There are the six different derivations of gas law as below;
BOYLE’S LAW
What is Boyle’s law?
PV(pressure and Volume) is constant at a constant temperature. It is Boyle’s law.
When increasing temperature, the molecular velocities also increase. According to the kinetic theory, the absolute Temperature (T) of gas is proportional to the mean kinetic energy, ½ mc2 per molecule.
At constant temperature, any gas’s mean kinetic energy per molecule (½ mc2 ) remains constant. Kinetic gas equation;
Now, the mass of gas is definite under consideration, and the number of molecules N of the gas is also constant.
At constant temperature, the quantity on the right side of equation (1) remains constant.
PV = constant
CHARLE’S LAW
What is Charle’s law?
At constant temperature, the volume of a gas mass is direct as the Absolute Temperature. It is Charle’s law.
The quantity of gas is definite (i.e., N = Constant) equation (1) at constant pressure write as,
At 1/2 mc2 quantity is a mean kinetic energy per molecule at different temperatures (T)
V ∝ T (At constant pressure)
AVOGADRO’S LAW
What is Avogadro’s law?
An identical number of all gases under the exact condition of Temperature and pressure have an equal number of molecules—it is Avogadro’s law.
For any two gases, a kinetic energy equation written as,
and
If the pressure and volume of two gases are the same, It is P1 =P2 and V1 =V2, and it follows that,
At the same temperature, two gases are also the same, and the mean molecular kinetic energy of each gas is the same,
Equation (3) divided by equation (4), we get,
IDEAL GAS EQUATION
Boyle’s law, Charle’s law, and Avogadro’s law combine three laws and find that the volume of gas depends on the pressure, Temperature, and number of moles, as below,
V ∝1/P (At constant Temperature & Number of moles) (Boyle’s law)
V ∝T (At constant pressure & Number of moles) (Charle’s law)
V∝ n (At constant Temperature & pressure) (Avogadro’s law)
V should be directly proportional to the product of the three terms, i.e.,
V ∝ nT/P
= R(nT/P)
Or
PV = nRT ——–(5)
Here, R = proportionality constant or Gas constant
The above equation (5) is known as the Ideal gas equation.
GRAHAM’S LAW OF DIFFUSION
What is Graham’s law of diffusion?
The gas diffusion rate is inversely proportional to the square root of gas density at a constant pressure it is Graham’s law of diffusion.
When PV = 1/3 mNC2 according to the kinetic energy gas equation,
Therefore, mN/V = total mass of gas/ volume = density of the gas (ρ)
The rate of diffusion [r] of gas will depend upon the mean velocity of molecules,
(at constant pressure)
DALTON’S LAW OF PARTIAL PRESSURES
N1 molecules have mass m1 of a gas A and are in a vessel of volume V. According to the kinetic equation, the pressure Pa of gas is,
C1 = root mean square velocity of molecules of gas A
Now, N2 molecules have mass m2 of other gas B, filled in the same vessel at identical Temperatures. No other gas was present at that time pressure Pb of this gas,
Here, C2 = root mean square velocity of molecules of gas B.
Both gases are present in the same vessel at the same time, total pressure P,
= Pa + Pb
For same, three, four or more gases are present, total pressure by,
It is Dalton’s law of partial pressures.
