Question

$A\to B+C$
Time t $\infty$
Total pressure of (A+B+C) $P_2$ $P_3$
Then k is :

• A. $k=\frac{1}{t}ln\frac{p_3}{2(p_3-p_2)}$
• B. $k=\frac{1}{t}ln\frac{p_2}{2(p_3-p_1)}$
• C. $k=\frac{1}{t}ln\frac{p_3}{2(p_1-p_2)}$
• D. $k=\frac{1}{t}ln\frac{p_2}{2(p_2-p_3)}$

Answer 1

The correct option is A $k=\frac{1}{t}ln\frac{p_3}{2(p_3-p_2)}$

When $t=\infty$, entire A has reacted. 1 mole of A gives 1 mole of B and 1 mole of C, $a=\frac{P_3}{2}$.

$t=t$, the total pressure is $a-x+x+x=a+x=P_2$.

Hence, $x=P_2-a$

$a-x=a-(P_2-a)=2a-P_2=P_3-P_2$

The integrated rate law for the first order reaction is:

$k=\frac{1}{t}ln\frac{[A{]}_0}{[A{]}_t}=\frac{1}{t}ln\frac{\frac{P_3}{2}}{P_3-P_2}=k=\frac{1}{t}ln\frac{p_3}{2(p_3-p_2)}$