Question

Which is correct relation in between $\frac{dc}{dt},\frac{dn}{dt}$ and $\frac{dP}{dt}$, where c, n, P, represents concentration, mole and pressure terms for gaseous phase reactant $A\left(g\right)\to product$?

• A. $-\frac{dc}{dt}=-\frac{1}{V}\frac{dn}{dt}=-\frac{1}{RT}\frac{dP}{dt}$
• B. $-\frac{dc}{dt}=\frac{dn}{dt}=-\frac{dP}{dt}$
• C. $-\frac{dc}{dt}=\frac{RT}{V}\frac{dn}{dt}=-\frac{dP}{dt}$
• D. all of the above

Answer 1

The correct option is A $-\frac{dc}{dt}=-\frac{1}{V}\frac{dn}{dt}=-\frac{1}{RT}\frac{dP}{dt}$

As we know,
$Rate=-\left[\frac{dc}{dt}\right]=[-\frac{dn}{dt}]\frac{1}{V}\therefore c=\frac{n}{V}$

Also, $c=\frac{P}{RT}$

$\therefore -\left[\frac{dc}{dt}\right]=-\frac{1}{RT}\left[\frac{dP}{dt}\right]$