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For a reaction A -> products, a plot of 1/[A]² versus time is a straight line of positive slope whose inclination is tan⁻¹(4 x 10⁻⁵). Determine the rate constant k for this reaction.

1. 4 x 10⁻⁵ M⁻¹ s⁻¹
2. 4/3 x 10⁻⁵ M⁻² s⁻¹
3. 2 x 10⁻⁵ M⁻² s⁻¹
4. 2/3 x 10⁻⁵ M⁻² s⁻¹

Correct answer: 2 x 10⁻⁵ M⁻² s⁻¹

Solution

Since 1/[A]² is linear in t, the integrated law is 1/[A]² = 1/[A0]² + 2kt; the slope tan(theta) = 4 x 10⁻⁵ = 2k, giving k = 2 x 10⁻⁵ M⁻² s⁻¹.

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