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Solids, Liquids and Gases

Solids, Liquids and Gases. Condensed States : much higher  than gases and they are hard to compress. This includes solids and liquids. Fluids : substances that flow freely or conform to their vessel. This includes liquids and gases.

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Solids, Liquids and Gases

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  1. Solids, Liquids and Gases • Condensed States: much higher  than gases and they are hard to compress. This includes solids and liquids. • Fluids: substances that flow freely or conform to their vessel. This includes liquids and gases. • Vapour: The gas phase of a substance that is generally in the presence of the solid or liquid phase. • Gases: • less dense than the condensed states • easily compressed • exert pressure on their surroundings & expand without limit • described in terms of P, V, n and T • diffuse into each other and are miscible

  2. Ideal Gas Law • PV = nRT • P = pressure of the gas • V = volume of the gas • n = moles of gas • R = Universal Gas Constant • T = temperature of the gas in KELVIN

  3. Boyles Law • If we hold n and T constant then • PV = k (constant n & T) • where k is a constant • or • V = 1/P * k • y = mx + b ; y = V ; x = 1/P ; m = k ; b = 0 • V  1/P • P1V1=k & P2V2=k then P1V1=P2V2(constant n, T)

  4. Charles Law • If we hold P and n constant then • V/T = k (constant n & P) • where, k is a constant • or • V = T * k • y = mx + b ; y = V ; x = T ; m = k ; b = 0 • V  T

  5. Avogadro’s Law • If we hold P and T constant then • V/n = k (constant P & T) • where, k is a constant • or • V = n * k • y = mx + b ; y = V ; x = n ; m = k ; b = 0 • V  n • V1/n1 = V2/n2

  6. Combined Laws • Boyle’s Law: V  1/P V1P1=V2P2 (constant n & T) • Charles Law: V T V1/T1=V2/T2 (constant P & n) • Combined Gas Laws: V  T/P V1P1/T1 = V2P2/T2 (constant n) • Avogadro’s Law: V n V1/n1 = V2/n2 (constant P & T) • summarized: V  nT/P (no restrictions) • Ideal Gas Law: PV = nRT

  7. Dalton’s Law of Partial Pressures • If we have a mixture of ideal gases • nTotal = nA + nB + nC + ...... (constant V, T) • multiply through by RT/V • (nTotalRT)/V = (nART)/V + (nBRT)/V + (nCRT)/V + ......... • PTotal = (nTotalRT)/V PA = (nART)/V ....... • PTotal = PA + PB + PC + ...... (constant V, T) • The total pressure of a mixture of ideal gases is the sum of the partial pressures of each gas.

  8. Gas Collection Over Water • For a gas collected over water @ T: PTotal = Pgas + PH2O • PH2O is the vapour pressure of water @ T • Temperature (oC) Vapour Pressure of H2O @ T (Torr) • 19 16.48 • 20 17.54 • 21 18.65 • 22 19.83 • 23 21.07 • 24 22.38 • 25 23.76

  9. Mole Fraction • mole fraction = XA = (nA)/(nTotal) • XA is a unitless quantity • XA = (PAV/RT)/(PTotalV/RT) • cancel V, R and T • XA =PA/PTotal • or • PA = XA * PTotal

  10. The Kinetic-Molecular Theory • 1) Gases consist of discrete molecules that are very far apart • 2) Gases are in continuous motion, travel in straight lines and have varying velocities. • 3) Gases undergo elastic collisions (no net loss of energy) • 4) There are no attractive or repulsive forces between the gas molecules.

  11. Kinetic Energy and Molecular Speed • Kinetic Energy - the energy a body possesses by virtue of its motion. • KE = (1/2) m u 2 • m = mass (kg) • u = velocity (m/s) or molecular speed • A sample of gas has a Maxwellian-Boltzmann distribution of molecular speeds and KE.

  12. _ _______ • u • T = temp. • M = molecular mass • If a sample of Xe and O2 were at the same temperature which sample would have the highest avg. molecular speed? • O2 • u1u2 • u12M1 = u22M2 • u1/u2=(M2/M1) u(O2)/u(Xe)=2 Xe O2 Ne

  13. Diffusion and Effusion • Diffusion - The movement of a substance into a space or the mixing of one substance with another. • Effusion - The escape of a gas through a small hole. • If one balloons is filled with H2 and one balloon is filled with O2 at the same temperature, which will escape faster and by how much? • u(H2)/u(O2) = (32 amu/2 amu) = 4 • Therefore, the H2 will escape approx. 4 times faster than the O2

  14. Real Gases - Deviation from ideality • Ideal Gas Law - PV=nRT • Two main assumptions: • 1) the gas molecules do not occupy any space • 2) there are no attractive or repulsive forces between molecules (no intermolecular forces) • van der Waals equations - (p + (n2/V2)a)(V-nb)=nRT • correction for assumption #1: (becomes significant @ high Pressure) • Vreal gas = Videal gas - nb • n = moles & b = exp. determined constant Videal > Vreal Volume occupied by an ideal gas Volume occupied by a real gas

  15. van der Waals equations - (p + (n2/V2)a)(V-nb)=nRT • correction for assumption #2 (no intermolecular interactions): (becomes significant @ high Pressure & low Temp.) • If we re-write the van der Waals equation solving for p: • p = ((nRT)/(V-b)) - (n2/V2) a • a is an experimentally determined constant like b and they are both temperature and pressure dependent • a is large at low temperatures and for polar molecules • pideal gas > preal gas

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