Question

For one mole of an ideal gas the slope of $V$ vs. $T$ curve at constant pressure of $2$ atm is $X$ lit $mol^{-1}K^{-1}$. The value of the ideal universal gas constant $‘R’$ in terms of $X$ is

• A. $X$ lit atm $mol^{-1}K^{-1}$
• B. $X/2$ lit atm $mol^{-1}K^{-1}$
• C. $2X$ lit atm $mol^{-1}K^{-1}$
• D. $2X$ atm $lit^{-1} mol^{-1}K^{-1}$

Answer 1

Answer: (C)

Ideal gas equation is
$p V=n R T$ or $ V=\frac{n R T}{p}+C$
or $ V=\frac{R T}{p}+0 $ (for $ 1 $ mol)
When $V$ vs $T$ is plotted, a straight line is obtained, slope of which is given by $R / p$.
Thus,
Slope $=\frac{R}{p} $
$\Rightarrow X=\frac{R}{2} $
or $R =2 \,X \,L$ atm $mol ^{-1}\, K ^{-1}$