Question

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

• A. $\left\lbrack \frac{dP}{dt} \right\rbrack$ =$\left\lbrack \frac{dn}{dt} \right\rbrack$ = $\left\lbrack \frac{dC}{dt} \right\rbrack$
• B. $\frac { 1 } { \mathrm { RT } }$ $\left\lbrack \frac{dP}{dt} \right\rbrack$ =$\left\lbrack \frac{dn}{dt} \right\rbrack$ = $\left\lbrack \frac{dC}{dt} \right\rbrack$
• C. $\left\lbrack \frac{dP}{dt} \right\rbrack$ =$\left\lbrack \frac{dn}{dt} \right\rbrack$ = $\left\lbrack \frac{dC}{dt} \right\rbrack$
• D. None of these

Answer 1

Answer: (B)

\frac { 1 } { \mathrm { RT } }$$\left\lbrack \frac{dP}{dt} \right\rbrack =$\left\lbrack \frac{dn}{dt} \right\rbrack$ = $\left\lbrack \frac{dC}{dt} \right\rbrack$

Answer 2

Rate = $\frac{dC}{dt}$

C = $\frac{n}{V}$ and C = $\frac{P}{RT}$

$\frac{dC}{dt}$ = $\left( \frac{n}{V} \right)$= $\frac{1}{V}$×$\left( \frac{dn}{dt} \right)$

$\left( \frac{P}{RT} \right)$ =$\frac{1}{RT}$× $\left( \frac{dP}{dt} \right)$