Question

For one mole of an ideal gas, the slope of $V$ vs. $T$ curve at constant pressure of $2atm$ is $XL{mol}^{-1}{K}^{-1}$. The value of the ideal universal gas constant ${}^{\prime }{R}^{\prime }$ in terms of $X$ is :

• A. $XLatm{mol}^{-1}{K}^{-1}$
• B. $\frac{X}{2}Latm{mol}^{-1}{K}^{-1}$
• C. $2XLatm{mol}^{-1}{K}^{-1}$
• D. $2Xatm{L}^{-1}{mol}^{-1}{K}^{-1}$

Answer 1

The correct option is C $2XLatm{mol}^{-1}{K}^{-1}$

Ideal gas equation is
$pV=nRT$ or $V=\frac{nRT}{p}+C$

or $V=\frac{RT}{p}+0$ (for 1 m)

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 $R=2XLatm{mol}^{-1}{K}^{-1}$

Option (C) is correct.