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Answer:
Z = 1 - a/VRT
Explanation:
Note :
Compressibility Factor, Z = PV / RT
Vander waal forces at Lower pressure is represented by the expression :
V[P + a/V²] = RT
Aim is to move PV /RT =Z to one side of the equation.
Using change of subject :
opening the bracket :
PV + aV / V² = RT
PV + a/V = RT
Divide through by RT
PV/RT + a/VRT = RT/RT
PV/RT + a/VRT = 1
Recall:
PV /RT = Z
equation becomes :
Z + a/VRT = 1
Subtract a/VRT from both sides
Z + a/VRT - a/VRT = 1 - a/VRT
Z = 1 - a/VRT