Answer:
14.8 atm
Step-by-step explanation:
(a) Ideal Gas Law
The equation for the Ideal Gas Law is
pV = nRT Divide each side by V
p = (nRT)/V
Data:
n = 15.0 mol
R = 0.082 06 L·atm·K⁻¹mol⁻¹
T = 23.9 °C
V = 4.00 L
Calculations:
(i) Convert temperature to Kelvins
T = (23.9 + 273.15) K
= 297.05 K
(ii) Calculate the pressure
p = (15.0 × 0.082 06 × 297.05)/4.00
= 91.4 atm
The pressure predicted by the Ideal Gas Law is 91.4 atm.
(b) van der Waals gas
The van der Waals equation is
[p + (n²a)/V²)](V - nb) = nRT Divide each side by (V - nb)
p + (n²a)/V² = (nRT)/(V - nb) Subtract (n²a)/V² from each side
p = (nRT)/(V - nb) - (n²a)/V²
(i) Data:
a=2.300 L²⋅atm·mol⁻²
b=0.0430 L·mol⁻¹
(ii) Calculation:
p = (15.0 × 0.082 06 × 297.05)/(4.00 – 15.0 × 0.0430)
- (15.0² × 2.300)/4.00²
= 365.6/(4.00 - 0.645) - 517.5/16
= 365.6/3.355 - 32.34
= 109.0 - 32.34
= 76.6 atm
The pressure predicted by the van der Waals equation is 76.6 atm.
(iii) The pressure difference
p(Ideal) - p(vdW) = 91.4 - 76.6
= 14.8 atm
