Gas+Laws

Ideal Gas Law
The Ideal Gas Law presumes no intermolecular interactions, i.e. the molar volume is low (atoms are greatly separated). This one law comprises of several other laws (below):

__Avogadro’s Law__: equal volumes of all gases, at a specified temperature and pressure, contain equal numbers of molecules.
 * **Ideal Gas Law** ||
 * **Discoverer** || **Law** || **Relationship** ||
 * Amedeo Avogadro (1811) || Avogadro’s Law || **n** = k**V** ||
 * Robert Boyle || Boyle’s Law || **PV** = constant ||
 * Jacques Charles || Charles’ Law || **V** = c(**T**+273 ||
 * Joseph Louis Gay-Lussac || Gay-Lussac's Law || **P**/**T** = k ||
 * The Law of Multiple Proportions: equal volumes of gases, at the same pressure and temperature, contain the same number of molecules. (A consequence of Avogadro's experiments).

__Boyle’s Law__: given number of moles of gas molecules, the pressure is inversely proportional to the volume if the temperature is held constant.

__Charles’ Law__: at constant pressure the volume of a given number of moles of gas is directly proportional to the absolute temperature.

__Gay-Lussac's Law__: The pressure of a gas of fixed mass and fixed volume is directly proportional to the gas's absolute temperature.

E_k = 3/2 * RT ||
 * **Kinetic Molecular Theory** ||
 * || **Predictions** || **Relationships** ||
 * || Molecular Motion || PV = 2/3 * E_k
 * || Molecular Speed || V_rms = (3RT/M)^0.5 ||
 * || Mean free path ||  ||
 * || Collision frequency ||  ||
 * //Transport Properties// || Diffusion || J = -D (del) phi ||
 * ^  || Viscosity || Tau = mu * gamma dot ||
 * ^  || Thermal Conductivity ||   ||

Molecular Motion: temperature is a measure of the motion of molecules

Molecular Speed: kinetic energy that is directly related to temperature

Mean free path: the distance a molecule travels between two successive collisions Collision frequency: commonness of collisions

Diffusion: mass diffuses from regions of high to low concentration, or down a concentration gradient.

Viscosity: slowly moving molecules diffuse into (and retard) rapidly moving fluid layers, and faster molecules diffuse into (and accelerate) the slow regions.

Thermal Conductivity: is the scattering of rapidly moving molecules into regions of slower ones.


 * **Discoverer** || **Law** || **Relationship** ||
 * John Dalton || Law of Partial Pressures || P = p_1 + p_2 + … = Sigma_j p_j ||
 * Thomas Graham (1846) || Law of Effusion || Rate_2/Rate_1 = v_2/v_2 = (M_1/M_2)^0.5 ||

__Law of Partial Pressures__: each component of a gas mixture behaves as if it were the only gas present.Therefore, the total pressure, is the sum of the partial pressures of the individual components of a gas mixture.

__Law of Effusion__: the rates of effusion of gases are inversely proportional to the square roots of their densities

Real Gases
Of course real gas molecules do interact. Therefore, there is a deviation from the ideal case where Z = PV/RT = 1. If Z < 1, the molecules attract. If Z < 1, the molecules repel. There are a number of equations to describe real gases. Most notably perhaps are equation proposed by van der Waals.

His equations account for the constant volume occupied by molecules (b) in a confined container that is unavailable to other molecules. Thus the real volume (V') is V' = V - b. Also, the energy of colliding molecules against the container walls is attenuated by the attractive force (a) between molecules. Therefore, //pressure is reduced in a real gas due to intermolecular attraction//. When the intermolecular attraction is included, the real pressure (P') is corrected a relation proportional to the inverse square of the volume: P' = P + a/V^2. The complete van der Waals equation is:

(P + a/V~^2)(V~ - b) = RT

Where V~ is the molar volume V~ = V/n. Constants a and b and chosen empirically and tabulated for several gases. b is related to the excluded volume which suggests that the true collision between two identical atoms is limited by distance between nuclei (a full diameter), thus the excluded interaction volume is proportional to the cube of an atomic diameter.

Pressure: the bombardment of gas molecules against a surface. P = F/A

Temperature: heat generated as atomic motion increases by compression.

k is normalized bu unit of 1. R is normalized by a unit of 6.02 x 10^-23 by chemists.