Gas Densities, Partial Pressures, and Kinetic-Molecular Theory Sections 10.5-10.8

Objectives Apply the ideal-gas equation to real gas situations. Interpret the kinetic-molecular theory of gases

Gas Densities and Molar Mass Rearrange the ideal-gas equation : n = P V RT Multiply both sides by molar mass, M nM = PM V RT Product of n/V and M = density in g/L Moles x grams = grams Liter mole liter

Gas Densities and Molar Mass Density is expressed: D = PM RT Density depends on pressure, molar mass, and temperature

Gas Mixtures and Partial Pressure Dalton’s Law of Partial Pressures: Total pressure of a mixture equals sum of the pressures that each would exert if present alone. Pt = P1 + P2 + P3 + ….

Gas Mixtures and Partial Pressures Thus: P1 = n1 (RT); P2 = n2 (RT); P3 = n3 (RT);… V V V And Pt = (n1 + n2 + n3 + ….) RT = nt (RT) V V

Mole Fraction, X P1 = n1 RT/ V = n1 Pt = nt RT/ V = nt Thus… P1 = (n1/nt)Pt = X1Pt

Example Mole fraction of N2 in air is 0.78 (78%). If the total pressure is 760 torr, what is the partial pressure of N2?

Homework 59-67, odd only

Kinetic-Molecular Theory Explains why gases behave as they do Developed over 100 year period Published in 1857 by Rudolf Clausius

Kinetic Molecular Theory * Theory of moving molecules You Must Know the 5 Postulates of the Kinetic Molecular Theory of Gases (page 421).

Root-mean-square speed, u Speed of a molecule possessing average kinetic energy Є = ½ mu2 Є is average kinetic energy m is mass of molecule Both Є and u increase as temperature increases

Application to Gas Laws Effect of a V increase at constant T: - Average kinetic energy does not change when T is constant. Thus rms speed is unchanged. With V increase, there are fewer collisions with container walls, and pressure decreases (Boyle’s Law).

Application to Gas Laws 2. Effect of a T increase at constant V: - Increase T means increase of both average kinetic energy and rms speed. No change in V means there will be more collisions with walls.

Molecular Effusion & Diffusion u = 3RT M *Derived equation from the k-m theory **Less massive gas molecules have higher rms speed

Effusion Escape of gas molecules through a tiny hole into an evacuated space

Diffusion Spread of one substance throughout a space or throughout a second substance

Graham’s Law of Effusion Effusion rate of a gas is inversely proportional to the square root of its molar mass. Rates of effusion of two gases: * At same T and P in containers with identical pinholes

Graham’s Law of Effusion

Diffusion and Mean Free Path Similar to Effusion (faster for lower mass molecules) BUT diffusion is slower than molecular speeds because of molecular collisions Mean Free Path: average distance traveled by a molecule between collisions

Homework 69, 71, 73, 75, 76, 77, and 79