Chemistry Chapter 2: Integrated Rate Laws

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Questions and Answers

What is the rate equation for a first-order reaction?

d[A]/dt = k[A]t^2

d[A]/dt = k/[A]t

d[A]/dt = -k[A] (correct)

d[A]/dt = -k[A]t

What is the integrated form of the rate equation for a first-order reaction?

ln[A] = αkt + ln[A]0

-ln[A] = αkt + ln[A]0

ln[A] = -αkt + ln[A]0 (correct)

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

What is the unit of the rate constant for a first-order reaction?

time, t

reciprocal time, s-1 (correct)

concentration, M

rate, M/s

What is the plot of ln[A] versus t for a first-order reaction?

a straight line Signup and view all the answers

What is the slope of the plot of ln[A] versus t for a first-order reaction?

-αk Signup and view all the answers

What is the initial concentration of the reactant in the rate equation for a first-order reaction?

[A]0 Signup and view all the answers

What is the expression for the rate of a first-order reaction?

VR = -k[A] Signup and view all the answers

What is the relationship between the rate constant and the concentration of the reactant in a first-order reaction?

k is independent of [A] Signup and view all the answers

What is the expression for the integral rate equation of a first-order reaction in terms of the extent of the reaction?

ln(a / (a - x)) = αkt Signup and view all the answers

What is the integrated rate equation for a second-order reaction?

αkt = 1/[A] - 1/[A]0 Signup and view all the answers

What is the unit of the rate constant (k) in a first-order reaction?

s^-1 Signup and view all the answers

What is the plot that is linear for a second-order reaction?

1/[A] versus t Signup and view all the answers

What is the characteristic of a pseudo-first-order reaction?

The reaction involves two reactants with different concentrations. Signup and view all the answers

What is the rate equation for a reaction with two reactants, A and B, where the reaction is first order with respect to both A and B?

rate = k[A][B] Signup and view all the answers

What is the half-life equation for a second-order reaction?

t1/2 = 1/(αk[A]0) Signup and view all the answers

What is the definition of a second-order reaction?

A reaction whose rate is proportional to the square of the concentration of A. Signup and view all the answers

What is the condition for the rate equation to be equivalent to the integrated rate equation for a second-order reaction?

[A]0 = [B]0 Signup and view all the answers

What is the expression for the rate law of a second-order reaction involving one reactant?

d[A] / dt = -k[A]^2 Signup and view all the answers

What is the unit of the rate constant (k) in a second-order reaction?

M^-1s^-1 Signup and view all the answers

What does the slope of the plot of 1/[A] versus t represent?

The second-order rate constant Signup and view all the answers

What is the dependence of the half-life of a second-order reaction on the initial concentration of the reactant?

The half-life is inversely proportional to the initial concentration Signup and view all the answers

What is the expression for the concentration of A at time t in a second-order reaction?

[A]t = [A]0 / (1 + kt[A]0) Signup and view all the answers

What is the relationship between the half-life (t1/2) and the rate constant (k) in a first-order reaction?

t1/2 = 0.693 / k Signup and view all the answers

What is the unit of the second-order rate constant?

M-2s-1 Signup and view all the answers

What is the units of the rate constant for a second-order reaction?

What is the form of the integrated rate equation for a second-order reaction in which the initial reactants are not in stoichiometric proportions?

kt = ln([A][B]o) / ([A]o - [B]o) Signup and view all the answers

What is the plot of versus t for a second-order reaction in which the initial reactants are not in stoichiometric proportions?

a linear plot of ln([A]/[B]) versus t Signup and view all the answers

What is the substitution in the integrated equation for the reaction A → Products?

a instead of [A]o and (a-x) instead of [A] Signup and view all the answers

What is the integral rate equation for the reaction A → Products in terms of the extent of reaction x?

kt = 1/(a-x) - 1/a Signup and view all the answers

What is the substitution in the integrated equation for the reaction A + B → Products?

a and b instead of [A]o and [B]o, and (a-x) and (b-x) instead of [A] and [B] Signup and view all the answers

What is the integral rate equation for the reaction A + B → Products in terms of the extent of reaction x?

kt = ln(a(b-x)/b(a-x)) Signup and view all the answers

What is the expression for the rate of reaction VR when the initial reactants are not in stoichiometric proportions?

VR = -k[A][B] Signup and view all the answers

Study Notes

First Order Reactions

The rate law for a first-order reaction is: d[A]/dt = -k[A]
The integrated rate equation is: ln[A] = -αkt + ln[A]0
The rate constant (k) has units of reciprocal time (time)-1, s-1
A plot of ln[A] versus t is a straight line with a slope of -αk

Derivation of Integral Rate Equation for First Order Reactions

The reaction is: A → products
At time = 0, [A] = [A]0
At time = t, [A] = [A]t
Substituting [A]0 and [A]t into the integrated equation, we get: ln(a) = αkt

Pseudo First Order Reactions

The reaction is: A → products
The rate law is: d[A]/dt = -k[A]
Pseudo first-order reactions occur when the concentration of one reactant is much higher than the other

Second Order Reactions

The rate law for a second-order reaction is: d[A]/dt = -k[A]^2
The integrated rate equation is: 1/[A] = αkt + 1/[A]0
The rate constant (k) has units of concentration-1 time-1
A plot of 1/[A] versus t is a straight line with a slope of αk

Second Order Reactions with One Reactant

The reaction is: A → products
The rate law is: d[A]/dt = -k[A]^2
The integrated rate equation is: 1/[A] = αkt + 1/[A]0
The half-life (t1/2) is: t1/2 = 1/(αk[A]0)

Second Order Reactions with Two Reactants

The reaction is: A + B → products
The rate law is: d[A]/dt = -k[A][B]
If [A]0 = [B]0, then the rate equation is: d[A]/dt = -k[A]^2
If [A]0 ≠ [B]0, then the integrated rate equation is: kt = ln([A]/[B])

Exercise 1.2

Derive the integral rate equation for the second-order reaction in terms of the extent of reaction x
For the reaction A → products, the integral rate equation is: kt = 1/(a-x) - 1/a
For the reaction A + B → products, the integral rate equation is: kt = ln(b(a-x)/a(b-x))

Half-Life

The half-life (t1/2) is the time taken for the concentration of the reactant to decrease to half its initial value
For a first-order reaction, the half-life is: t1/2 = 0.693/k
For a second-order reaction, the half-life depends on the initial concentration of the reactant

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Description

This quiz covers the basics of integrated rate laws, including first-order reactions and rate equations. Topics include the definition of first-order reactions, rate equations, and integration.