Phy 202: General Physics II Chapter 14: The Ideal Gas & Kinetic Theory

Counting Atoms 1 mole = x units The number x is called Avogadro’s number (N A ) 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 = g/mol {1 mole of H has a mass of grams} O = g/mol {1 mole of O has a mass of grams} e.g. Molecular mass of ____. H 2 = 2 x g/mol = g/mol {1 mole of H 2 has a mass of grams} H 2 O = g/mol = g/mol {1 mole of H 2 O has a mass of 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 = J/mol. K n is # of moles & R is the Universal Gas Constant (2)PV/NT = k = 1.380x J/K n is numerical quantity & k is Boltzmann’s Constant Note: k = R/N A

Development of the Ideal Gas Law Boyle (1662) : –PV = constant (at constant n & T) –Pressure increases as volume decreases & vice versa… P 1 V 1 = P 2 V 2 = …= constant Avogadro (1811) : –V/n = constant (at constant P & T) –Volume increases as # of particles increases & vice versa… V 1 /n 1 = V 2 /n 2 = …= constant Charles (unpublished ~1787, 1802 by Gay-Lussac) : –V/T = constant (at constant n & P) –Volume increases as temperature increases & vice versa… V 1 /T 1 = V 2 /T 2 = …= constant Gay-Lussac (1802) : –P/T = constant (at constant n & V) –Pressure increases as temperature increases & vice versa… P 1 /T 1 = P 2 /T 2 = …= constant

Jacques Charles ( ) 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 ( )

Kinetic Theory of Gases Gas pressure is due to molecular collisions between gas particles and the walls of the container The average kinetic energy (KE avg ) of a gas particle is KE avg = ½ mv rms 2 = 3 / 2 (kT) –Average (kinetic) energy of a particle is proportional to its temperature or v rms = (3kT) 1/2 –This is the relationship between particle motion & temperature The internal energy (U) of a gas is U = N. KE avg = 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 = C high - C low ) To determine the rate of mass diffusion: m/  t = D(A.  C)/L D is called the diffusion constant (SI units are m 2 /s)

Calcium Diffusion Across a Biological Membrane An intracellular membrane system, called the sarcoplasmic reticulum (SR), is responsible for regulating calcium ion (Ca 2+ ) movement into/out of the muscle (the diffusion constant is D = 12 x m 2 /s) A “calcium channel” protein allows the Ca 2+ to diffuse across the SR membrane. Its dimensions are –Length of the channel pore is 6.0 x m –Diameter of the pore is 1.2 x m The concentration of Ca 2+ : –0.1 mol/L inside the SR (What is it in kg/m 3 ?) –0.5x10 -6 mol/L inside the SR (What is it in kg/m 3 ?) Question: What is the rate of diffusion through Ca 2+ channel?