Question

What is the percent deviation from ideal behavior is found when 1.00 mol NO2 is compressed into 500.0 mL at 300. K? (Hint: calculate pressure using both the ideal gas law and the van der Waals equation.)

Answer 1

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 = 0.5/1 = 0.5

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

(P + 5.354/(0.5^2))*(0.5 -0.04424) = 0.08314*300

P = 0.08314*300/(0.5 -0.04424)-5.354/(0.5^2)

P =33.31 bar

b) ideal

P = nRT/V

P = 1*0.08314*300/0.5

P = 49.884 bar

% deviation = (33.31 -49.884)/33.31 *100 =49.75%