Question

In this case, we have (Consider it as a first-order reaction)
$A\to B+C$
Time $t$ $\infty$
Total pressure $p_2$ $p_3$
Then $k$ is:

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

Answer 1

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