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

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-1K-1. The value of the ideal universal gas constant ‘R’ in terms of X is (A) X lit atm mol-1K-1 (B) X/2 lit atm mol-1K-1 (C) 2X lit atm mol-1K-1 (D) 2X atm lit-1 mol-1K-1

Tardigrade Admin · Accepted Answer

Ideal gas equation is p V=n R T or V=(n R T/p)+C or V=(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 =(R/p) ⇒ X=(R/2) or R =2 X L atm mol -1 K -1

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

$X$ lit atm $m o l^{- 1} K^{- 1}$

$X /2$ lit atm $m o l^{- 1} K^{- 1}$

$2 X$ lit atm $m o l^{- 1} K^{- 1}$

$2 X$ atm $l i t^{- 1} m o l^{- 1} K^{- 1}$

Ideal gas equation is
$p V = n RT$ or $V = \frac{n RT}{p} + C$
or $V = \frac{RT}{p} + 0$ (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 $m o l^{- 1} K^{- 1}$

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

X lit atm mol−1K−1

X/2 lit atm mol−1K−1

2X lit atm mol−1K−1

2X atm lit−1mol−1K−1