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## Monday, December 4, 2017

### Behavior of Gases

Boyle’s Law: Boyle's lawstates that the absolute pressure and volume of a given mass of confined gas are inversely proportional, if the temperature remains unchanged within a closed system.

Mathematically, V ∝ 1/p; when temperature T is constant
Or V = K./p
Thus PV = K where K is constant
P1V1 = P1V1

Charle’s Law - Assuming that pressure remains constant, the volume and absolute temperature of a certain quantity of a gas are directly proportional.

Mathematically, this can be represented as:
Temperature = Constant x Volume
or
Volume = Constant x Temperature
or
Volume/Temperature = Constant

Substituting in variables, the formula is:
V/T=K

Because the formula is equal to a constant, it is possible to solve for a change in volume or temperature using a proportion:
V/T = V1/T1

Gay Lussac’s Law - The ratio of the volumes of gases consumed or produced in a chemical reaction is
equal to the ratio of simple whole numbers (coefficients in the balanced equation).

e.g.  Carbon monoxide combines with oxygen in a 2:1 ratio by volume

Avogadro's Hypothesis- The Volume of a gas is directly proportional to the moles of the gas, n at constant P and T.

V ∝ n

The hypothesis that equal volumes of different gases at the same temperature
and pressure contain the same number of particles.

Ideal Gas Law - An ideal gas is defined as one in which all collisions between atoms or molecules are perfectly eleastic and in which there are no intermolecular attractive forces. One can visualize it as a collection of perfectly hard spheres which collide but which otherwise do not interact with each other. In such a gas, all the internal energy is in the form of kinetic energy and any change in internal energy is accompanied by a change in temperature.

Ideal Gas Law : PV = nRT = NkT

An ideal gas can be characterized by three state variables: absolute pressure (P), volume (V), and absolute temperature (T). The relationship between them may be deduced from kinetic theory and is called the

n = number of moles
R = universal gas constant = 8.3145 J/mol K
N = number of molecules
k = Boltzmann constant = 1.38066 x 10-23 J/K = 8.617385 x 10-5 eV/K
k = R/NA
NA = Avogadro's number = 6.0221 x 1023 /mol

Diffusion of Gases- Inter mixing of two or more gases to form a homogeneous mixture without any chemical change is called "DIFFUSION OF GASES" . Diffusion is purely a physical phenomenon. Gases diffuse very quickly due to large empty spaces among molecules. Different gases diffuse with different rates (velocities).

Graham’s Law of Diffusion - Graham's law, known as Graham's law of effusion, was formulated by Scottish physical chemist Thomas Graham in 1846. Graham found experimentally that the rate of effusion of a gas is inversely proportional to the square root of the mass of its particles. This formula can be written as:

Rate (R1/R2) =√(M2/M1)

where:

Rate1 is the rate of effusion of the first gas (volume or number of moles per unit time).
Rate2 is the rate of effusion for the second gas.
M1 is the molar mass of gas 1
M2 is the molar mass of gas 2.

Dalton's Law of Partial Pressure:
The pressure of a mixture of gases is equal to the sum of the pressures of all of the constituent gases alone.

Mathematically, this can be represented as:
P Total = P1 + P 2 ... Pn