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Gas Laws. Boyle’s Law. Volume and pressure are inversely related at constant temperature P 1 V 1 = P 2 V 2 @ constant T. Boyle’s Law and Kinetic Theory. If the average speed of the molecules stays the same…
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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 • K = oC + 273 • oC = 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.
Combined Gas Law • A combination of Boyle’s, Charles’s, and Gay-Lussac’s Laws, where nothing need be held constant
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
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 = 0.082 (atm)(L)/(mol)(K) • R = 8.31 (kPa)(L)/(mol)(K) • R = 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 + .......
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.