Question

For a gaseous reaction, the rate is expressed in terms of $\frac{d P}{d t}$ in place of $\frac{d C}{d t}$ or $\frac{d n}{d t}$ , where $C$ is concentration, $n$ is number of moles and $′P′$ is pressure of reactant. The three are related as -

• A. $\left[\frac{d P}{d t}\right]=\frac{R T}{V}\left[\frac{d n}{d t}\right]=\left[\frac{d C}{d t}\right]$
• B. $\frac{1}{R T}\left[\frac{d P}{d t}\right]=\frac{1}{V}\left[\frac{d n}{d t}\right]=\left[\frac{d C}{d t}\right]$
• C. $\left[\frac{d P}{d t}\right]=\left[\frac{d n}{d t}\right]=\left[\frac{d C}{d t}\right]$
• D. None of these

Answer 1

Answer: (B)

$Rate=\frac{d C}{d t}$

$C=\frac{n}{V}$ and $C=\frac{P}{R T}$

$\frac{d C}{d t}=\frac{d}{d t}\left(\frac{n}{V}\right)=\frac{1}{V}\times \left(\frac{d n}{d t}\right)$

$\frac{d}{d t}\left(\frac{P}{R T}\right)=\frac{1}{R T}\times \left(\frac{d P}{d t}\right)$