The compression factor (compressibility factor) for one mole of a van der Waals gas at 0^(@)C and 100 atm pressure is found to be 0.5. Assuming that the volume of a gas molecule is negligible, calculate the van der Waals constant a.

The compression factor (compressibility factor) for one mole of a van

1.	The compression factor (compressibility factor) for one mole of a van der Waals gas at 0^(@)C and 100 atm pressure is found to be 0.5. Assuming that the volume of a gas molecule is negligible, calculate the van der Waals constant a.
Answer» Solution :`Z=(PV)/(NRT),i.e., 0.5=(100xxV)/(1xx0.082xx273)"or"V=0.1119" L"` `(P+(a)/(V^(2)))(V-B)=RT` for 1 MOL Neglecting b, `(P+(PV)/(V^(2)))V=RT "or"PV+(a)/(V)=RT"or" (PV)/(RT)+(a)/(VRT)=1` or `"" a=(1-(PV)/(RT))VRT=(1-0.5)0.1119xx0.082xx273=1.252" atm "L^(2)mol^(-2)`