100 g of acetylene (#"C"_2"H"_2#) gas is placed in a 20.0 L container at 298 K. (i) Use the ideal gas equation to calculate the pressure? (ii) Use van der Waals equation to calculate the pressure? (#a="4.390 L"^2cdot"atm/mol"^2#, #b="0.0513 L/mol"#)
1 Answer
(i)
This tells you that the van der Waals equation of state picks up on the attractive interactions in acetylene that the ideal gas law assumes is not present.
Explanation:
(a) Ideal gas
The equation for the Ideal Gas Law is
#color(blue)(bar(ul(|color(white)(a/a)pV = nRTcolor(white)(a/a)|)))" "#
Then,
#p = (nRT)/V#
The pressure predicted by the Ideal Gas Law is 4.70 atm.
(b) van der Waals Equation
The van der Waals equation is
#color(blue)(bar(ul(|color(white)(a/a) (P + (n^2a)/V^2)(V - nb) = nRTcolor(white)(a/a)|)))" "#
#P + (n^2a)/V^2 = (nRT)/(V - nb)#
#P = (nRT)/(V - nb)- (n^2a)/V^2#
For this problem,
The pressure predicted by the van der Waals equation is 4.58 atm, lower than for the ideal gas law.