Chapter 4: Gases

Pressure and Temperature macroscopic – large when compared to the molecular scale macroscopic properties – relatively small set of quantities used to characterize macroscopic systems also called thermodynamic properties Pressure, P, and temperarure, T, are two important thermodynamic properties

Units of Pressure 1 pascal (Pa) = 1 N m -2 1 bar = 10 5 Pa = 0.1 MPa 1 atm = bar (exactly) 1 torr = 1/760 atm (exactly) 1 mmHg = torr Barometer

Sea level1 atm 4 miles0.5 atm 10 miles0.2 atm

Manometers Used to Measure Gas Pressures Open manometer Closed manometer

The Ideal Gas Equation Equation of State: Pressure = P(T,V,n) Ideal Gas Equation of State: limiting law - a scientific law that becomes exact only in some well- defined limit universal gas constant

Dalton’s Law of Partial Pressures V and T are constant P1P1 P2P2 P total = P 1 + P 2

Consider a case in which two gases, A and B, are in a container of volume V. P A = n A RT V P B = n B RT V n A is the number of moles of A n B is the number of moles of B P T = P A + P B x A = nAnA n A + n B x B = nBnB n A + n B P A = x A P T P B = x B P T mole fraction

2KClO 3 (s) 2KCl (s) + 3O 2 (g) Bottle full of oxygen gas and water vapor P T = P O + P H O 22

Vapor Pressure of Water and Temperature

Kinetic Molecular Theory of Gases 1.A gas is composed of molecules that are separated from each other by distances far greater than their own dimensions. The molecules can be considered to be points, that is, they possess mass but have negligible volume. 2.Gas molecules are in constant motion in random directions, and they frequently collide with one another. Collisions among molecules are perfectly elastic. 3.Gas molecules exert neither attractive nor repulsive forces on one another.

Pressure of a Gas Molecular view in cubic box of length, L. Effect of an elastic collision

Pressure based on collisions

denotes averaging. molecular speed mean square velocity

Temperature and Kinetic Energy

Mean kinetic energy of a molecule is proportional to the temperature. Boltzmann’s constant root-mean-square (rms) speed

Maxwell-Boltzmann Distribution of Molecular Speeds Maxwell-Boltzmann distribution of molecular speeds range u to u+ dumolecules (N u )

The distribution of speeds for nitrogen gas molecules at three different temperatures The distribution of speeds of three different gases at the same temperature most probable molecular speed

Fraction of molecules with speeds in a given interval Interval: a to b approximation

Apparatus for studying molecular speed distribution

The path traveled by a single gas molecule.

Gas diffusion is the gradual mixing of molecules of one gas with molecules of another by virtue of their kinetic properties. NH 3 17 g/mol HCl 36 g/mol NH 4 Cl r1r1 r2r2 M2M2 M1M1  =