Question

How reliable is the perfect gas law in comparison with the van der waals equation?calculate the difference in pressure of 10.00g of CO2 confined to a container of volume 100cm3 at 25 degree centigrade between treating it as a perfect gas and a van der waals gas

Answer 1

Answer:

The perfect gas law is reliable at the limit of pressure tending to zero. That is to say, at low pressure. The Van der Waals law instead can be used at higher pressures.

Explanation:

The perfect law equation is

$P.V = n.R.T$

The perfect gas law considers that the gas molecules have no interaction between each other and each molecule has null volume. This condition happens at the limit of pressure tending to zero.

The Van der Waals equation is

$(P +\frac{n^{2}.a}{V^{2}})(V-n.b) = n.R.T$

On the other hand, the Van der Waals law has two extra terms, one to consider the interaction of the molecules (n2a/V2) and other to consider the volume of the molecules (V-nb). These terms make a better approximation to a real gas.

Using the two equations to calculate the pressure (P) for CO2 with

V = 100cm3 = 0.1L

T = 25ºC = 298K

n = 10g/(44g/mol) = 0.23mol

a = 3.658 atm.L2/mol2

b = 0.0429 L/mol

With the perfect law equation:

$P = \frac{n.R.T}{V} = \frac{0.23molx0.082\frac{atm.L}{K.mol}x298K }{0.1L} = 56.2atm$

With the Van del Waals law:

$P = \frac{n.R.T}{V-n.b} -\frac{n^{2}.a}{V^{2} }$

$P = \frac{0.23molx0.082\frac{atm.L}{K.mol}x298K}{0.1L - 0.23molx0.0429\frac{L}{mol} }-\frac{(0.23mol)^{2}x3.658\frac{atm.L^{2}}{mol^{2}}}{(0.1L)^{2}} = 43 atm$

At this case the difference between the results of the two equations is due to the big mass of CO2 which produce a high pressure.