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Ideal Gas Law

Ideal Gas Law. Why bother with Gases? Properties of a Gas Animation P, V, T, n Ideal Gas Law Examples of Ideal Gas Law Ideal Gas Law - #molecules version. Temperature and Gases. Gas Simplest material phase – all kinetic energy.

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Ideal Gas Law

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  1. Ideal Gas Law • Why bother with Gases? • Properties of a Gas • Animation P, V, T, n • Ideal Gas Law • Examples of Ideal Gas Law • Ideal Gas Law - #molecules version

  2. Temperature and Gases • Gas • Simplest material phase – all kinetic energy. • Energy “reservoir” – convert disordered KE to useful mechanical work. • Properties of a Gas • Pressure • Volume • Temperature • Quantity • 4 Properties are interrelated • Animation • Ideal gas law

  3. Ideal Gas Animation • Gas/piston animation (Java animation) (sorry about the Bosnian!) • Gas/piston animation http://www.chem.ufl.edu/~itl/2045/MH_sims/ideal_nav.swf • Other animations http://www.mhhe.com/physsci/chemistry/animations/chang_7e_esp/gam2s2_6.swf

  4. Ideal Gas Observations • Observations of P, V, T, n • Pressure vs. Volume (Boyle’s Law) P proportional to 1/V • Pressure vs. Temperature (Gay-Lussac’s Law) P proportional to T • Volume vs. Temperature (Charle’s law) V proportional to T • Pressure vs. quantity P proportional to n • Volume vs. quantity V proportional to n

  5. Ideal Gas Law – Primary units • Ideal gas law combines Boyle’s, Charles, Gay-Lussac’s PV = nRT • P proportional 1/V • P proportional T • V proportional T • P proportional n • V proportional n • Units • P in Pascals = N/m2 • V in m3 • T in K° (not C °) • n in moles • R = 8.314 J/mol-K • Definition of Mole n = mass/molecular mass (N2=28g/mol, O2= 32g/mol, etc.)

  6. Ideal Gas Law – Alternative units • Ideal gas law combines Boyle’s, Charles, Gay-Lussac’s PV = nRT • P in atmospheres • V in liters • T in K° • n in moles • R = .0821 L-atm/mol-K • Use either primary units or alternative units completely, don’t mix n’ match! • Use primary units for First Law (Ch 15) calculations.

  7. Celsius vs. Kelvin (again) • Degree sizes same! • Kelvin = Celsius with zero shifted to absolute zero. • May use Celsius when only relative changes important. • Thermal Expansion • Specific and Latent Heat problems • Thermal Conduction • Must use Kelvin when absolute temperature important. • Ideal Gas Law • Kinetic Theory • Thermal Radiation • First and Second Law Thermodynamics Similar to Gauge vs. Absolute Pressure

  8. Example 13-10 - volume 1 mole at STP • STP = 0C (273K), 1 atm (101.3 kPa) • Primary units • Alternative units

  9. Example 13-11 - helium balloon • Volume of 18 cm radius sphere • Number of moles in alternative units (just being different) • Mass of Helium

  10. Example 13-12 - mass of air in room • Volume of 5 x 3 x 2.5 m room • Number of moles • Mass of Air @ 29 g/mol (N2 28 g/mol, O2 32 g/mol)

  11. Example 13-13 – automobile tire An automobile tire is filled to a gauge pressure of 200 kPaat 10°C. After a long drive the temperature as risen to 40°. What is the pressure now? • Strategy – Put all constant quantities on same side of Ideal Gas Law • Convert 200 kPa gauge pressure to 301 kPa absolute pressure • Solve Convert 333 kPa absolute pressure back to 232 kPa gauge pressure

  12. More examples of ideal gas • Problem 29 V2 = V1 (P1/P2) (T2/T1) • Problem 30 T2 = T1 (P2/P1) (V2/V1) • Problem 31 ρ = 32 x 10-3/22.4 x 10-3 • Problem 32 P2 = P1 (n2/n1) • Problem 33 • Problem 36 n2 = n1 (P2/P1) • Problem 39 P2 = P1 (V1/V2)(T2/T1)

  13. Problem 29 – V change with P, T • First move all constant quantities to one side • Then solve for V2 Note: Mixed units OK, since only ratios important

  14. Problem 30 – T change with P, V • Move all constant quantities to one side • Solve for T2 (Diesel car) Note: Mixed units OK, since only ratios important

  15. Problem 31 – Density of O2 • Volume of 1 mole at STP 22.4 L = 0.0224 m3 (shown earlier) • Mass of a mole O2 32 g = .032 kg (lookup in table) • Density

  16. Problem 32 – Gas substitution • Calculate mole ratio for equal mass CO2 and N2 (since mass equal) • Move all constant quantities to one side • Solve for P2

  17. Problem 36 – Gas substitution • First find #moles O2 • Move all constant quantities to one side • Solve for n2 670 moles • Then find mass 670 moles Helium

  18. Problem 39 – P change with V, T • Move all constant quantities to one side • Solve for V2 Note: Arbitrary units OK, since only ratios important

  19. Ideal Gas Law - #molecules version • Ideal Gas Law can also be written: • where • (N number of molecules) • (NA Avagadro’s number) • P in Pascals (no alternative units) • V in m3 • T in K° • Boltzman’s constant • k = R/NA = 1.38e-12 J/K

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