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Chemical Kinetics

Question

Thermal decomposition of a compound is of first order. If 50% of a sample of the compound is decomposed in 120 minutes, how long will it take for 90% of the compound to decompose.

Solution

For half time period

k = \frac{0.693}{t_{1 / 2}} = \frac{0.693}{120} = 5.77 \times 10^{- 3} \min^{- 1}

For a first order reaction

k = \frac{2.303}{t} \log \frac{1}{a - x} a = 100, x = 90 ∴ 5.77 \times 10^{- 3} = \frac{2.303}{t} \log \frac{100}{100 - 90} t = \frac{2.303}{5.77 \times 10^{- 3}} \log 10 = 399 \min .