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Gas Laws

Gas Laws. Ch 13.3. 4 variables affecting gas behavior. Pressure (P) Volume (V) Amount of gas (n) Temperature (T). Boyle’s Law. Pressure is inversely proportional to volume. (at the same temperature) P 1 V 1 = P 2 V 2 In a closed system, as volume goes down, pressure goes up.

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Gas Laws

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  1. Gas Laws Ch 13.3

  2. 4 variables affecting gas behavior • Pressure (P) • Volume (V) • Amount of gas (n) • Temperature (T)

  3. Boyle’s Law • Pressure is inversely proportional to volume. • (at the same temperature) P1V1 = P2V2 • In a closed system, as volume goes down, pressure goes up. • Marshmallow in syringe • Cartesian diver

  4. Boyle’s Law example • 5 liters of gas at 1 atmosphere of pressure are compressed to 1.25 liters. What is the final pressure? • P1V1= P2V2 • Solve for P2 • P1V1/V2 = P2 • (5 liters)(1 atm)/(1.25 liters)= 4 atm

  5. Charles’s Law • Temperature and volume are directly proportional. • T1/V1 = T2/V2 or • T1V2 = T2V1 • In a closed, expandable system, as temperature goes up, volume goes up. • Balloon in hot car

  6. Charles’s Law Example • A balloon with a volume of 0.5 liters at 20C is left in a 120 C car all day. What is the final volume of the balloon? • Convert temperatures to Kelvin: 20C =293K, 120 C = 393 K • T1V2 = T2V1 • Solve for V2 • V2 = T2V1 /T1 • 0.7 liters =(393 K)(0.5 liters)/293K

  7. Combined Gas Law • You can combine Charles and Boyles to solve problems with pressure, volume and temperature • P1V1/T1= P2V2/T2 • A fixed container has 5.5L of gas at STP. What is the pressure at 300K? • If one of the variables doesn’t change, you can cancel it out. P1/T1= P2/T2 • Solve for P2: P1T2 /T1=P2(1 atm)(300K)/273K=1.1 atm

  8. Avogadro’s Law • Amount is directly proportional to volume. • How much gas, or number of moles of gas = n • V1/n1 = V2/n2 • The more gas you have, the more space it takes up at the same pressure. • Therefore, we can compare the amount of gas in moles to calculate a final volume, if temperature and pressure remain constant.

  9. Example • 0.5 moles of O2 has a volume of 12.2 liters at standard temperature and pressure. If all the O2 is converted to O3 at the same temperature and pressure, what is the final volume? • Given: 3O2(g) 2O3(g) • V1/n1 = V2/n2 • Solve for V2 • n2V1/n1= V2(n2)/n2 • (2 moles)(12.2 L)/3 moles = 8.1 L

  10. Ideal Gas Law • The ideal Gas law defines how an “ideal gas” behaves. • Most gas behaviors can be approximated with this formula at STP. • PV = nRT • n = moles • R = .08206 L atm/K mol • R is the universal gas constant

  11. Example • A sample of hydrogen gas at 1.5 atm and 273K has a volume of 8.56 L. how many moles of H2 are present? • PV = nRT: solve for n • PV/RT = n • (1.5 atm)(8.56 L)/(.08206 Latm/Kmol)(273K) = • 0.57 moles H2

  12. Dalton’s Law of Partial Pressures • The sum of the partial pressures of gases in a gas mixture is equal to the total pressure. • Pt = Pa + Pb + Pc + … • Example: Calculate the partial pressure in atmospheres of each gas in the mixture: • Pt = 10 atm • 1.0 mol CO2, 2.0 mol O2, 3.0 mol N2 • 10 = 1x + 2x + 3x = 6x, x= 1.67 • 1.67 atm + 3.33 atm + 5.00 atm = 10 atm

  13. Graham’s Law • The ratio of the rates of effusion of two gases is equal to the square root of the inverse ratio of their molecular masses or densities. • The effusion rate of a gas is inversely proportional to the square root of its molecular mass. • Mathematically, this can be represented as:Rate1 / Rate2 = square root of (Mass2 / Mass 1)

  14. Calculating effusion rate • Nitrogen, has a molecular mass of 28.0 g. O2, Oxygen, has a molecular mass of 32.0 g. Therefore, to find the ratio, the equation would be: • RateN2/RateO2 = square root of (32.0 g/28.0 g): • RateN2/RateO2 = 1.07 • This tells us that N2 is 1.07 times as fast as O2.

  15. Calculating molecular mass • Gas A is 0.68 times as fast as Gas B. The mass of B is 17 g. What is the mass of A? • 0.68 = square root of 17 g/MassA. • Squaring both sides gets: • 0.4624 = 17 g/MassA • Mass A = 17g/0.4624 • = 36.7647 g

  16. Gas Law Summary • Boyle’s Law P is inversely proportional to V P1V1=P2V2 • Charles’s Law V is proportional to T V1/T1 = V2T2 • Avogadro’s Law V is proportional to n V1/n1=V2/n2 • Dalton’s Law Pt is sum of partial pressures Pt = Pa + Pb + Pc + …

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