Concentration Changes Over Time

AP Chemistry· difficulty 2/5

A first-order radioactive decay yields the table below.

t (min) [A] (M) 0 1.000 10 0.500 20 0.250 30 0.125

What is the half-life and rate constant?

  • A

    t₁/₂ = 10 min, k = 6.93 min⁻¹

  • B

    t₁/₂ = 5 min, k = 0.14 min⁻¹

  • C

    t₁/₂ = 20 min, k = 0.035 min⁻¹

  • D

    t₁/₂ = 10 min, k = 0.069 min⁻¹

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Explanation

[A] halves every 10 min ⇒ t₁/₂ = 10 min. k = ln 2 / t₁/₂ = 0.693/10 = 0.0693 min⁻¹.

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