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For the first-order reaction A(aq) -> B(aq) + C(aq), the optical rotation of the mixture is measured. Specific rotations are A = 20 deg, B = 30 deg and C = -40 deg per mole. Starting from pure A, the observed rotation is 2.5 deg at t = 6.93 minutes and -5 deg at infinite time. Find the rate constant (in min⁻¹).

1. 0.1
2. 0.05
3. 0.2
4. 0.693

Correct answer: 0.1

Solution

From the infinite-time rotation the initial concentration a = 0.5; at 6.93 min exactly half of A has reacted, so 6.93 min is the half-life and k = 0.693/6.93 = 0.1 min⁻¹.

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