Gases Courtesy of nearingzero.net

Elements that exist as gases at 250C and 1 atmosphere

Physical Characteristics of Gases Gases assume the volume and shape of their containers. Gases are the most compressible state of matter. Gases will mix evenly and completely when confined to the same container. Gases have much lower densities than liquids and solids.

Force Pressure = Area Units of Pressure 1 pascal (Pa) = 1 N/m2 Barometer Pressure = (force = mass x acceleration) Units of Pressure 1 pascal (Pa) = 1 N/m2 1 atm = 760 mm Hg = 760 torr = 101,325 Pa = 14.7 psi = 29.92 in. Hg Measures atmospheric pressure

Atmospheric Pressure Varies with Altitude 10 miles 0.2 atm 4 miles 0.5 atm Sea level 1 atm

Gas Laws of Boyle, Charles, Avogadro, and Gay-Lussac Plus the Combined Gas Law

Boyle’s Law PV = k This means Pressure and Volume are INVERSELY PROPORTIONAL if moles and temperature are constant (do not change). For example, P goes up as V goes down. P1V1 = P2 V2 Robert Boyle Used for changing conditions.

Charles’s Law If n and P are constant, then V α T V and T are directly proportional. V1 V2 = T1 T2 If one temperature goes up, the volume goes up! Jacques Charles

Gay-Lussac’s Law If n and V are constant, then P α T P and T are directly proportional. P1 P2 = T1 T2 If one temperature goes up, the pressure goes up!

Combined Gas Law The good news is that you don’t have to remember all three gas laws! Since they are all related to each other, we can combine them into a single equation. BE SURE YOU KNOW THIS EQUATION! P1 V1 P2 V2 = T1 T2

Avogadro’s Law For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas. Obeyed by gases at low pressure. Amedeo Avogadro

STP allows us to compare amounts of gases between different pressures and temperatures Standard Pressure = 1 atm (or an equivalent) Standard Temperature = 0 deg C (273 K)

Ideal Gas Law 1 Boyle’s law: V a (at constant n and T) P Charles’ law: V a T (at constant n and P) Avogadro’s law: V a n (at constant P and T) These relationships can be combined as follows: V = constant x = R nT P R is the gas constant PV = nRT More familiar form of the Ideal Gas Law

Remember the conditions 0 0C and 1 atm are called standard temperature and pressure (STP). Experiments show that at STP, 1 mole of an ideal gas occupies 22.414 L. PV = nRT R = PV nT = (1 atm)(22.414L) (1 mol)(273.15 K) The gas constant, R, has this value when using pressure is in atm and V is in liters. R = 0.082057 L • atm / (mol • K)

Important! The ideal gas law is best regarded as a limiting law – it expresses behavior that real gases approach at low pressures and high temperatures. Therefore, an ideal gas is a hypothetical substance. Most gases obey the ideal gas law closely enough at pressures below 1 atm that only minimal errors result from assuming ideal behavior.

Molar Mass of a Gas The ideal gas law can be used to calculate the molar mass of a gas from its measured density. d = density of gas T = temperature in Kelvin P = pressure of gas R = universal gas constant

Gas Stoichiometry What is the volume of CO2 produced at 370 C and 1.00 atm when 5.60 g of glucose are used up in the reaction: C6H12O6 (s) + 6O2 (g) 6CO2 (g) + 6H2O (l) g C6H12O6 mol C6H12O6 mol CO2 V CO2 1 mol C6H12O6 180 g C6H12O6 x 6 mol CO2 1 mol C6H12O6 x 5.60 g C6H12O6 = 0.187 mol CO2 0.187 mol x 0.0821 x 310.15 K L•atm mol•K 1.00 atm = nRT P V = = 4.76 L

Dalton’s Law of Partial Pressures V and T are constant P1 P2 Ptotal = P1 + P2 The symbols P1 and P2 represent each partial pressure, the pressure that a particular gas would exert if it were alone in the container.

Dalton’s Law of Partial Pressures For a mixture of gases in a container, the total pressure exerted is the sum of the pressures that each gas would exert if it were alone. PTOTAL = P1 + P2 + P3 + ……. The symbols P1, P2, P3, and so on represent the partial pressure.

