Gas Law Calculations V PV = k T = k PV = nRT PV T = k Boyle’s Law Charles’ Law V T = k P and V change n, R, T are constant Ideal Gas Law PV = nRT T and V change P, n, R are constant Gas Law Calculations P, V, and T change n and R are constant Combined Gas Law PV T = k

Gas Law Calculations P1V1 = P2V2 V1 = V2 PV = nRT P1V1 = P2V2 T1 = T2 Boyle’s Law P1V1 = P2V2 Bernoulli’s Principle Fast moving fluids… create low pressure Avogadro’s Law Add or remove gas Manometer Big = small + height Charles’ Law T1 = T2 V1 = V2 Combined T1 = T2 P1V1 = P2V2 Ideal Gas Law PV = nRT Graham’s Law diffusion vs. effusion Gay-Lussac T1 = T2 P1 = P2 Any set of relationships between a single quantity (such as V) and several other variables (P, T, n) can be combined into a single expression that describes all the relationships simultaneously. The following three expressions V  1/P (at constant n, T) V  T ( at constant n, P) V  n (at constant T, P) can be combined to give V  nT or V = constant (nT/P) • The proportionality constant is called the gas constant, represented by the letter R. • Inserting R into an equation gives V = RnT = nRT P P Multiplying both sides by P gives the following equation, which is known as the ideal gas law: PV = nRT • An ideal gas is defined as a hypothetical gaseous substance whose behavior is independent of attractive and repulsive forces and can be completely described by the ideal gas law. • The form of the gas constant depends on the units used for the other quantities in the expression — if V is expressed in liters (L), P in atmospheres (atm), T in kelvins (K), and n in moles (mol), then R = 0.082057 (L•atm)/(K•mol). • R can also have units of J/(K•mol) or cal/(K•mol). A particular set of conditions were chosen to use as a reference; 0ºC (273.15 K) and 1 atm pressure are referred to as standard temperature and pressure (STP). The volume of 1 mol of an ideal gas under standard conditions can be calculated using the variant of the ideal gas law: V = nRT = (1 mol) [0.082057 (L•atm)/(K•mol)] (273.15 K) = 22.41 L P 1 atm • The volume of 1 mol of an ideal gas at 0ºC and 1 atm pressure is 22.41 L, called the standard molar volume of an ideal gas. • The relationships described as Boyle’s, Charles’s, and Avogadro’s laws are simply special cases of the ideal gas law in which two of the four parameters (P, V, T, n) are held fixed. Density T1D1 = T2D2 P1 = P2 Dalton’s Law Partial Pressures PT = PA + PB 1 atm = 760 mm Hg = 101.3 kPa R = 0.0821 L atm / mol K

History of Science Gas Laws Gay-Lussac’s law Dalton announces his atomic theory Avagadro’s particle Number theory Boyle’s law Charles’s law 1650 1700 1750 1800 1850 Mogul empire in India (1526-1707) Constitution of the United States signed U.S. Congress bans importation of slaves United States Bill of Rights ratified Napoleon is emperor(1804- 12) Latin American countries gain independence (1791- 1824) Haiti declares independence Herron, Frank, Sarquis, Sarquis, Schrader, Kulka, Chemistry, Heath Publishing,1996, page 220

Scientists Evangelista Torricelli (1608-1647) Published first scientific explanation of a vacuum. Invented mercury barometer. Robert Boyle (1627- 1691) Volume inversely related to pressure (temperature remains constant) Jacques Charles (1746 -1823) Volume directly related to temperature (pressure remains constant) Joseph Gay-Lussac (1778-1850) Pressure directly related to temperature (volume remains constant)

Gas Demonstrations Gas: Demonstrations Gas: Demonstrations Eggsplosion Effect of Temperature on Volume of a Gas VIDEO Effect of Temperature on Volume of a Gas VIDEO Air Pressure Crushes a Popcan VIDEO Air Pressure Crushes a Popcan VIDEO Gas:  Demonstrations Air Pressure Inside a Balloon (Needle through a balloon) VIDEO Air Pressure Inside a Balloon (Needle through a balloon) VIDEO Effect of Pressure on Volume (Shaving Creme in a Belljar) VIDEO Effect of Pressure on Volume (Shaving Creme in a Belljar) VIDEO http://www.unit5.org/chemistry/GasLaws.html