Second-order half-life

Worked example

A second-order reaction (rate = k[A]²) has k = 0.58 dm³ mol⁻¹ s⁻¹. What is the first half-life when [A]₀ = 0.74 mol dm⁻³?

1. 1. Half-life (second order): solve for t½

   $t_{1/2} = \dfrac{1}{k[\mathrm{A}]_0}$

   = 2.330 s

Answer: t½ = 2.33 s

Method

t½ = 1/(k[A]₀). Unlike first order, it depends on the starting concentration.

Common mistakes

• ln 2 belongs to the first-order half-life. For second order, t½ = 1/(k[A]₀).

Formulas used

• Half-life (second order)

  $t_{1/2} = \dfrac{1}{k[\mathrm{A}]_0}$

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