At 300 k and 20 atm, the compression factor of a gas is 0.86. calculate (a) the volume occupied by 8.2 mmol of the gas under these conditions and (b) an approximate value of the second virial coefficient b at 300 k. (20 pts)

Answer :

(a) The volume occupied by 8.2 mmol of the gas under these conditions is, 0.0087 L.

(b) The value of the second virial coefficient 'b' at 300 K is -0.16

Explanation :

Part (a) :

The formula for compression factor of a gas (Z) is:

where,

Z = impressibility factor = 0.86

P = pressure of gas = 20 atm

= volume of gas = ?

T = temperature of gas = 300 K

n = number of moles of gas = 8.2 mmol = 0.0082 mol    (1 mmol = 0.001 mol)

R = gas constant  = 0.0821 L.atm/mol.K

Now put all the given values in the ideal gas equation, we get:

Thus, the volume occupied by 8.2 mmol of the gas under these conditions is, 0.0087 L.

Part (b) :

First we have to calculate the volume for ideal gas.

Formula used :

Now we have to calculate the value of the second virial coefficient 'b' at 300 K.

Thus, the value of the second virial coefficient 'b' at 300 K is, -0.16

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