Calculate pressure exerted by 1 mole of a van der Waal gas at a temperature of 80-0821K in a 12 L container- if the volume of the molecule is assumed to be negligible and van der Waal-s constant a - 2 atm L2 mol-2

Using van der Waal's equation for 1 mol: ( P + aV^2_m ) (V_m b)= RT Since the volume is negligible, neglecting b in the above equation we get: ( P + aV^2_m ) V ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XI

Chemistry

Van der Waal's Forces

Calculate pre...

Question

Calculate pressure exerted by 1 mole of a van der Waal gas at a temperature of $\frac{8}{0.0821} K$ in a $\frac{1}{2} L$ container, if the volume of the molecule is assumed to be negligible and van der Waal's constant $a = 2 {atm L}^{2} {mol}^{- 2}$

Open in App

Solution

Using van der Waal's equation for 1 mol:
$(P + \frac{a}{V_{m}^{2}}) (V_{m} - b) = R T$
Since the volume is negligible, neglecting $b$ in the above equation we get:
$(P + \frac{a}{V_{m}^{2}}) V_{m} = R T$
Given : $T = \frac{8}{0.0821} K$
$P V_{m} + \frac{a}{V_{m}} = R \times \frac{8}{0.0821}$
$P V_{m}^{2} - 8 V_{m} + a = 0$
According to the question, $V_{m} = \frac{1}{2} L = 0.5 L$ so,
$P (0.5)^{2} - 8 (0.5) + 2 = 0$
$P = 8 atm$

Suggest Corrections

Similar questions

Q. Calculate pressure exerted by 1 mole of a van der Waal gas at a temperature of

\frac{8}{0.0821} K

in a

\frac{1}{2} L

container, if the volume of the molecule is assumed to be negligible and van der Waal's constant

a = 2 {atm L}^{2} {mol}^{- 2}

Q. The compressibility factor for

1

mole of a Van der Waal's gas at

t^{0}

C and

p

atm pressure is found to be

Z

. Assuming that the volume of a gas molecule is negligible, calculate the van der Waals constant,

a

Q. Calculate the pressure (in atm as nearest integer) exerted by one mole of

C O_{2}

gas at 273 K, if the van der Waal's constant

^{'} a^{'} = 3.592 d m^{6} a t m m o l^{- 2}

. Assume that the volume occupied by

C O_{2}

molecules is negligible.

Q. Calculate the pressure exerted by one mole of

C O_{2}

gas at 273 K if the van der Waal's constant,

a = 3.592 d m^{6} a t m m o l^{- 2}

. Assume that the volume occupied by

C O_{2}

molecules is negligible.

Q. The compression factor (compressibility factor) for one mole of a van der Waals gas at

0^{0} C

and 100-atmosphere pressure is found to be 0.5. Assuming that the volume of a gas molecule is negligible, calculate the van der Waals constant

^{'} a^{'}

(a t m L^{2} m o l^{- 2})

Join BYJU'S Learning Program

Calculate pressure exerted by 1 mole of a van der Waal gas at a temperature of 80.0821K in a 12 L container, if the volume of the molecule is assumed to be negligible and van der Waal's constant a=2 atm L2 mol−2

Using van der Waal's equation for 1 mol: (P+aV2m)(Vm−b)=RT Since the volume is negligible, neglecting b in the above equation we get: (P+aV2m)Vm=RT Given : T=80.0821K PVm+aVm=R×80.0821 PV2m−8Vm+a=0 According to the question, Vm=12 L=0.5 L so, P(0.5)2−8(0.5)+2=0 P=8 atm

Calculate pressure exerted by 1 mole of a van der Waal gas at a temperature of $\frac{8}{0.0821} K$ in a $\frac{1}{2} L$ container, if the volume of the molecule is assumed to be negligible and van der Waal's constant $a = 2 {atm L}^{2} {mol}^{- 2}$