JEE Advance - Chemistry (2008 - Paper 1 Offline - No. 6)
Under the same reaction conditions, initial concentration of 1.386 mol dm$$^{-3}$$ of a substance becomes half in 40 seconds and 20 seconds through first order and zero order kinetics, respectively. Ratio $$\left( {{{{k_1}} \over {{k_0}}}} \right)$$ of the rate constants for first order ($$k_1$$) and zero order ($$k_0$$) of the reactions is:
0.5 mol$$^{-1}$$ dm$$^3$$
1.0 mol dm$$^{-3}$$
1.5 mol dm$$^{-3}$$
2.0 mol$$^{-1}$$ dm$$^3$$
Explanation
Rate constant for first order kinetics:
$${k_1} = {{0.693} \over {{t_{1/2}}}} = {{0.693} \over {40\,{s^{ - 1}}}}$$ ..... (i)
Rate constant for zero order kinetics:
$${k_0} = {{{A_0}} \over {2{t_{1/2}}}} = {{1.386} \over {2 \times 20}}$$ mol dm$$^{-3}$$ s$$^{-1}$$ ..... (ii)
Divide (i) by (ii)
$${{{k_1}} \over {{k_0}}} = {{0.693} \over {40}} \times {{40} \over {1.386}} = {{0.693} \over {1.386}}$$ mol$$^{-1}$$ dm$$^{-3}$$ = 0.5 mol$$^{-1}$$ dm$$^{3}$$
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