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Phy 202: General Physics II

Phy 202: General Physics II. Chapter 14: The Ideal Gas & Kinetic Theory. Counting Atoms. 1 mole = 6.022 x 10 23 units The number 6.022 x 10 23 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.

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Phy 202: General Physics II

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

  2. 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}

  3. 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

  4. 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(at constant P & T) • Volume increases as # of particles increases & vice versa… V1/n1 = V2/n2 = …= constant • Charles (unpublished ~1787, 1802 by Gay-Lussac): • V/T = constant (at constant n & P) • Volume increases as temperature increases & vice versa… V1/T1 = V2/T2 = …= constant •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

  5. 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 Jacques Charles (1746-1823) Joseph Gay-Lussac (1778-1850)

  6. 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)

  7. 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 (DC = Chigh - Clow) • To determine the rate of mass diffusion: m/Dt = D(A.DC)/L D is called the diffusion constant (SI units are m2/s)

  8. 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?

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