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The Gas State

The Gas State. Gases are everywhere – atmosphere, environmental processes, industrial processes, bodily functions Gases have unique properties from liquids and solids Gases are compressible (very important for storage) Gas particles are widely separated and move at very fast speeds

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The Gas State

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  1. The Gas State • Gases are everywhere – atmosphere, environmental processes, industrial processes, bodily functions • Gases have unique properties from liquids and solids • Gases are compressible (very important for storage) • Gas particles are widely separated and move at very fast speeds • Most gases have relatively low densities • Gas have relatively low viscosity (resistance to movement) allowing them move freely through pipes and even small orifices

  2. The Gas State • Chemical behavior of gases depends on composition • Physical behavior of all gases is similar • Gases are miscible mixing together in any proportion • Behavior of gases described by ideal gas law and kinetic-molecular theory, the cornerstone of this chapter • Gas volume changes greatly with pressure • Gas volume changes greatly with temperature • Gas volume is a function of the amount of gas

  3. Cylinders of Gas

  4. The Empirical Gas Laws • Gas behavior can be described by pressure, temperature, volume, and molar amount • Holding any two constant allows relations between the other two • Boyle’s Law : The volume of a sample of gas at a given temperature varies inversely with the applied pressure Vα 1/P PV= constant P1V1=P2V2

  5. The Empirical Gas Laws Boyle’s Law Gas Pressure-Volume Relationship

  6. Practice Problem Boyle’s Law A sample of chlorine gas has a volume of 1.8 L at 1.0 atm. If the pressure increases to 4.0 atm (at constant temperature), what would be the new volume? using P1V1=P2V2 V2 = P1V1/P2 = (1.0 atm) × (1.8 L) / (4.0 atm) V2= 0.45 L

  7. The Empirical Gas Laws Charles’s Law The volume occupied by any sample of gas at constant pressure is directly proportional to its absolute temperature. Vα T abs Assumes constant moles and pressure Temperature on absolute scale (oC + 273.15) V/T = constant V1/T1 = V2/T2 (Tabs (K) = oC + 273.15)

  8. The Empirical Gas Laws Charles’s Law: Linear Relationship of Gas Volume and Temperature at Constant Pressure V = at + b 0 = a(-273.15) + b b = 273.15b V = at + 273.15a = a(t + 273.15)

  9. Practice Problem Charles’s Law A sample of methane gas that has a volume of 3.8 L at 5.0°C is heated to 86.0°C at constantpressure. Calculate its new volume. using V1/T1 = V2/T2 Convert temperature (°C ) to absolute (kelvin) 50 °C = 5.0 +273.15 = 278.15 K 86.0 °C = 86.0 + 273.15 = 359.15 K V2 = (T2/T1) V1 = (359.15 K /278.15 K ) × 3.8 L V2 = 4.9 L

  10. The Combined Gas Law P1V1 = P2V2 (fixed T,n) Boyle’s Law V x P= const 1662 V1 / V2 = T1 / T2 (fixed P,n) Charles’ Law V / T= const 1787 P1V1/T1 = P2V2/T2 Combined Gas Law: In the event that all three parameters, P, V, and T, are changing, their combined relationship is defined as follows assuming the mass of the gas (number of moles) is constant.

  11. Avagadro’s Law Avogadro’s Law • The volume of a sample of gas is directly proportional to the number of moles of gas, n Vα n V/n = constant • Equal volumes of any two gases at the same temperature and pressure contain the same number of molecules (mol) V1/n1 = V2/n2

  12. Avagadro’s Law Avogadro’s Law • The volume of one mole of gas is called the: molar gas volume, Vm • Volumes of gases are often compared at standard temperature and pressure (STP), chosen to be • 0 oC (273.15 oK) and 1 atm pressure • At STP, the molar volume, Vm, that is, the volume occupied by one mole of any gas, is 22.4 L/mol VSTP/NSTP = Vm = 22.4 L ( at STP )

