Question

At high pressures, real gases do not behave ideally. Calculate the pressure exerted by 33.0 g H₂ at 20.0°C in a 1.00 L container assuming in Part 1 non-ideal behavior and in Part 2 ideal behavior.

Part 1)Use the van der Waals equation and data in the hint to calculate the pressure exerted= ____atm

Part 2)Now, calculate the pressue excerted assuming that the gas behaves as an ideal gas.= _____ atm

Answer 1

PART 1

nonideal

The Van der Waals equation is a description of real gases, it includes all those interactions which we previously ignore in the ideal gas law.

It considers the repulsion and collision, between molecules of gases. They are no longer ignored and they also are not considered a"point" particle.

The idel gas law:

PV = nRT

P(V/n) = RT ; let V/n = v; molar volume

P*v = RT

now, the van der Waals equation corrects pressure and volume

(P+ a/v^2) * (v - b) = RT

where;

R = idel gas law; recommended to use the units of a and b; typically bar/atm and dm/L

T = absolute temperature, in K

v = molar volume, v = Volume of gas / moles of gas

P = pressure of gas

Knowing this data; we can now substitute the data

given

a = 3.6551

b = 0.04281

v = V/n = V/(mass/MW) = 1/(33/2) = 0.06061

(P+ a/v^2) * (v - b) = RT

P = RT/(v-b) - a/v^2

P = (0.0831)(20+273)/(0.06061 - 0.02661) - 0.2476/(0.06061^2) = 648.726 bar

For ideal gas

P = nRT/V

P = (16.5)/(0.08314)(20+273)/1

P = 58148.9 bar

dV = 58148.9 - 648.726 = 57500.174 bar