Mole Fraction 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. Since the mole fraction of each component in a mixture of ideal gases is directly related to its partial pressure: can be rearranged Thus, the partial pressure of a particular component of a gaseous mixture is the mole fraction of that component times the total pressure.

A sample of natural gas contains 8. 24 moles of CH4, 0 A sample of natural gas contains 8.24 moles of CH4, 0.421 moles of C2H6, and 0.116 moles of C3H8. If the total pressure of the gases is 1.37 atm, what is the partial pressure of propane (C3H8)? P1 = X1 PT PT = 1.37 atm 0.116 8.24 + 0.421 + 0.116 Xpropane = = 0.0132 Ppropane = 0.0132 x 1.37 atm = 0.0181 atm

A mixture of gases results whenever a gas is collected by displacement of water. In this situation, the gas in the bottle is a mixture of water vapor and the oxygen being collected. Bottle full of oxygen gas and water vapor 2KClO3 (s) 2KCl (s) + 3O2 (g) PT = PO + PH O 2 Water vapor is present because molecules of water escape from the surface of the liquid and collect in the space above the liquid.

Kinetic Molecular Theory of Gases Simple model that attempts to explain the properties of an ideal gas. The particles are so small compared with distances between them that the volume of the individual particles can be assumed to be negligible (zero). The particles are in constant motion. The collisions of the particles with the walls of the container are the cause of the pressure exerted by the gas. Gas molecules exert neither attractive nor repulsive forces on one another. The average kinetic energy of a collection of gas particles is assumed to be directly proportional to the Kelvin temperature of the gas. Any two gases at the same temperature will have the same average kinetic energy.

Kinetic theory of gases and … Compressibility of Gases (decreasing the volume) Boyle’s Law (volume is decreased, pressure is increased) decrease in volume = gas particles hit the walls more often = increase pressure Charles’ Law (at constant pressure, volume and temperature are directly proportional) higher temperature = speeds of molecules increase and hit walls more often and with more force = if pressure is kept constant volume must increase

Kinetic theory of gases and … Avogadro’s Law (gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas) increase in number of particles = volume must increase to keep pressure and temperature constant Dalton’s Law of Partial Pressures Molecules do not attract or repel one another P exerted by one type of molecule is unaffected by the presence of another gas Ptotal = SPi

Velocity of a Gas Although the molecules in a sample of gas have an average kinetic energy (and therefore an average speed) the individual molecules move at various speeds, i.e. they exhibit a DISTRIBUTION of speeds; some move fast, others relatively slowly. Collisions change individual molecular speeds but the distribution of speeds remains the same. At the same temperature, lighter gases move, on average, faster than heavier gases.

To into account the distribution of speeds we use the root mean square velocity to determine the average velocity of gases. R = 8.3145 J/K∙mol (molar gas constant) T = temperature in Kelvin M = mass of a mole in kilograms Remember J = kg ∙m2/s2 urms = 3RT M 

Diffusion Gas diffusion is the gradual mixing of molecules of one gas with molecules of another by virtue of their kinetic properties. NH4Cl NH3 17 g/mol HCl 36 g/mol

HCl and NH3 diffuse from opposite ends of tube. Gases meet to form NH4Cl HCl heavier than NH3 Therefore, NH4Cl forms closer to HCl end of tube.

Effusion Effusion – term used to describe the passage of a gas through a tiny orifice into an evacuated chamber.

Graham’s Law of Effusion Rate of effusion measures the speed at which the gas is transferred into the chamber. Rate of effusion of a gas is inversely proportional to the square root of the mass of its particles. Graham’s Law of Effusion Where M1 and M2 represent the molar masses of the gases. Thomas Graham, 1805-1869. Professor in Glasgow and London.

Real Gases We must correct for non-ideal gas behavior when: Pressure of the gas is high. Temperature is low. Under these conditions: Concentration of gas particles is high. Attractive forces become important.

( ) } } Van der Waals equation nonideal gas an2 P + (V – nb) = nRT V2 corrected volume } corrected pressure Correction to ideal gas law to account for real gas behavior. Real gases occupy volume so correction is made to volume. Real gases have attractive forces so pressure must be corrected to account for gas particles hitting walls of container less often.