Question

For the reaction, $A(g)\to B(g)+C(g)$
Rate law is $\frac{-d[A]}{dt}=k[A]$
At the state, pressure is $100mm$ and after $10min$, pressure is $120mm$. Thus, rate constant (in $mi{n}^{-1}$ ) is

• A. $\frac{2.303}{10}\log \frac{5}{4}$
• B. $\frac{2.303}{10}\log 5$
• C. $\frac{2.303}{10}\log \frac{6}{5}$
• D. $\frac{2.303}{10}\log \frac{5}{6}$

Answer 1

Answer: (A)

It is a gaseous phase reaction.



Thus, total pressure at time $t=p_i-x+x+x=\left(p_i+x\right)$

$\therefore x=\left(p_t-p_i\right)$

$\therefore \left(p_i-x\right)=\left(2p_i-p_t\right)$

$\therefore =(200-120)=80mm$

$k=\frac{2.303}{t}\log \frac{p_i}{\left(p_i-x\right)}$

$=\frac{2.303}{10min}\log \frac{100}{80}=\left(\frac{2.303}{10}\log \frac{5}{4}\right)mi{n}^{-1}$