Question

For the first order reaction $A_{\left(g\right)}\to 2B_{\left(g\right)}+C_{\left(g\right)}$, the initial pressure is $P_A=90mm$ Hg, the pressure after 10 minutes is found to be 180 mm Hg. The rate constant of the reaction is:

• A. $1.15\times {10}^{-3}se{c}^{-1}$
• B. $2.3\times {10}^{-3}se{c}^{-1}$
• C. $3.45\times {10}^{-3}se{c}^{-1}$
• D. $6\times {10}^{-3}se{c}^{-1}$

Answer 1

The correct option is A $1.15\times {10}^{-3}se{c}^{-1}$

$A\to 2B+C$
P 0 0
P-x 2x x
At equilibrium,
$180=P-x+2x+x$

$180=90+2x$

$2x=90,x=45$

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

$=\frac{2.303}{10}log\frac{90}{90-45}=\frac{2.303}{10}log2=\frac{0.6932}{10}$

$=0.6932=\frac{0.06932}{60}=1.1555\times {10}^{-3}se{c}^{-1}$.