Question

To be able to predict and calculate properties of real gases.

Kinetic molecular theory makes certain assumptions about gases that are, in fact, not true for real gases. Therefore, the measured properties of a gas are often slightly different from the values predicted by the ideal gas law. The van der Waals equation is a more exact way of calculating properties of real gases. The formula includes two constants, a and b, that are unique for each gas.

The van der Waals equation is (P+an2V2)(V−nb)=nRT, where P is the pressure, n the number of moles of gas, V the volume, T the temperature, and R the gas constant.

All real gases possess intermolecular forces that can slightly decrease the observed pressure. In the van der Waals equation, the variable P is adjusted to P+an2V2, where a is the attractive force between molecules.

The volume of a gas is defined as the space in which the gas molecules can move. When using the ideal gas law we make the assumption that this space is equal to the volume of the container. However, the gas molecules themselves take up some space in the container. So in the van der Waals equation, the variable V is adjusted to be the volume of the container minus the space taken up by the molecules, V−nb, where b is the volume of a mole of molecules.

Part C

12.0 moles of gas are in a 4.00 L tank at 24.2 ∘C . Calculate the difference in pressure between methane and an ideal gas under these conditions. The van der Waals constants for methane are a=2.300L2⋅atm/mol2 and b=0.0430 L/mol.

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

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

v = V/n = 4/12 = 0.333

(P + (2.3)/(0.333^2)) * (0.333 - 0.043) = 0.082*(24.2+273.15)

P =  0.082*(24.2+273.15)/(0.333 - 0.043) - (2.3)/(0.333^2) = 63.33 atm

b)

Ideal gas law:

PV = nRT

P = n/VRT = (12/4)*0.082*(24.2+273) = 73.111

dP = 63.33 73.111 = 9.781

prediction is 9.781 atm lower for van der Waals