Question

The sketch shows the plot of $Z$ v/s $P$ for a hypothetical gas for one mole at three distinct temperature. Boyle's temperature is the temperature at which a gas shows ideal behavior over a pressure range in the low-pressure region. Boyle's temperature $\left(T_b\right)$= $\frac{a}{Rb}$.If a plot is obtained at temperatures well below Boyle's temperature then the curve will show negative deviation, in the low-pressure region and positive deviation in the high-pressure region. Near critical temperature, the curve is more likely as $C{O}_2$ and the temperature well above critical temperature curve is more like $H_2$ at $O^{o}C$ as shown above.At high pressure suppose all the constant temperature curve varies linearly with pressure according to the following equation $Z=1+\frac{Pb}{RT}(R=2calmo{l}^{-1}{K}^{-1}$)

For 500 $K$ plot value of $Z$ changes from 2 to 2.2 ,if pressure is varied from 1000 $atm$ to 1200 $atm$ (high pressure) then the value of $\frac{b}{RT}$ will be:

• A. ${10}^{-3}at{m}^{-1}$
• B. $2\times {10}^{-3}at{m}^{-1}$
• C. $5\times {10}^{-4}at{m}^{-1}$
• D. ${10}^{-4}at{m}^{-1}$

Answer 1

Answer: (A)

${10}^{-3}at{m}^{-1}$

At high pressure all the constant temperature curve varies linearly with pressure according to the following equation

$Z=1+\frac{Pb}{RT}$

Given $Z=2.2$ at $1000atm$, by substituting the value of $2.2$ in given equation, we get,

$2.2=1+500\times \frac{b}{RT}$

$\frac{b}{RT}$= ${10}^{-3}$ ${atm}^{-1}$