Phy 202: General Physics II

Chapter 14: The Ideal Gas & Kinetic Theory

Counting Atoms• 1 mole = 6.022 x 1023 units• The number 6.022 x 1023 is called Avogadro’s number (NA)• Why the mole? Because, a one mole quantity of any element has a mass (in grams)

equal to its atomic mass.– It’s the relationship between mass and numerical quantity of any element or compound

e.g. Atomic mass of ____.H = 1.008 g/mol {1 mole of H has a mass of 1.008 grams}

O = 16.00 g/mol {1 mole of O has a mass of 16.00 grams}

e.g. Molecular mass of ____.

H2 = 2 x 1.008 g/mol = 2.016 g/mol{1 mole of H2 has a mass of 2.016 grams}

H2O = 2.016+16.00 g/mol =18.016 g/mol{1 mole of H2O has a mass of 18.016 grams}

The Ideal Gas Law• The measurable physical parameters that describe the state of a gas are:

– Pressure (P)– Volume (V)– Number of gas particles/molecules (n or N)– Temperature (T)

• An equation state describes how these parameters are related is called the Ideal Gas Law , which takes 2 forms:

(1) PV/nT = R = 8.314 J/mol.K n is # of moles & R is the Universal Gas Constant

(2) PV/NT = k = 1.380x10-23 J/K n is numerical quantity & k is Boltzmann’s Constant

Note: k = R/NA

Development of the Ideal Gas Law• Boyle (1662):

– PV = constant (at constant n & T)– Pressure increases as volume decreases & vice versa…

P1V1 = P2V2 = …= constant• Avogadro (1811):

– V/n = constant (at constant P & T)– Volume increases as # of particles increases & vice versa…

V1/n1 = V2/n2 = …= constant• Charles (unpublished ~1787, 1802 by Gay-Lussac):

– V/T = constant (at constant n & P)– Volume increases as temperature increases & vice versa…

V1/T1 = V2/T2 = …= constant• Gay-Lussac (1802):

– P/T = constant (at constant n & V)– Pressure increases as temperature increases & vice versa…

P1/T1 = P2/T2 = …= constant

Jacques Charles (1746-1823)• Esteemed member of the French

Academy of Science

• Invented the hydrogen-filled balloon

• Credited for discovering the relationship between the volume of an enclosed gas & its temperature

• Prominent French chemist & rival of John Dalton

• Flew in balloons to measure the earth’s magnetic properties

• Conducted experiments on gases in chemical reactions

Joseph Gay-Lussac (1778-1850)

Kinetic Theory of Gases• Gas pressure is due to molecular collisions between gas particles and the

walls of the container• The average kinetic energy (KEavg) of a gas particle is

KEavg = ½ mvrms2 = 3/2(kT)

– Average (kinetic) energy of a particle is proportional to its temperature

or

vrms = (3kT)1/2 – This is the relationship between particle motion & temperature

• The internal energy (U) of a gas is

U = N.KEavg = N[3/2(kT)] = 3/2(NkT)Or

U = 3/2(nRT)

Diffusion• The process by which particles move from high

concentration to low concentration (analogous to heat)• The rate of mass diffusion is related to:

– The length of the particle pathway (L)– The cross-sectional area of the pathway (A)– The concentration difference between the ends of the pathway

(C = Chigh - Clow)

• To determine the rate of mass diffusion:

m/t = D(A.C)/LD is called the diffusion constant (SI units are m2/s)

Calcium Diffusion Across a Biological Membrane

• An intracellular membrane system, called the sarcoplasmic reticulum (SR), is responsible for regulating calcium ion (Ca2+) movement into/out of the muscle (the diffusion constant is D = 12 x 10-10 m2/s)

• A “calcium channel” protein allows the Ca2+ to diffuse across the SR membrane. Its dimensions are– Length of the channel pore is 6.0 x 10-8 m– Diameter of the pore is 1.2 x 10-8 m

• The concentration of Ca2+:– 0.1 mol/L inside the SR (What is it in kg/m3?)

– 0.5x10-6 mol/L inside the SR (What is it in kg/m3?)

Question: What is the rate of diffusion through Ca2+ channel?