GEN CHEM 2 | First-Order Reactions and Half-Life

Refer to Rates of Reaction Knowt for Rate Laws

Integrated Rate Laws

helps determine the reactant concentrations at any time during the reaction

Overall Order of Reaction

m + n

First-Order Reactions

• a reaction whose rate depends on the reactant concentrations raised to the first power

• for a reaction “A → product”, rate is expressed as “Rate = -(∆[A]/∆t)”.

• Rate law is “rate = k[A]”, therefore “k[A] = -(∆[A]/∆t)”.

Determining k in First-Order Reactions

k = -(∆[A]/[A])(1/∆t)

ln([A]_t/[A]₀ = -kt) // Equation 1.1

ln[A]_t = -kt +ln [A]₀ // Equation 1.2

where [A]_t is the A concentration at time t and [A]₀ is the A concentration at the start

Using Integrated Rate Laws for First-Order Rwactions

• Use Equation 1.2 to determine the concentration of the reactant after a certain time elapsed.

• Use Equation 1.1 to determine how much time passed to get a certain concentration of the reactant.

Solving First-Order Reaction Problems

1. Write the given quantities and their respective variables

2. Choose which equation is more useful for the problem.

3. Substitute the given values into the chosen equation.

4. Manipulate the equation to solve the problem.

5. Evaluate what the answer means and if it makes sense.

Half-Life (t_1/2)

• Time required for the concentration of a reactant to decrease to half its initial concentration.

• Only depends on the rate constant for first-order reactions

Equations for Half-Life

• t_1/2 = ln 2/k // for half-life

• [A]_t = [A]₀(1/2)ⁿ // for concentration after n half lives

• _t = t_1/2(n) // for elapsed time after n half lives