Chemical Kinetics and Nuclear ChemistryHard

Question

The half-life of a first-order reaction is 10 minutes. In what time, the rate of reaction will decrease from 6.0 × 1021 molecules ml−1 s−1 to 4.5 × 1025 molecules litre−1 min−1? (NA = 6.0 × 1023)

Options

A.10 min
B.20 min
C.30 min
D.40 min

Solution

r0 = 6.0 × 1021 molecules ml–1 s–1 = 6 × 1021 × 103 × 60 = 36 × 1025 molecules L–1 min–1

Now, $t = \frac{t_{1/2}}{\log 2}.\log\frac{r_{0}}{r} = \frac{10min}{\log 2\log\frac{36 \times 10^{25}}{4.5 \times 10^{25}}\text{ min}}$

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