Question

A substance A is mixed with equal quantities of the substance B and C. At the end of 1000 second, half of the mass of A has reacted. The fractions of A will be left unreacted at the end of 2000 second are x and y, if the reaction is (a) zero-order with respect to A and (b) 2${}^{nd}$ order with respect to A. Then 3(x+y) is:

Answer 1

The half-life period is 1000 seconds.

(a) For zero order reaction, $k=\frac{a}{2t_{1/2}}=\frac{a}{2\times 1000}=\frac{a}{2000}$

Also $x=kt=\frac{a}{2000}\times 2000=a$

Hence, the fraction of A left unreacted for zero order reaction $X=\frac{a-x}{a}=\frac{a-a}{a}=0$

(b) For second order reaction,

$k=\frac{1}{a{t}_{1/2}}=\frac{1}{a\times 1000}$

Also, $k=\frac{1}{t}\frac{x}{a(a-x)}$

$\frac{1}{1000a}=\frac{1}{2000}\frac{x}{a(a-x)}$

$2a=3x$

$x=\frac{2}{3}a$

Hence, the fraction of A left unreacted for second order reaction $Y=\frac{a-x}{a}=\frac{a-\frac{2}{3}a}{a}=\frac{1}{3}a$.
Thus, $3(X+Y)=3(0+1/3)=1$.