Transcript Boyle's Law
Gas Laws Boyle’s Law • Volume and pressure are inversely related at constant temperature • P1V1 = P2V2 @ constant T Boyle’s Law and Kinetic Theory • If the average speed of the molecules stays the same… • and the tank volume increases… • the molecules hit the sides of the container less often. Absolute Temperature • Absolute temperature is measured in Kelvins (K) • One Kelvin is equal in size to one Celsius degree o • K = C + 273 o • C = K - 273 Charles’s Law • Volume and temperature are directly related at constant pressure • V1/T1 = V2/T2 @ constant P Charles’s Law and Kinetic Theory • If the number of collisions stays the same… • and the tank volume increases… • the molecules must be moving faster on average. Gay-Lussac’s Law • Pressure and temperature are directly related at constant volume • P1/T1 = P2/T2 @ constant V Gay-Lussac’s Law and Kinetic Theory • If the volume of the container stays the same… • and the molecules are moving faster on average… • the molecules must be colliding with the walls of the container more often and with more force. PV PV 11 2 2 T T 1 2 Combined Gas Law • A combination of Boyle’s, Charles’s, and Gay-Lussac’s Laws, where nothing need be held constant P1V 1 P 2V 2 T1 T2 Gas Laws Avagadro’s Hypothesis • Equal volumes of gases contain equal numbers of moles (n) when compared at the same temperature and pressure • molar volume of “any” gas: 1 mol = 22.4L @ STP • If P, V & T are the same, then n is the same (constant) PV n T PV nR or, PV nRT T Ideal Gas Law • Combines all four key physical properties of gases • PV = nRT • R = 0.082 (atm)(L)/(mol)(K) • R = 8.31 (kPa)(L)/(mol)(K) • R = 62.4 (mmHg)(L)/(mol)(K) R= R= R= (atm)(L) 0.082 /(mol)(K) (kPa)(L 8.31 )/(mol)(K) 62.4 (mmHg)(L)/(mol)(K) •STP: T=273K •P= 101.3 kPa • = 1.0 atm • = 760 mmHg Dalton’s Law of Partial Pressures • The total pressure of a mixture of gases is the sum of the partial pressures of the individual gases • PT = P1 + P2 + P3 + ....... Dalton’s Law Effusion • Effusion is the movement of gas molecules through an extremely tiny opening into a region of lower pressure • helium escaping a balloon • air leaking from a tire Diffusion • Diffusion is the tendency of molecules to move toward areas of lower concentration until the concentration is uniform throughout the system • mixing of gases Graham’s Law of Effusion • The rate of effusion (or diffusion) of a gas is inversely proportional to the square root of its molar mass (at constant T and P). • Molecules of lower molar mass diffuse and effuse faster. • Due to kinetic energy considerations (KE = 1/2mv2), when two bodies of different mass have the same kinetic energy (~ same T), the lighter body moves faster.