Reaction Orders, Integrated Rate Laws, and Half-Life

Flashcards covering reaction orders, integrated rate laws, half-life, and related concepts for zero-, first-, and second-order reactions in chemical kinetics.

Individual Reaction Order

The dependence of a reaction rate on the concentration of a single reactant.

First Order Reaction (with respect to a reactant)

A reaction where the rate doubles when the concentration of that reactant doubles (rate depends on the reactant concentration raised to the power of 1).

Second Order Reaction (with respect to a reactant)

A reaction where the rate quadruples when the concentration of that reactant doubles (rate depends on the reactant concentration raised to the power of 2).

Zero Order Reaction (with respect to a reactant)

A reaction where the rate does not change when the concentration of that reactant doubles (rate is independent of the reactant concentration).

Overall Reaction Order

The sum of the individual reaction orders with respect to each reactant in the rate law.

Determining Reaction Orders

Reaction orders must be determined experimentally and cannot be deduced directly from the stoichiometric coefficients of the balanced chemical equation.

Integrated Rate Law

An equation that includes time as a variable and relates reactant concentrations at different times to the rate constant.

First-Order Integrated Rate Law

ln[A]t = -kt + ln[A]0, where [A]t is concentration at time t, [A]0 is initial concentration, and k is the rate constant.

Reaction Half-Life (t1/2)

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

First-Order Half-Life

t1/2 = ln2/k; it is constant and does not depend on the initial reactant concentration.

Second-Order Integrated Rate Law

1/[A]t = kt + 1/[A]0, where [A]t is concentration at time t, [A]0 is initial concentration, and k is the rate constant.

Second-Order Half-Life

t1/2 = 1/(k[A]0); it is inversely proportional to the initial reactant concentration.

Zero-Order Integrated Rate Law

[A]t = -kt + [A]0, where [A]t is concentration at time t, [A]0 is initial concentration, and k is the rate constant.

Zero-Order Half-Life

t1/2 = [A]0/(2k); it is directly proportional to the initial reactant concentration.

Graphical Determination of First Order

A plot of ln[A]t versus time yields a straight line with a slope of -k.

Graphical Determination of Second Order

A plot of 1/[A]t versus time yields a straight line with a slope of k.

Graphical Determination of Zero Order

A plot of [A]t versus time yields a straight line with a slope of -k.

Units of Rate Constant (Zero Order)

mol/L·s

Units of Rate Constant (First Order)

1/s

Units of Rate Constant (Second Order)

L/mol·s

Radioactive Decay

A type of process that follows first-order kinetics, where its half-life indicates stability.