Chapter 5 - Gases DE Chemistry Dr. Walker

Properties of Gases Gases expand to fill their containers Gases are fluid – they flow Gases have low density 1/1000 the density of equivalent moles of liquid or solid Gases are compressible

It’s all in your mind… Ideal gases are imaginary gases that fit all of the assumption of the kinetic molecular theory Gases consist of tiny particles that are far apart relative to their size (this is true…) Collisions between gas particles and between particles and the container walls are elastic (lose no kinetic energy in the process)….our big assumption!

More on Ideal Gases Gas particles are in constant, rapid motion and possess kinetic energy as a result There are no forces of attraction between gas particles (assumption….the attractions are small, but present) The average kinetic energy of gas particles depends on temperature, not the identity of the particle (partially true….but still an assumption)

You’ve Got Me Under Pressure Force is acceleration of a mass Force is measured in Newtons (N) 1 N = 1 kg x m/s2 Pressure is force exerted over a specific area, in this case, with the walls of a container The SI unit for pressure is the Pascal (Pa) 1 Pa = 1 N/m2

Units of Pressure Unit Symbol Definition/Relationship Pascal Pa SI pressure unit 1 Pa = 1 newton/meter2 Millimeter of mercury mm Hg Pressure that supports a 1 mm column of mercury in a barometer Atmosphere atm Average atmospheric pressure at sea level and 0 C Torr torr 1 torr = 1 mm Hg

Measuring Pressure The first device for measuring atmospheric pressure was developed by Evangelista Torricelli during the 17th century. The device was called a “barometer” “Baro” = weight “Meter” = measure

The Kelvin Scale

Why Kelvin? Remember two things The Kelvin scale is directly proportional to kinetic energy Based on the equations you will learn, negative temperatures can cause calculations yielding negative pressures and/or volumes which are not possible Absolute zero = 0 K = -273 C = -459 F

STP Standard Temperature and Pressure 273 K (0 oC) 1 atm 101.3 kPa 14.7 psi (lbs/in2) 760 mm Hg (760 torr)

Boyle’s Law Pressure is inversely proportional to volume when temperature is held constant. P1V1 = P2V2

Side Note to Boyle’s Law It was the experiments of Boyle that showed that showed that at low pressures PV = constant This constant was equal to 22.4 L . Atm. This is the origin of the 22.4 number you learned last year. Avogadro’s discovery of 1 mole being equal to a equal volume of any gas led to the idea of 1 mole = 22.4 L at STP. It is only valid at STP and low pressures

Charles’ Law The volume of a gas is proportional to Kelvin temperature at constant pressure Extrapolates to zero at zero Kelvin (this has never been accomplished experimentally)

Gay-Lussac’s Law The pressure and temperature of a gas are directly proportional at constant volume Temperature must be in Kelvin

Combining Boyle, Charles, and Gay-Lussac The Combined Gas Law!! Relates temperature, pressure, and volume of a fixed amount of gas

Avogadro’s Law For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas (at low pressures) V = an a = proportionality constant V = volume of gas n = number of moles of gas

Ideal Gas Law Combining Avogadro, Boyle, Charles, and Gay-Lussac…. PV = nRT P = pressure (typically in atm) V = volume in liters n = moles R = universal gas constant (0.08206 L. atm/mol . K) T = temperature (Kelvin) Works best at pressures under 1 atm

Real Gases Pideal Videal At high pressure (smaller volume) and low temperature (attractive forces become important) you must adjust for non-ideal gas behavior using van der Waal’s equation ­ ­ corrected pressure corrected volume Pideal Videal

Gas Density Density = mass/volume For gases this becomes D = molar mass/molar volume (22.4 L @ STP)

Density and the Ideal Gas Law When combining density with the Ideal Gas Law, and rearranging algebraically: M = Molar Mass P = Pressure R = Gas Constant T = Temperature in Kelvins

Gas Stoichiometry If reactants and products are at the same conditions of temperature and pressure, then mole ratios of gases are also volume ratios. 3 H2(g) + N2(g)  2NH3(g) 3 moles H2 + 1 mole N2  2 moles NH3 3 liters H2 + 1 liter N2  2 liters NH3

Gas Stoichiometry Example Example: N2 + 3 H2  2 NH3 How many liters of ammonia could be produced from 6 liters of N2 and excess H2?

