Gas laws

Dalton's Law Of Partial Pressure

It stats that total pressure exerted by a mixture of gases is equal to the sum of the partial pressure of the individual gas when there is no chemical interaction between them.
$P = \frac{P _{1} V _{1}}{V _{1} + V _{2}} + \frac{P _{2} V _{2}}{V _{1} + V _{2}}$ .

On temperature keeping constant, the volume of the given mass of a gas is inversely proportional to the pressure.
$P \propto \frac{1}{V}$ .
Gas do not obey Boyle's law strictly at all values of temperature and pressure. The law is obeyed by the gases at high temperature and low pressure but is not obeyed at low temperature and high pressure
PV=constant or, $P_{1} V_{1} = P_{2} V_{2}$
Slope of curve = $\frac{d p}{d V} = \frac{- p}{V}$

It states that the volume of the given mass of a gas at constant pressure increases or decreases by a constant fraction of its volume at 0 $°$ C for each degree rise or fall in temperature.
Also, it states that on pressure keeping constant, the volume of a given mass of the gas is directly proportional to the absolute temperature.
i.e. $V \propto T$
or, $\frac{V}{T} = co n s t an t$
or, $\frac{V _{1}}{T _{1}} = \frac{V _{2}}{T _{2}}$
Volume Coefficient( $γ_{p}$ ) = Change in volume per unit original volume per degree change in temperature at constant pressure is same for all gases. which is volume coefficient.
$γ_{p} = \frac{1}{273} /° C$ for all gases.
Also, Volume coefficient = $\frac{Δ V}{V Δ T}$

At constant volume of given mass of gas, pressure is directly proportional to absolute temperature.
Charle's law fails at low temperature.
$P \propto T$ .
or, $\frac{P}{T} = co n s t an t$ .
or, $\frac{P _{1}}{T _{1}} = \frac{P _{2}}{T _{2}}$
Pressure Coefficient ( $γ_{v}$ ) = Change in pressure per unit original pressure per degree change in temperature at constant volume is same for all gases value of it is $\frac{1}{273} /° C$ for all gases.
Pressure Coefficient = $\frac{Δ P}{P Δ T}$

For given mass of gas,

$\frac{P _{1} V _{1}}{T _{1}} = \frac{P _{2} V _{2}}{T _{2}}$

or $\frac{P V}{T} = co n s t an t$

For 1 mole of gas at STP,

P= $1.01 \times 1 0^{5} N / m^{2}$ , $V = 22.4 lt s = 22.4 \times 1 0^{- 3} m^{3}$ , T=273K so,

$\frac{P V}{T} = R$

Where R is the universal molar gas constant and equal to 8.31 J/(mol K)

For 1 mole of gas PV=RT
for n moles of gas PV=nRT
$n = \frac{m}{M}$ so, PV=mrT , where r= $\frac{R}{M}$ is called gas constant per unit mass.
$r = \frac{P V}{m T} = \frac{P}{ρT}$ .

Note:

Pressure and Volume coefficient are equal when the gas obeys Boyle's law.
At low pressure and high temperature, the behavior of real gases approach the idea gas behavior.
Graph of PV versus P for a given mass of a gas at constant temperature is a straight line parallel to the pressure axis.
Charle's law fails at low temperature.
We cannot change the temperature of a gas by keeping pressure and volume constant.
The value of gas constant R for one mole of a gas is independent of the atomicity of the gas.