Unit 8 Gases

Overview Characteristics of Gas Pressure Gas Laws Ideal Gases Partial Pressures Mole Fractions Gas Laws Boyles Law Charles Law Avogadro’s Law Guy-Lussac’s Law Ideal Gas Law Ideal Gases Real Gases Density of Gases Volumes of Gases Standard molar volume Gas stoichiometry Effusion/Diffusion Graham’s Law

Characteristics of Gases Expansion – gases expand to fill their containers Compression – gases can be compressed Fluids – gas particles flow past each other Density – gases have low density 1/1000 the density of the equivalent liquid or solid Gases effuse and diffuse

Kinetic Molecular Theory Gases consist of large numbers of tiny particles that are far apart relative to their size. Collisions between gas particles and between particles and container walls are elastic. Elastic collision – collision in which there is no net loss of kinetic energy Gas particles are in continuous, rapid, random motion. They therefore possess kinetic energy. There are no forces of attraction between gas particles. The temperature of a gas depends on the average kinetic energy of the particles of the gas.

Kinetic Energy of Gas Particles At the same conditions of temperature, all gases have the same average kinetic energy m = mass v = velocity At the same temperature, small molecules move FASTER than large molecules

Speed of Molecules V = velocity of molecules M = molar mass R = gas constant T = temperature

Pressure A force that acts on a given area Pressure = Force Area

Measuring Pressure The first device for measuring atmospheric pressure was developed by Evangelista Torricelli during the 17th century Called a barometer The normal pressure due to the atmosphere at sea level can support a column of mercury that is 760 mm high

Units of Pressure 1 atmosphere (atm) 760 mm Hg (millimeters of mercury) 760 torr 1.013 bar 101300 Pa (pascals) 101.3 kPa (kilopascals) 14.7 psi (pounds per square inch)

Temperature

STP Standard Temperature and Pressure (STP) 1 atmosphere 273 K

Dalton’s Law of Partial Pressures Partial pressure – pressure exerted by particular component in a mixture of gases Dalton’s Law states that the total pressure of a gas mixture is the sum of the partial pressures of the component gases Pt = P1 + P2 + P3+…

Mole Fraction P1 = Pt or P1 = X1Pt X1 = mole fraction of gas 1 Mole fraction – expresses the ratio of the number of moles of one component to the total number of moles in the mixture P1 = Pt or P1 = X1Pt X1 = mole fraction of gas 1 Example: The mole fraction of N2 in air is 0.78 (78% of air is nitrogen). What is the partial pressure of nitrogen in mmHg? PN2 = (0.78)(760 mmHg) = 590 mmHg

Collecting Gas Over Water Gas collected by water displacement is always mixed with a small amount of water vapor Must account for the vapor pressure of the water molecules Ptotal = Pgas + PH2O Note: The vapor pressure of water varies with temperature

The Gas Laws Robert Boyle Amadeo Avogadro Joseph Louis Gay-Lussac Jacques Charles

Boyles Law Pressure is inversely proportional to volume when temperature is held constant.

Temperature MUST be in KELVINS! Charles Law The volume of a gas is directly proportional to temperature. (P = constant) Temperature MUST be in KELVINS!

Temperature MUST be in KELVINS! Gay-Lussac’s Law The pressure and temperature of a gas are directly related, provided that the volume remains constant. Temperature MUST be in KELVINS!

Combined Gas Law Expresses the relationship between pressure, volume and temperature of a fixed amount of gas

For example, doubling the moles will double the volume of a 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 = constant × n V = volume of the gas n = number of moles of gas For example, doubling the moles will double the volume of a gas

Ideal Gases Imaginary gases that perfectly fit all of the assumptions of the kinetic molecular theory

Ideal Gas Law PV = nRT P = pressure V = volume n = moles R = ideal gas constant T = temperature (Kelvin) Numerical Value of R Units 0.0821 (atm∙L)/(mol∙K) 8.314 J/(mol∙K) 62.4 (mmHg∙L)/(mol∙K) Note: 1 J = 1 Pa∙m3

Standard Volume STP of 1 mole of gas = 1 atm and 273K PV = nRT (1atm)(V) = (1mol)(.0821)(273) V = 22.4 L Volume of 1 mole of gas at STP = 22.4 liters

Real Gases Real Gas – does not behave completely according to the assumptions of the kinetic molecular theory At high pressure (smaller volume) and low temperature gases deviate from ideal behavior Particles will be closer together so there is insufficient kinetic energy to overcome attractive forces

Real Gases The Van der Waals Equation adjusts for non-ideal behavior of gases (p. 423 of book) ­ ­ corrected pressure corrected volume Pideal Videal

Density of Gases … so at STP…

Density of Gases Combine density with the ideal gas law (V = p/RT) M = Molar Mass P = Pressure R = Gas Constant T = Temperature in Kelvins

Gas Stoichiometry #1 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 #2 3 H2(g) + N2(g)  2NH3(g) How many liters of ammonia can be produced when 12 liters of hydrogen react with an excess of nitrogen? 3 H2(g) + N2(g)  2NH3(g) 12 L H2 2 L NH3 = L NH3 8.0 3 L H2

Gas Stoichiometry #3 How many liters of oxygen gas, at STP, 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 22.4 L O2 122.55 g KClO3 2 mol KClO3 1 mol O2 = 13.7 L O2

Stoichiometry #4 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 = 16.7 L

Diffusion Spontaneous mixing of two substances caused by the random motion of particles The rate of diffusion is the rate of gas mixing The rate of diffusion increases with temperature Small molecules diffuse faster than large molecules

Effusion Process by which gas particles pass through a tiny opening

Graham’s Law of Effusion Rate of effusion of gases at the same temperature and pressure are inversely proportional to the square roots of their molar masses. M1 = Molar Mass of gas 1 M2 = Molar Mass of gas 2