JEE Advanced2025ChemistryStates of MatterActual
Molar volume (V_m ) of a van der Waals gas can be calculated by expressing the van der Waals equation as a cubic equation with V_m as the variable. The ratio (in mol dm ⁻³ ) of the coefficient of V_m^2 to the coefficient of V_m for a gas having van der Waals constants a=6.0 dm ^6 ~atm ~mol ⁻² and b=0.060 dm ^3 ~mol ⁻¹ at 300 K and 300 atm is _____ . Use: Universal gas constant (R)=0.082 dm ^3 ~atm ~mol ⁻¹ ~K ⁻¹
Correct answer
0
Step-by-step solution
aligned & (P+ a V_m^2 ) (V_m-b )=R T & P V_m-b P+ a V_m - a b V_m^2 -R T=0 & P V_m^2-(b P+R T) V_m^2+a V_m-a b=0 aligned Coefficient of V _ m ^2=-( bP + RT ) Coefficient of V _ m = a Ratio =- ( bP + RT ) a =- [ 0.06 300+24.6 6 ]=-7.1 .