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: Vt=V0(1+at)=cT, at constant n,p pt=p0(1+a’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.

• pj=njRT/V=(nj/n)(nRT/V)=xjptotal

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/Videal=p/pideal

=pV/(nRT)

Z1, when p0 Z>1, when p is large

enough (repulsions dominant)

mostly Z<1, when p is not too large (attractions dominant)

Boyle temperature

Z1, 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