Question

For a first order gaseous reaction $6A\left(g\right)\to A_6\left(g\right)$; $k$= disappearance constant of $A$. If $P_t$ is the total pressure of the gaseous mixture after time $t$ & $P_{\infty }$ after a very long time then correct relationship is:

• A. $k=\frac{1}{t}ln[\frac{5P_{\infty }}{P_T-P_{\infty }}$]
• B. $k=\frac{1}{t}ln[\frac{6P_{\infty }}{30P_{\infty }-5P_T}$]
• C. $k=\frac{1}{t}ln[\frac{5P_{\infty }}{11P_{\infty }-P_T}$]
• D. None of these

Answer 1

The correct option is A $k=\frac{1}{t}ln[\frac{5P_{\infty }}{P_T-P_{\infty }}$]

$6A\left(g\right)\to A_6\left(g\right)$
Initially $P_0$
At time t $P_0-xx/6$
At infinite time: $0P_0/6$
Also,
$k=\frac{1}{t}ln\left[\frac{a}{a-x}\right]$] so
$k=\frac{1}{t}ln[\frac{5P_{\infty }}{P_T-P_{\infty }}$]