Gas behavior is all about molecular motion. Pressure comes from molecules hitting container walls, while temperature relates to their average kinetic energy. The ideal gas law connects these macroscopic properties to the microscopic world of molecules.
Gases in mixtures exert partial pressures, adding up to the total pressure. Molecules constantly collide, with their mean free path and depending on conditions. The describes the range of molecular speeds in a gas.
Kinetic Theory of Gases
Microscopic vs macroscopic gas properties
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9.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law – Chemistry View original
Pressure caused by gas molecules colliding with container walls
Directly proportional to number of collisions per unit time and average force per collision
Example: higher pressure in a tire due to more frequent and forceful collisions of air molecules with tire walls
Temperature related to average kinetic energy of gas molecules
Higher temperature means higher average kinetic energy and faster moving molecules
Example: molecules in a hot air balloon move faster than those in a cold room
Systems in have the same temperature and average kinetic energy
(vrms) measures average speed of gas molecules
Calculated using , where k is Boltzmann constant, T is absolute temperature, and m is mass of a single molecule
Example: of nitrogen molecules at room temperature (20℃) is about 511 m/s
Ideal gas law [PV = nRT](https://www.fiveableKeyTerm:PV_=_nRT) relates pressure (P), volume (V), number of moles (n), gas constant (R), and absolute temperature (T)
Describes behavior of ideal gases under various conditions
Example: increasing temperature of a gas in a closed container increases its pressure
The number of molecules in one mole of any substance is given by
Partial pressures in gas mixtures
###'s_Law_0### states total pressure of a gas mixture is sum of partial pressures of each component gas
, where P1,P2,...,Pn are partial pressures of each gas in mixture
Example: in air, of oxygen is about 21% of total atmospheric pressure
of a gas in a mixture is pressure gas would exert if it occupied entire volume alone
Calculated using , where Pi is partial pressure of gas i, xi is of gas i, and Ptotal is total pressure of mixture
Example: in a 60% nitrogen, 40% oxygen mixture at 1 atm total pressure, partial pressure of nitrogen is 0.6 atm and oxygen is 0.4 atm
Molar fraction is ratio of number of moles of a particular gas to total number of moles in mixture
Calculated using , where ni is number of moles of gas i and ntotal is total number of moles in mixture
Example: in a mixture of 3 moles of helium and 1 mole of neon, molar fraction of helium is 0.75 and neon is 0.25
Molecular motion in gases
Mean free path (λ) is average distance a molecule travels between collisions
Calculated using λ=2πd2n1, where d is diameter of molecule and n is number density (molecules per unit volume)
Example: mean free path of air molecules at room temperature and pressure is about 68 nm
Collision frequency (z) is average number of collisions per unit time for a single molecule
Calculated using , where d is diameter of molecule, n is number density, and vrms is
Example: collision frequency of nitrogen molecules at room temperature and pressure is about 7×109 collisions per second
Higher pressure and temperature lead to:
Shorter mean free paths due to more molecules in a given volume
Higher collision frequencies due to faster moving molecules
Example: in a high-pressure gas cylinder, molecules have shorter mean free paths and higher collision frequencies compared to the same gas at atmospheric pressure
Statistical distribution of molecular speeds
The describes the probability distribution of molecular speeds in a gas
The states that energy is equally distributed among all degrees of freedom in a system
is the net movement of particles from regions of high concentration to low concentration
occurs when gas molecules escape through a small hole in a container