Gas laws are study of any two of quantities like pressure, volume and temperature, when the third is kept constant
A. Boyle's law
"At constant temperature, the volume of a given mass of gas is inversely proportional to pressure." Thus
V ∝ 1/P
Or, PV = constant(1)
If P_{1}, V_{1}are initial pressure and volumes and P_{2}, V_{2}be final values then,
P_{1}V_{1}= P_{2}V_{2}
Graph between P and V at temperature T_{1} and T_{2} such that T_{1}<T_{2} are shown below,
Graph above shows that Boyle's law is strictly not obeyed by gases at all values of P and T but it obeys this law only at low pressure and high temperature i.e., at law density
B. Charle's Law
Charle's Law is stated as follows :
"When pressure of a gas is constant the volume of a given mass of gas is directly proportional to its absolute temperature".
V/T = Constant(2)
Graph between V and T is
This graph shows that experimental graph deviates from straight line. Theoretical and experimental graphs are in agreement at high temperature.
Ideal gas equation
We can combine Boyle' law eqn (1) and Charle's' law eqn (2) in to a single eqn i.e.,
PV/T = Constant(3)
If n moles is the mass of gas then we write
PV = nRT(4)
where, n is number of moles of gas, R=N_{A}K_{B} is the universal constant known as gas constant and T is the absolute temperature.
A gas satisfying eqn (4) at all values of pressures and temperatures is said to be an ideal gas
now no of moles of gas
n = m/M = N/N_{A}
where
m - mass of gas containing N molecules
M - molar mass
N_{A} - Avogadro' number.
From this,
P = ρRT/M
ρ - mass density of gas.
Dalton law of partial pressures
Consider a mixture of non-interacting ideal gases with n_{1} moles of gas 1,n_{2} of gas 2 and so on
Gases are enclosed in an enclosure with volume V, temperature T and pressure P.
Equation of state of mixture
PV = (n_{1}+ n_{2})RT
orP = n_{1}RT/V + n_{2}RT/V + - - - -
= P_{1} + P_{2} + - - --
where,
P_{1} = n_{1}RT/V
is pressure the gas 1 would exert at same V and T if no other gases were present in the enclosure. This is know as law of partial pressure of the gases.
The total pressure of mixture of ideal gases is sum of partial pressures of individual gases of which mixture is made of.
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