Gas Stoichiometry Example Example: N2 + 3 H2  2 NH3 How many liters of ammonia could be produced from 6 liters of N2 and excess H2? 6 L N2 2 L NH3 = 12 moles NH3 1 L N2

Gas Stoichiometry – The Old Way 2 KClO3 (s) 2 KCl (s) + 3 O2 (g) How many liters of oxygen are produced from the decomposition of 244 g KClO3?

Gas Stoichiometry – The Old Way 2 KClO3 (s) 2 KCl (s) + 3 O2 (g) How many liters of oxygen are produced from the decomposition of 244 g KClO3? Using proportion 244 g KClO3 Liters O2 3 mole O2 x 22.4 L O2 2 mole KClO3 x 122.55 g/mole KClO3 Liters O2 = 66.90 L (answer!!)

Gas Stoichiometry – Dimensional Analysis 2 KClO3 (s) 2 KCl (s) + 3 O2 (g) How many liters of oxygen are produced from the decomposition of 244 g KClO3? 244 g KClO3 1 mol KClO3 3 mol O2 22.4 L O2 122.55 g KClO3 2 mol KClO3 1 mol O2 = 66.9 L O2

Gas Stoichiometry Remember that 1 mole = 22.4 L applies ONLY at STP. If the gas exists at another set of conditions, you must use the Ideal Gas Law to find your volume Find volume first if starting with a gas Find volume last if ending with a gas Proportion method doesn’t really work here

Volume of Gas as a Product How many liters of oxygen gas, at 37.0C and 0.930 atmospheres, can be collected from the complete decomposition of 50.0 grams of potassium chlorate? 2 KClO3(s)  2 KCl(s) + 3 O2(g)

Volume of Gas as a Product How many liters of oxygen gas, at 37.0C and 0.930 atmospheres, can be collected from the complete decomposition of 50.0 grams of potassium chlorate? 2 KClO3(s)  2 KCl(s) + 3 O2(g) 50.0 g KClO3 1 mol KClO3 3 mol O2 0.612 = mol O2 122.55 g KClO3 2 mol KClO3

Volume of a Gas as a Reactant How many grams of magnesium can react in a closed container of 1 liter of oxygen gas at 25 oC and 0.980 atm?

Volume of a Gas as a Reactant How many grams of magnesium can react in a closed container of 1.00 liter of oxygen gas at 25 oC and 0.980 atm? 2 Mg + O2 2 MgO Find moles of oxygen with ideal gas law = 0.400 moles

Volume of Gas as a Reactant How many grams of magnesium can react in a closed container of 1.00 liter of oxygen gas at 25 oC and 0.980 atm? 2 Mg + O2 2 MgO Plug into dimensional analysis 0.0400 moles O2 2 mol Mg 24.31 g Mg = 1.95 g Mg 1 mol Mg 1 mol O2

Dalton’s Law of Partial Pressures For a mixture of gases in a container, PTotal = P1 + P2 + P3 + . . . This is particularly useful in calculating the pressure of gases collected over water.

Kinetic Molecular Theory 1. pertaining to motion. 2. caused by motion. 3. characterized by movement: Running and dancing are kinetic activities. Origin: 1850–55; < Gk kīnētikós moving, equiv. to kīnē- (verbid s. of kīneîn to move) + -tikos Source: Websters Dictionary

Properties of Gases Gases expand to fill their containers Gases are fluid – they flow Gases have low density 1/1000 the density of equivalent moles of liquid or solid Gases are compressible

Kinetic Molecular Theory (Ideal Gases) Particles of matter are ALWAYS in motion Volume of individual particles is  zero. Collisions of particles with container walls cause the pressure exerted by gas. Particles exert no forces on each other. Average kinetic energy is proportional to Kelvin temperature of a gas.

Kinetic Energy of Gases At the same conditions of temperature, all gases have the same average kinetic energy. m = mass v = velocity Different gases have different masses, so if KE is the same, the velocities must be different! Smaller mass means higher velocity to reach the same KE At the same temperature, small molecules move FASTER than large molecules

Temperature Kelvin temperature is an index of the random motions of gas particles (higher T means greater motion.) This is derived from the Ideal Gas Law and explained on p. 203-204. The units will not cancel when plugging in numbers.

Diffusion Diffusion describes the mixing of gases. The rate of diffusion is the rate of gas mixing. Diffusion is the result of random movement of gas molecules The rate of diffusion increases with temperature More movement, more diffusion Small molecules diffuse faster than large molecules Faster movement, more overall diffusion

Effusion Effusion: describes the passage of gas into an evacuated chamber.

Graham’s Law of Effusion M1 = Molar Mass of gas 1 M2 = Molar Mass of gas 2