Properties of Gases

Basic features Free move and fill any container it occupies homogeneously, continuously, and uniformly Collection of molecules (or atoms) in random motion, with average speeds increasing as temperature raised Except collisions, mostly the molecules are widely separated and weakly interacted with each other

States of gases: n, T, V, p Equation of state: p=f(n,T,V)

States of gases: n, T, V, p Equation of state: p=f(n,T,V)

The perfect gas law Perfect gas (ideal gas) equation Boyle-Marriote’s law: pV=constant, at constant n,T Charles-Gay-Lussac’s law: V t =V 0 (1+  t)=cT, at constant n,p p t =p 0 (1+  ’t)=c’T, at constant n,V Avogadro’s principle: equal V at same T and p contains same number of molecules, or V ∝ n, at constant T,p

The perfect gas law

Mixtures of gases: Dalton’s law The pressure exerted by a mixture of ideal gases is the sum of the pressures to which each contributes as if it occupies the container alone. p j =n j RT/V=(n j /n)(nRT/V)=x j p total

Real gases Important at high p and low T, especially when close to condensing. Size of molecules Intermolecular interactions: Repulsive forces assist expansion thus increase pressure or volume, while attractive forces assist compression thus decrease pressure or volume

The compression factor Z=V/V ideal =p/p ideal =pV/(nRT)  Z  1, when p  0  Z>1, when p is large enough (repulsions dominant)  mostly Z<1, when p is not too large (attractions dominant)

Boyle temperature  Z  1, when p is small  High-T: Z>1 (repulsions dominant)  Low-T: Z<1 (attractions dominant)

Virial equation of state and virial coefficients Z

Virial coefficients