Unit 6 Gas Laws

5.1 Pressure P = Force / Area Gas pressure is created when gas molecules run into impermeable surfaces. Pressure is measured by a barometer. 1 atm = 760 mm Hg = 760 torr = 14.7 psi 1 atm = 101,325 Pa Pa = N / m2

5.2 Boyle, Charles, and Avogadro These laws are derived from simple gas experiments. We did tests on all of these last year (remember the wooden blocks and syringes). Now you do need to remember the laws and whose is whose.

5.2 Boyle’s Law PV = k This is an inverse relationship (as one variable increases the other decreases). Only holds true at low pressures (pressures we can create in lab). Temperature is held constant. Can be used to predict changes in pressure and volume.

Example Ne is found in some fluorescent lighting. If a light bulb has a volume of 500 mL at sea level, but is transported to the Rocky Mountains where the pressure is 80% that of sea level, what will be the new volume of the gas? (625 mL)

5.2 Charles’s Law V / T = k Remember to use Kelvin (K = oC + 273) Absolute zero can be extrapolated from this formula. EC if you can figure out how to find absolute zero. Do I really need to do an example?

Example Sure I do!!!! Volume is 12.3 L and the temperature is 100 oC. What is the new volume if the temperature is decreased to 0 oC? (9.0 L)

Gay-Lussac Law P / T = k Remember to use Kelvin (K = oC + 273) Absolute zero can be extrapolated from this formula. EC if you can figure out how to find absolute zero.

5.2 Avogadro’s Law Guessed that equal volumes of gases at equal temperature and pressure will contain an equal number of particles. So…….V = kn, where n = moles. Number of moles is proportional to volume (at equal temp and pressure)

5.3 The Ideal Gas Law PV = nRT P = atm, V = Liters, n = moles, R = 0.08206, T = Kelvin. Can be used for the other laws, just move everything that is constant to one side.

Example A sample of diborane gas (B2H6), a substance that bursts into flame when exposed to air, has a pressure of 345 torr at a temperature of -15oC and a volume of 3.48 L. If conditions are chaged so the temperature is 36oC and the pressure is 468 torr, what will be the volume of the sample? (3.07 L) COMBINED GAS LAW P1 V1 T2 = P2 V2 T1 V2 = P1 V1 T2 / (P2 T1 ) V2 = (345 x 3.48 x 309) / (468 x 258)

5.4 Gas Stoichiometry. STP: 1 atm and 273 K 1 mole of any gas takes up 22.42 L. Molar Mass = dRT / P

Example The density of a gas was measured at 1.50 atm and 32oC and found to be 2.01 g/L. Calculate the molar mass of the gas. (33.6 g /mol)

5.5 Dalton’s Law of Partial Pressures The total pressure exerted is the sum of the pressures that each gas would exert if it were alone. Ptotal = P1 + P2 + P3 + … If the gas behaves ideally, then nRT/V can be substituted in for P. Mole Fraction: the ratio of the number of moles of a given component in a mixture to the total number of moles in the mixture.

Example The partial pressure of oxygen was observed to be 200 torr in a hyperbaric chamber which had a total pressure of 800 torr. Calculate the mole fraction of oxygen present. (.25)

Collecting gas over water. When gas is collected over water some of the water molecules escape into the gas. So….Pexperiment = Pgas + Pwater This is also called the vapor pressure of water and it varies with temperature. This is important for yesterday's lab.

5.6 Kinetic Molecular Theory of Gases This model explains why the ideal gas law works. Gas particles are so small and the distance between them is so large, that the volume of the individual particles can be said to be zero. The particles are in constant motion. Collisions with the container cause gas pressure. The particles do not interact with one another. The average kinetic energy of a collection of gas particles is proportional to the temperature of the gas in Kelvin.

Hold on!!!! These do not hold true as gases do have volume and the particles to interact. But…….the theory does a really good job at low pressures (at or near 1 atm). The four laws we just heard about verify this theory.

Four Laws Boyle’s Charles’s: As temp increases, volume increases. As volume decreases, pressure increases. Charles’s: As temp increases, volume increases. Gay-Lussac: As temp increases, pressure increases. Avogadro’s The volume depends on the number of particles. Dalton’s If more particles are added to an expandable system, the system will expand to return to the original pressure.

Boyle’s Law

Charles’s Law

Avogadro’s Law

Temperature The temperature of a gas is proportional to the average kinetic energy of its particles. This holds true for all gases. R = 8.3145 J/K  mol KE is in J/mole

However, The average kinetic energy (which equals ½ mv2) is related to the molar mass of the gas in question. Therefore, under constant conditions, gases with lower masses will travel at high velocities.

Root Mean Square Velocity The equation provides the average velocity of a gas’s particles at a given temperature. M = mass in kg of the gas multiplied by Avogadro’s number (mass of one mole or molar mass)

5.7 Effusion and Diffusion Diffusion is the mixing of gas particles in a space. Chipotle, elevator full of people…are we getting this? Effusion is used to describe the passage of gas through a tiny orifice. Law of Effusion determined by Graham.

5.8 Real Gases Real gases have particles with volume Real gases have particles that interact with one another. The more polar a gas is (such as NO or NO2) the more it interacts with itself or other gases. Some example gases and amount of IM interaction. H2 < N2 < CH4 < CO2