Question

For the first order reaction, $A\left(g\right)\to 2B\left(g\right)+C\left(g\right)$, the initial pressure is $P_A=90$ mm Hg. Then pressure after 10 minutes is found to be 180 mm Hg. The half-life period of the reaction is:

• A. $1.15\times {10}^{-3}se{c}^{-1}$
• B. $600sec$
• C. $3.45\times {10}^{-3}se{c}^{-1}$
• D. $200sec$

Answer 1

The correct option is B $600sec$

$A\to 2B+C$
$P$ $0$ $0$
$P-x$ $2x$ $x$
Total pressure after 10 minute is $180=P-x+2x+x$
$180=90+2x$
$2x=90,x=45$

$k=\frac{2.303}{t}log\frac{P}{P-x}$

$=\frac{2.303}{10}log\frac{90}{90-45}$

$=\frac{2.303}{10\times 60}log2$

$=1.1555\times {10}^{-3}se{c}^{-1}$
$\therefore t_{\frac{1}{2}}=0.692/k$

$\approx 600sec$