Question

For the ideal gaseous reaction, the rate is generally expressed in terms of $\frac{dP}{dt}$ instead of $\frac{dC}{dt}$ or $\frac{dn}{dt}$ (where $C=n/v$ is concentration and $n$ is the number of moles). What is the relation among these three expressions if $T$ and $V$ are constant?

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

Answer 1

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

$C=\frac{n}{V}=\frac{P}{RT}\therefore \frac{dC}{dt}=\frac{1}{V}\frac{dn}{dt}=\frac{1}{RT}\left(\frac{dP}{dt}\right)$
Since $T$ and $V$ are constants.