  13. The Ideal Gas Law From the empirical gas laws, we see that volume varies in proportion to pressure, absolute temperature, and the mass of gas (moles) present Boyle law Vα 1/P V= constant x 1/P Charles law Vα T abs V = constant x T Avogadros law Vα n V = constant x n

  14. The Ideal Gas Law This implies that there must exist a proportionality constant governing these relationships Combining the three proportionalities, we can obtain the following relationship. V m = “R” x n x (T abs/P)where “R” is the proportionality constant referred to as the Ideal Gas Constant, which relates Molar Volume (V) to the ratio of Temperature to Pressure T/P

  15. The Ideal Gas Law P = Pressure (in atm) V = Volume (in liters) n = Number of atoms (in moles) R = Universal gas constant 0.0821 L.atm/mol.K T = Temperature (in 0 Kelvin = °C + 273.15) The ideal gas equation is usually expressed in the following form: PV = nRT

  16. The Ideal Gas Law PV = nRT What is R, universal gas constant? the R is independent of the particular gas studied

  17. Practice Problem A steel tank has a volume of 438 L and is filled with 0.885 kg of O2. Calculate the pressure of oxygen in the tank at 21oC use PV = nRT V = 438 L, R = 0.0821 L.atm/mol.K, T = 21 + 273.15 = 294.15 K , n = 885/32 = 27.7 mol. So the pressure = nRT/V = 27.7 mol x 0.0821 L.atm/mol.K x 294.15 K/438 L = 1.53 atm

  18. Density and Molar Mass of a Gaseous Substance The ideal gas equation can be applied to determine the density or molar mass of a gaseous substance

  19. Density and Molar Mass of a Gaseous Substance

  20. Example A chemist has synthesized a greenish-yellow gaseous compound of chlorine and oxygen and finds that its density is 7.71 g/L at 36C and 2.88 atm. Calculate the molar mass of the compound and determine its molecular formula. Solution

  21. Mixtures of Gases Dalton’s Law of Partial Pressures The total pressure of a mixture of gases equals the sum of the partial pressures of the individual gases.

  22. Real Gases: Deviations from Ideality • Real gases behave ideally at ordinary temperatures and pressures. • At low temperatures and high pressures real gases do not behave ideally. • The reasons for the deviations from ideality are: • The molecules are very close to one another, thus their volume is important. • The molecular interactions also become important.

  23. Real Gases:Deviations from Ideality • van der Waals’ equation accounts for the behavior of real gases at low temperatures and high pressures. • The van der Waals constants a and b take into account two things: • a accounts for intermolecular attraction • For nonpolar gases the attractive forces are London Forces • For polar gases the attractive forces are dipole-dipole attractions or hydrogen bonds. • b accounts for volume of gas molecules • At large volumes a and b are relatively small and van der Waal’s equation reduces to ideal gas law at high temperatures and low pressures.

  24. Real Gases:Deviations from Ideality • Calculate the pressure exerted by 84.0 g of ammonia, NH3, in a 5.00 L container at 200. oC using the ideal gas law. PV = nRT P = nRT/V n = 84.0g * 1mol/17 g T = 200 + 273 P = (4.94mol)(0.08206 L atm mol-1 K-1)(473K) (5 L) P = 38.3 atm

  25. Real Gases: Deviations from Ideality • Calculate the pressure exerted by 84.0 g of ammonia, NH3, in a 5.00 L container at 200. oC using the van der Waal’s equation. The van der Waal's constants for ammonia are: a = 4.17 atm L2 mol-2 b =3.71x10-2 Lmol-1 n = 84.0g * 1mol/17 g T = 200 + 273 P = (4.94mol)(0.08206 L atm mol-1 K-1)(473K) (4.94 mol)2*4.17 atm L2 mol-2 5 L – (4.94 mol*3.71E-2 L mol-1) (5 L)2 P = 39.81 atm – 4.07 atm = 35.74

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