Chapter 13: Gases

13.1 The Gas Laws

Boyle’s Law Robert Boyle (1627-1691) described the relationship between the pressure and the volume of a gas Boyle’s Law states that the volume of a fixed amount of gas held at a constant temperature varies inversely with the pressure P1V1 = P2V2 P1V1 : Initial conditions P2V2 : New conditions

Charles’ Law Jacques Charles (1746-1823) studied the relationship between volume and temperature of a gas As temperature increases particles move faster, striking the walls more frequently and with more force. For the pressure to stay constant the volume must increase. Absolute zero (0 Kelvin) represents the lowest possible theoretical temperature at which atoms are all in the lowest possible energy state.

Charles’ law states that the volume of a given amount of gas is directly proportional to its Kelvin temperature at constant pressure V1/T1 = V2/T2 Temperature must be expressed in Kelvins TK = 273 + TC

Gay-Lussac’s Law Joseph Gay-Lussac found that a direct proportion exists between Kelvin temperature and pressure Gay-Lussac’s law states that the pressure of a fixed amount of gas varies directly with the Kelvin temperature when the volume remains constant P1/T1 = P2/T2

The Combined Gas Law Boyle’s, Charles’, and Gay-Lussac’s laws can be combined into a single law The combined gas law states the relationship between pressure, temperature, and volume of a fixed amount of gas (P1V1)/T1 = (P2V2)/T2 When 5 of the 6 variables are known you can solve for the 6th

13.2 The Ideal Gas Law

Avogadro’s Principle States that equal volumes of gases at the same temperature and pressure contain equal numbers of particles The molar volume of a gas is the volume that one mole occupies at 0.00°C and 1.00 atm pressure These conditions of temperature and pressure are known as standard temperature and pressure (STP) 1 mole of any gas occupies a volume of 22.4 L at STP 22.4 L / 1 mol conversion factor

The Ideal Gas Law Changing the number of gas particles will affect at least one of the other three variables (pressure, volume, temperature) For a specific sample of gas… (PV)/T = constant Both volume and pressure are directly proportional to the number of moles, n, so n can be incorporated into the combined gas law: PV/nT = constant

Units of P Numerical value of R Atm 0.0821 kPa 8.314 mm Hg 62.4 Experiments using known values of P,T, V, and n have determined the value of this constant, called the ideal gas constant (R) The value of R depends on the units of pressure Units of P Numerical value of R Atm 0.0821 kPa 8.314 mm Hg 62.4

Substituting R for the constant in the equation and rearranging the variables provides the ideal gas law: PV= nRT The ideal gas law describes the physical behavior of an ideal gas in terms of pressure, volume, temperature, and number of moles of gas present

The Ideal Gas Law – Molar Mass and Density To find the molar mass of a gas sample, the mass, temperature, pressure, and volume of the gas must be known n = mass (m) / molar mass (M) Therefore the n in the ideal gas law equation can be replaced: M = (mRT)/(PV)

The ideal gas law can be used to find the density of a gas D = mass(m) / volume (V) After rearranging the ideal gas equation to solve for molar mass, you can substitute D and rearrange the equation to solve for density: D = MP/RT

Real versus ideal gases Ideal gases follow the assumptions of the kinetic-molecular theory Particles take up no space Experience no intermolecular attractive forces Constant, random motion Elastic collisions Follows the gas laws under all conditions of temperature and pressure

No gas is truly ideal All gas particles have some volume, however small, and are subject to intermolecular interactions Most gases will behave like ideal gases at a wide range of temperatures and pressures Real gases deviate most from ideal gas behavior at high pressures and low temperatures Amount of space between particles decreases Particle speed decreases Polar gas molecules have larger attractive forces and do not behave as ideal gases Larger gas particles tend to exhibit greater departure from ideal behavior

13.3 Gas Stoichiometry

Stoichiometry of Reactions Involving Gases A balanced chemical equations tells you the molar ratios of substances in a reaction Since Avogadro’s principle states that equal volumes of gases at the same temperature and pressure contain equal numbers of particles the coefficients in a balanced equation also represent relative volumes

Stoichiometry and Volume –Volume Problems To find the volume of a gaseous reactant or product in a reaction, you must know the balanced chemical equation for the reaction and the volume of at least one other gas involved in the reaction The coefficients represent volume ratios for gasses taking part in the reaction

Stoichiometry and Volume –Mass Problems Need to know: Balanced equation At least one mass or volume value for a reactant or product Conditions of the reactions Balanced chemical equation provides ratios for moles and gas volumes All masses must be converted to moles or volumes before being used as part of a ratio Temperature units used must be kelvins