/2 = 1/k[A]0= 1/0.100×0.35= 29 min

The dimerization of butadiene proceeds according to second-order kinetics. If the rate constant at a particular temperature is 0.100 M-1 ⋅ min-1, calculate the half-life for an initial reactant concentration of 0.35 M.

1/[A] versus time

Which of the following plots will give a straight line for a reaction that follows second-order kinetics? The reaction is represented by A → products.

The rate law includes the rate constant for the reaction. The rate law relates the rate of reaction to the concentrations of the reactants.

Which of the following statements correctly describe a rate law for a reaction? Select all that apply. (Assume that the reaction is not reversible to any appreciable extent.)

The average rate is an average of instantaneous rates for a given period of time. The initial rate is an instantaneous rate at t = 0.

Which of the following statements correctly describe average rate, instantaneous rate, and initial rate? Select all that apply.

The value of k can be calculated from a single experiment once the reaction orders are known. If there is more than one reactant present the reaction orders will usually be determined individually. The rate law is determined by measuring the initial reaction rate for different reactant concentrations.

Which of the following statements correctly describe how a rate law is determined? Select all that apply.

Rate = k[HI]2kHI2 k = 4.00 × 10−2 M−1·s−1k = 4.00 × 10-2 M-1·s-1

Determine the overall rate law and the value of the rate constant, k, for the reaction 2HI (g) → H2 (g) +I2 (g)2HI (g) → H2 (g) + I2 (g) from the data provided.

The function of [A] versus time that gives a straight line plot indicates the reaction order. The rate constant is related to the slope of the straight line obtained.

The order of a reaction and its rate constant can be determined graphically. Select all the statements that correctly describe this process.

0.375 M

The reaction AB (g) → A (g) + B (g) follows second-order kinetics. If k = 0.200 L/mol⋅s and [AB]0 = 1.50 M, what is the concentration of AB after 10.0 s?

false

True or false: Based on the balanced equation N2 (g) + 3H2 (g) → 2NH3 (g), the rate law is given by rate = k[N2][H2]3.

true

True or false: For a zeroth-order reaction, the rate constant k is equal to the rate of the reaction.

The reaction is second order with respect to NO. If [NO] is doubled while [H2] remains the same, the reaction will occur 4 times faster.

Which of the following options correctly interpret the rate law rate = k[H2][NO]2? Select all that apply.

1/[A]t = kt + 1/[A]0

Which of the following options gives the correct expression for the integrated rate law for a reaction that follows second-order kinetics? The reactant is represented by the equation A → products.