The van der Waals contants a and b have been determined for a gas over a range o
ID: 811510 • Letter: T
Question
The van der Waals contants a and b have been determined for a gas over a range of temperatures to be
a = 18.57 atm dm6mol-2
b = 0.1193 dm3mol-1.
The molar volume, Vm, of the gas measured at 300K is 53.2 dm3mol-1.
Justify the use of the ideal gas equation for the gas at 300K.
(Hint: You do not need to plug numbers into the van der Waals or ideal equations of state, although looking at the derivation of the van der Waals equation of state, the meaning of van der Waals constants, and an understanding of relative magnitudes of numbers will help you to formulate an answer.)
Explanation / Answer
Van der Waals Equation
The Van der Waals equation is an equation similar to the Real Gas Law, but includes two constants, a and b, to account for deviations from ideal behavior.
The van der Waals equation is:
[P + (n2a/V2)](V - nb) = nRT
Where:
P - pressure,
V - volume,
n - number of moles,
T - temperature,
R - ideal gas constant. If the units of P, V, n and T are atm, L, mol and K, respectively, the value of R is 0.0821
a and b - constants, which are chosen to fit experiment as closely as possible to individual gas molecule.
When the volume, temperature and the number of moles of the gas molecule are known, the pressure can be calculated:
P = [nRT/(V - nb)] - n2a/V2
To calculate Volume:
To calculate the volume of a real gas, V in term n2a/V2 can be approximated as: nR/TP
as ideal gas. Then, V can be calculated as:
V = nR3T3/(PR2T2+aP2) + nb
The van der Waals constants a and b of molecular N2 is 1.390000 and 0.039100, respectively.
To calculate Pressure:
According to the van der Waals equation,
P = nRT/(V - nb) - n2a/V2
Example:
P = 1.500 x 0.0821 x 3.000x102 / (2.000 - 1.500 x 0.039100) - (1.500)2 x 1.390000 /(2.000)2
= 1.825x10 atm
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