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Exploring The Ideal Gas Law & Kinetic Theory in Physics

Dive into the fascinating world of Ideal Gas Law and Kinetic Theory. Learn about Avogadro's number, gas behavior, energy, diffusion, and more within the realm of General Physics. Understand the relationship between gas properties and atomic structure.

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Exploring The Ideal Gas Law & Kinetic Theory in Physics

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constant P & T) • Volume increases as # of particles increases & vice versa… V1/n1 = V2/n2 = …= constant • Charles (unpublished ~1787, 1802 by Gay-Lussac): • V/T = constant (at constant n & P) • Volume increases as temperature increases & vice versa… V1/T1 = V2/T2 = …= constant •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