Question

Calculate the pressure exerted by 11.1 moles of neon gas in a volume of 5.45 L at 25°C using (a) the ideal gas equation and (b) the van der Waals equation. (For neon, a = 0.211 atm · L2/mol2 and b = 0.0171 L/mol.)

Answer 1

Answer:

49.82414 atm

50.74675 atm

Explanation:

P = Pressure

V = Volume = 5.45 L

R = Gas constant = 0.08205 L atm/mol K

T = Temperature = 25°C

a = 0.211 atm L²/mol²

b = 0.0171 atm L²/mol²

From ideal gas law we have

$PV=nRT\\\Rightarrow P=\dfrac{nRT}{V}\\\Rightarrow P=\dfrac{11.1\times 0.08205(273.15+25)}{5.45}\\\Rightarrow P=49.82414\ atm$

The pressure is 49.82414 atm

From Van der Waals equation we have

$\left(P+\frac{an^2}{V^2}\right)\left(v-nb\right)=nRT\\\Rightarrow P=\dfrac{nRT}{V-nb}-\dfrac{an^2}{V^2}\\\Rightarrow P=\dfrac{11.1\times 0.08205\times (273.15+25)}{5.45-(11.1\times 0.0171)}-\dfrac{0.211\times 11.1^2}{5.45^2}\\\Rightarrow P=50.74675\ atm$

The pressure is 50.74675 atm