Question

For gaseous reaction, the rate is often expressed in terms of dP/dt instead of dc/dt or dn/dt (where c is the concentration and n the number of mol). What is the relation among these three expressions ?

• A. $\frac{dc}{dt}=\frac{1}{V}\left(\frac{dn}{dt}\right)=\frac{1}{RT}\left(\frac{dP}{dt}\right)$
• B. $\frac{dc}{dt}=\left(\frac{dn}{dt}\right)=\left(\frac{dP}{dt}\right)$
• C. $\frac{dc}{dt}=\left(\frac{dn}{dt}\right)=\frac{V}{RT}\left(\frac{dP}{dt}\right)$
• D. None of these

Answer 1

The correct option is A $\frac{dc}{dt}=\frac{1}{V}\left(\frac{dn}{dt}\right)=\frac{1}{RT}\left(\frac{dP}{dt}\right)$

According to ideal gas equation,
$PV=nRT$
$c=\frac{n}{V}=\frac{P}{RT}$
$\therefore \frac{dc}{dt}=\frac{1}{V}\frac{dn}{dt}=\frac{1}{RT}\frac{dP}{dt}$