JEE Advance - Chemistry (1999 - No. 15)
The rate constant for an isomerisation reaction, A $$\to$$ B is 4.5 $$\times$$ 10-3 min-1. If the initial concentration of A is 1 M, calculate the rate of the reaction after 1 h.
4.5 x 10-3 M min-1
1.0 x 10-3 M min-1
3.4354 x 10-3 M min-1
6.8708 x 10-3 M min-1
0.764 M min-1
Explanation
The unit of rate constant = min$$-$$1 implies that the reaction is of first order.
For a first order reaction, $$k = {{2.303} \over t}\log {a \over {a - x}}$$
or, $$k = {{2.303} \over t}\log {{{{[A]}_0}} \over {[A]}}$$ or, $$4.5 \times {10^{ - 3}} = {{2.303} \over {60}}\log {1 \over {[A]}}$$
Hence, after 1 hour concentration of A, [ A ] = 0.764 (M)
$$\therefore$$ Reaction-rate after 1 hour = $$k[A] = 4.5 \times {10^{ - 3}} \times 0.746$$
= 3.438 $$\times$$ 10$$-$$3 mol L$$-$$1min$$-$$1
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