Gases

Manometers: measure P of a gas Closed-end: difference in Hg levels (Dh) shows P of gas in container compared to a vacuum http://www.chm.davidson.edu/ChemistryApplets/GasLaws/Pressure.html closed

2. Open-end: Difference in Hg levels (Dh) shows P of gas in container compared to Patm

Gas Laws Make a data table to put the numbers so you can eliminate the words. Make sure that any Celsius temperatures are converted to Kelvin (add 273). Rearrange the equation before substituting in numbers. If you are trying to solve for T2, get it out of the denominator first by cross-multiplying. If one of the variables is constant, then eliminate it. Try these problems!

Gas Law Problem 1 A 2.00 L sample of N2 gas at STP is compressed to 4.00 atm at constant temp-erature. What is the new volume of the gas? V2 = P1V1 / P2 = (1.00 atm)(2.00 L) / (4.00 atm) = 0.500 L

Gas Law Problem 2 To what temperature must a 3.000 L sample of O2 gas at 300.0 K be heated to raise the volume to 10.00 L? T2 = V2T1/V1 = (10.00 L)(300.0 K) / (3.000 L) = 1000. K

Gas Law Problem 3 A 3.00 L sample of NH3 gas at 100.0 kPa is cooled from 500.0 K to 300.0 K and its pressure is reduced to 80.0 kPa. What is the new volume of the gas? V2 = P1V1T2 / P2T1 = (100.0 kPa)(3.00 L)(300. K) / (80.0 kPa)(500. K) = 2.25 L

Gay Lussac’s Law of Combining Volumes When measured at the same temperature and pressure, the ratio of the volumes of reacting gases are small whole numbers. N2 1 volume + 3 H2 3 volumes → 2 NH3 2 volumes 1. Students write balanced equation for reaction. Note balancing coefficients are same as volume in Liters.

Gay Lussac’s Law of Combining Volumes When measured at the same temperature and pressure, the ratio of the volumes of reacting gases are small whole numbers.

Avogadro’s Law Equal volumes of different gases at the same temperature and pressure contain the same number of molecules.

22.4 L at STP is known as the molar volume of any gas. Mole-Mass-Volume Relationships Volume of one mole of any gas at STP = 22.4 L. 22.4 L at STP is known as the molar volume of any gas.

atmospheres nT V a P Number of molecules or moles affects other three quatities. Increase #, increase collision rate, increase pressure.

Determination of Density Using the Ideal Gas Equation Density = mass/volume Density varies directly with molar mass and pressure and inversely with Kelvin temp D = MP/ RT

Mole fraction (X): Ratio of moles of one component to the total moles in the mixture (dimensionless, similar to a %) Ex: What are the mole fractions of H2 and He in the previous example?

Collecting Gases “over Water” When a gas is bubbled through water, the vapor pressure of the water (partial pressure of the water) must be subtracted from the pressure of the collected gas: PT = Pgas + PH2O ∴ Pgas = PT – PH2O See Appendix B for vapor pressures of water at different temperatures.

Graham’s Law of Effusion The rates of effusion of gases at the same temperature and pressure are inversely proportional to the square roots of their molar masses. Rate of effusion of A = MB Rate of effusion of B MA M = molar masses, density of a gas varies directly with molar mass, can replace molar mass with density