Question

24. For the first order reaction, 2N2O3(g) → 4NO2(g) 02(g) (2011) (a) the concentration of the reactant decreases exponentially with time (b) the half-life of the reaction decreases with increasing temperature (c) the half-life of the reaction depends on the initial concentration of the reactant (d) the reaction proceeds of 99.6% completion in eight half-life duration

SSC CGL

Chemistry

Solution

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24. (a) For a first order reaction, the concentration of reactant remaining after time ( t ) is given by ( [A]=[A]_{0} e^{-k t} ) Therefore, concentration of reactant decreases exponentially with time. (b) Rise in temperature increases rate constant ( (k) ) and therefore decreases half-life ( left(t_{1 / 2}right) ) as [ t_{1 / 2}=frac{ln 2}{k} ] (c) Half-life of first order reaction is independent of initial concentration. (d) For a first order reaction, if 100 moles of reactant is taken initially, after ( n ) half-lives, reactant remaining is given by [ % A=100left(frac{1}{2}right)^{n}=100left(frac{1}{2}right)^{8}=0.3906 ] ( Rightarrow A ) reacted ( =100-0.3906=99.6 % )