Gases Chapter 5

What you need to know… PV = nRT for gas stoichiometry Partial pressures for kinetics and equilibrium later Water vapor pressure calculations KMT for explaining behavior of atoms/molecules in Gas laws (esp. graham’s law) Differences between real and ideal gases (spec. what causes deviations from ideal behavior)

Pressure & Temperature Force per unit of area Standard pressure is 1 atm (760 mmHg, 760 torr, kPa) Standard temp is 0 o C (273 K) ALL gas calculation must be done in K!!!

Gas Laws Boyle’s: P 1 V 1 = P 2 V 2 ; as pressure goes up, volume goes down (T & n stay constant) Charles’: V 1 /T 1 = V 2 /T 2 ; as temp goes up, volume goes up (P & n stay constant) Gay-Lussac’s: P 1 /T 1 = P 2 /T 2 ; as temp goes up, pressure goes up (V & n stay constant) Avogadro’s: V 1 /n 1 = V 2 /n 2 ; as number of moles goes up, volume goes up (P & T stay constant)

More gas laws Avogadro’s other law: one mole of any gas at STP will have a volume of 22.4 L Combined: P 1 V 1 /T 1 = P 2 V 2 /T 2 (n stays constant) One final law…

Ideal Gas Law PV = nRT or PVM = mRT or MP = DRT Where: P = pressure (atm) V = volume (L) n = number of moles (mol) R = ideal gas constant ( L atm / mol K T = temp (K) M = molar mass (g/mol) m = mass (g) D = density (g/L)

Ideal v. Real Gases Ideal gas law is only an approximation of gas behavior b/c there is no such thing as an ideal gas Most gases behave close to ideal when the pressure is below 1 atm and the temp is above 25 o C non-polar gases behave more ideal than polar Smaller gases behave more ideal than larger ones

Ideal Practice Gasoline is a mixture of many hydrocarbon compounds, but its chemical formula can be approximated as C 8 H 18. How many liters of carbon dioxide gas are formed at 25.0 o C and 712 torr when 3.80 L of liquid gasoline is burned in excess oxygen? Liquid gasoline has a density of g/mL.

Partial Pressures Dalton figured out that because gas particles are so spread out, even when mixed with other gases they don’t really interact, so their respective pressures simply add up. P total = P 1 + P 2 + P 3 + … There’s also mole fraction: X 1 = n 1 /n t and ideal gas: P 1 = n 1 RT/V and partial pressure again: P 1 = P t (n 1 /n t )

What was all that stuff again? Mole fraction – ratio of moles of a specific gas to total moles of gas in a mixture Why is pressure the only thing affected by all these gases? Because volume and temp are the same for all gases in the same container, only pressure adds up

Partial Pressures practice A mixture of 9.00 g of oxygen, 18.0 g of argon, and 25.0 g of carbon dioxide exert a pressure of 2.54 atm. What is the partial pressure of each gas in the mixture?

Water Vapor Pressure The easiest way to collect gas in the lab is over water, but this causes water vapor to be mixed in with the gas. To cancel this out, the water vapor pressure must be added into the mix To figure out the pressure of the gas collected: P atm = P water + P gas

Practice Hydrogen is produced by the action of sulfuric acid on zinc metal and collected over water in a 255 mL container at 24.0 o C and 718 torr. The vapor pressure of water under these conditions is torr. How many moles of hydrogen gas are produced and how many grams of zinc react?

Kinetic Molecular Theory Know the 5 points of the KMT Pressure is caused by gas particles hitting the walls of the container (how often and how hard) Absolute temp is measure if the kinetic energy of the gas particles

Effusion and Diffusion Effusion is gas escaping through a tiny hole Diffusion is random mixing of gases through space/another medium Graham’s law inversely relates effusion rate and molecular mass (heavier gases effuse/diffuse more slowly) r 1 /r 2 = √ (M 1 /M 2 ) where r is rate at which gas effuses (mol/time)

Effusion Practice At a particular temperature and pressure, neon gas effuses at a rate of 16.0 mol/s. What is the rate of effusion for argon under the same conditions? Under a different set of conditions, 3.0 mol of argon effuse in 49.0 seconds. How long will it take and equal amount of helium to effuse?

van der Waals van der Waals equation predict the behavior of real gases at low temp &/or high pressure. you do not need to know the equation, just that it implies more deviation from ideal behavior under the following conditions: large molecular mass low volume/high pressure low temperature

More Practice Arrange the following gases in order of increasing deviation from ideal behavior: H 2 O, CH 4, Ne. Justify your reasoning.