Chemistry Reaction Rates and Laws

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Questions and Answers

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

[A] = [A]_0 - kt
ln[A] = ln[A]_0 - kt
t_{1/2} = k[A]_0
1/[A] = 1/[A]_0 + kt (correct)

What does the half-life of a zero-order reaction depend on?

The temperature alone.
The activation energy.
Only the rate constant.
The initial concentration and the rate constant. (correct)

In the context of the Arrhenius equation, what does the symbol $E_a$ represent?

The equilibrium constant.
The universal gas constant.
The activation energy. (correct)
The rate constant.

Which of the following equations represents the half-life for a first-order reaction?

t_{1/2} = rac{0.693}{k} (B) Signup and view all the answers

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

Rate = k (C) Signup and view all the answers

For a first-order reaction, how does the natural logarithm of the concentration change over time?

$ln[A] = ln[A]_0 - kt$ (C) Signup and view all the answers

What occurs to the rate constant $k$ as the temperature increases, based on the Arrhenius equation?

It increases exponentially. (C) Signup and view all the answers

Which of the following expressions correctly represents the half-life of a zero-order reaction?

$t_{1/2} = rac{[A]_0}{2k}$ (C) Signup and view all the answers

In a second-order reaction, how does the concentration relate to time according to the integrated rate law?

$rac{1}{[A]} = kt + rac{1}{[A]_0}$ (A) Signup and view all the answers

How does the activation energy $E_a$ affect the rate constant $k$ according to the linear Arrhenius form?

Higher $E_a$ decreases $k$ at any temperature. (B) Signup and view all the answers

Flashcards

Reaction Rate

The change in concentration of a reactant over time, measured in units of molarity per unit time (e.g., M/s).

Rate Law

A mathematical expression that relates the rate of a reaction to the concentrations of reactants. It includes a rate constant (k) and exponents for each reactant (m, n).

Half-Life

The time it takes for the concentration of a reactant to decrease to half its initial value.

Arrhenius Equation

An equation that describes the relationship between the rate constant (k) and temperature (T). It includes the activation energy (Ea) and the pre-exponential factor (A).

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Integrated Rate Laws

The mathematical forms of the rate laws that are integrated over time. They allow us to calculate the concentration of a reactant at any given time.

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Study Notes

Reaction Rates and Integrated Rate Laws

Reaction Rate: The rate of a reaction is expressed as the change in concentration of a reactant or product per unit time. The equation is: d[A]/dt = k[A]^m[B]^n, where k is the rate constant, [A] and [B] are reactant concentrations, and m and n are the reaction orders (typically integers).

Zero-Order Reaction

Integrated Rate Law: [A] = [A]₀ - kt (where [A]₀ is the initial concentration of A)
Half-life: t_1/2 = [A]₀ / 2k

First-Order Reaction

Integrated Rate Law: ln[A] = ln[A]₀ - kt
Half-life: t_1/2 = 0.693 / k

Second-Order Reaction

Integrated Rate Law: 1/[A] = 1/[A]₀ + kt
Half-life: t_1/2 = 1 / k[A]₀

Arrhenius Equation

Equation: k = Ae^-Ea/RT
describes the temperature dependence of the rate constant, k, where:
A = pre-exponential factor
Ea = activation energy
R = ideal gas constant
T = absolute temperature

Linear Arrhenius Form

Equation: ln k = -Ea/RT + ln A
This form of the Arrhenius equation allows for determination of activation energy by plotting ln k vs 1/T.

Integrated Rate Laws (Summary)

Zero-Order: [A] = [A]₀ - kt
First-Order: ln[A] = ln[A]₀ - kt
Second-Order: 1/[A] = 1/[A]₀ + kt

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Description

This quiz covers the concepts of reaction rates and integrated rate laws, focusing on zero, first, and second-order reactions. It includes the Arrhenius equation and discusses the mathematical relationships governing these reactions, helping students understand how to calculate reaction rates and half-lives effectively.