Gases Gas laws Constant temperature (Boyle's law) P₁V₁ = P₂V₂ P₂ = P₁V₁/V₂ V₂ = P₁V₁/P₂ Constant pressure (Charles's law) V₁/T₁ = V₂/T₂ T₁/V₁ = T₂/V₂ V₂ = V₁T₂/T₁ T₂ = T₁V₂/V₁ Constant volume (Gay-Lussac's law) P₁/T₁ = P₂/T₂ P₂ = P₁T₂/T₁ T₂ = T₁P₂/P₁ Combined Gas law P₁V₁/T₁ = P₂V₂/T₂ V₂ = P₁V₁T₂/T₁P₂ pressure and temperature are absolute Avogadro's law V₁/n₁ = V₂/n₂ n = number of moles Ideal gas law PV = nRT n = number of moles R = gas constant = 0.08206 (atm∙L)/(mol∙K) 8.314 L∙kPa/mol∙K or J/mol•K 0.08314 L∙bar/mol∙K 62.36 L∙torr/mol∙K 62.36 L∙mmHg/mol∙K T = temperature in kelvins P = absolute pressure in atm, kPa, bar, torr V = volume in liters PV = kRT k is the Boltzmann constant (1.381e−23 J/K N is the number of gas molecules PM = ρRT ρ = density in g/L M is molar mass in g/mol alternate: 8.314 m³•Pa/K•mol Volume in m³, Pressure in Pa 62.36 L•Torr/K•mol Volume in Liters, Pressure in Torr 8.206e-5 m³•atm/K•mol Volume in m³, Pressure in atm Kinetic energy of a gas Average KE of one molecule gas = (3/2)kʙT Average KE of 1 mole gas = (3/2)kʙNaT kʙ is Boltzmann constant 1.3806×10^−23 J/K Na is Avogadro constant 6.022x10^23 molecules/mole T is temp in kelvins van der Waals equation (P + (n²a/V²))(V – nb) = nRT n = number of moles R = gas constant = 0.08206 (atm∙L)/(mol∙K) 8.314 L∙kPa/mol∙K 0.08314 L∙bar/mol∙K 62.36 L∙torr/mol∙K 62.36 L∙mmHg/mol∙K T = temperature in kelvins P = absolute pressure in atm, kPa, bar, torr V = volume in liters b = volume occupied by 1 mole of the gas molecules in L/mol a = a constant that depends on the gas, is a measure of the average attraction between particles, in L²•bar/mol² or L²kPa/mol² One mole of any ideal gas at STP has a volume of 22.41L (old def of STP, 1 atm) One mole of any ideal gas at STP has a volume of 22.71L (new def of STP, 100 kPa) One mole of any ideal gas at RTP has a volume of 24.47L (old def of RTP, 1 atm) One mole of any ideal gas at RTP has a volume of 24.79L (new def of RTP, 100 kPa) STP = 0ºC & 1 ATM (new 100 kPa) RTP = 25ºC & 1 ATM (new 100 kPa) Work on a gas at constant pressure Volume increases with temperature. Take a cylinder with the top a piston of area A moving up by distance d W = Fd = (F/A)(Ad) W = P(Ad) = PΔV Work on a gas at constant volume no work is done Work on a gas at constant temperature Take a cylinder with the top a piston of area A moving up by distance d. We can keep the temperature constant by having the system in contact with a heat reservoir. W = nRT ln(Vf/Vi) n = number of moles R = gas constant = 0.08206 (atm∙L)/(mol∙K) T = temperature in kelvins P = absolute pressure in atm V = volume in liters Graham's Law Graham's law states that the rate at which gas molecules diffuse is inversely proportional to the square root of its density. Combined with Avogadro's law (i.e. since equal volumes have equal number of molecules) this is the same as being inversely proportional to the root of the molecular weight. Dalton's law of partial pressures states that the pressure of a mixture of gases simply is the sum of the partial pressures of the individual components. Dalton's Law is as follows: Ptotal = P₁ + P₂ + P₃ + ... Pn or Ptotal = Pgas + Ph₂o where PTotal is the total pressure of the atmosphere, Pgas is the pressure of the gas mixture in the atmosphere, and Ph₂o is the water pressure at that temperature. KE/velocity of molecules Kinetic Energy of a gas per mole = 12.47T J where T is temperature in kelvins at STP Kinetic Energy of a gas per mole = 3406 J Vrms = √(3kʙT/m) T is temp in kelvins m is the mass of one molecule kʙ = Boltzmann constant, 1.381×10^−23 J/K Speed of molecules Vrms = √(3kʙT/m) kʙ = Boltzmann constant, 1.381×10^−23 J/K m is mass of molecule in kg T is temp in kelvins Units of Pressure 1 Pa = 1 N/m² 1 torr = 1/760 of a standard atmosphere 1 standard atmosphere = 101.325 kPa = 1.01325 bar = 14.7 PSI = 10.33 meters of water = 29.92 inch of mercury 1 bar = 100 kPa = 14.5 PSI 1 PSI (lb/in²) = 6,894.8 Pa = 6.895x10^-3 N/mm² = 0.06895 bar Vacuum, 100 micron = 13 Pa = 0.1 mm Hg Air specific heat of dry air is 1.006 kJ/kgC Density of Air 1.164 kg/m³ at 30ºC and 101.325kPa Density of Air 1.204 kg/m³ at 20ºC and 101.325kPa Density of Air 1.247 kg/m³ at 10ºC and 101.325kPa Density of Air 1.292 kg/m³ at 0ºC and 101.325kPa Density of Air 1.341 kg/m³ at –10ºC and 101.325kPa Density of Air 1.394 kg/m³ at –20ºC and 101.325kPa Oxygen Atomic Number 8 Atomic weight 16.00 g/mol 1 mole = 16 g Density (0°C, 101.325 kPa) 1.429 g/L Liquid density at b.p. 1.141 g/cm³ Melting point 54.36 K, –218.79 °C, –361.82 °F Boiling point 90.20 K, –182.95 °C, –297.31 °F Heat of fusion (O₂) 0.444 kJ/mol Heat of vaporization (O₂) 6.82 kJ/mol Specific heat capacity (25 °C) (O₂) 29.378 J/mol·K Nitrogen Atomic Number 7 Atomic weight 14.01 g/mol 1 mole = 14.01 g density 1.251 g/cm³ at 0°C Melting point -210°C 63.05K Boiling point -195.8°C 77.36K Heat of Vaporization 199.1 kJ/kg Liquid density at BP 0.808 g/cm³ liquid specific heat at BP 2.042 kJ/kgK Other Density of Hydrogen gas 0.089 kg/m³ Specific Heat of Hydrogen gas at 28C 14.31 kJ/kgC Density of Helium gas 0.18 kg/m³ Density Helium is (0 °C, 101.325 kPa) 0.1786 kg/m³ Ammonia liquid density: 682 kg/m³ |
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