Question

For the first order reaction $A_{\left(g\right)}\to 2B_{\left(g\right)}+C_{\left(g\right)}$, the initial pressure is $P_A=90mmHg$ and the pressure after $10$ minutes is found to be $180mmHg$. 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 $1.15\times {10}^{-3}se{c}^{-1}$

$A\to 2B+C$

$P00$
$P–x2xx$

So at equilibrium

$⟹180=P–x+2x+x$

$⟹180=90+2x$

$⟹2x=90,x=45$

$k=\frac{2.303}{t}\log \frac{P}{P-x}=\frac{2.303}{10}\log \frac{90}{45}$

$k=1.15\times {10}^{-3}se{c}^{-1}$

Hence, the correct option is $\text{A}$