Derive ideal gas equation and expressed in terms of density of gas
Answers
There are several ways to derive the Ideal Gas Law, but the simplest way is to use the three simple gas laws.
AVOGADRO'S LAW states the volume of a gas is directly proportional to the number of moles.
V ∝ n
BOYLE'S LAW states that the volume of a gas is inversely proportional to its pressure.
V ∝ 1/P
CHARLES'S LAW states that the volume of a gas is directly proportional to its Kelvin temperature.
V ∝ T
If we combine these laws, we get
V ∝ nT/P
We covert the proportionality to an equality
V = knT/P
We replace k with the universal gas constant R and get
V = nRT/P
This can be rearranged to give the IDEAL GAS LAW
PV = nRT
The density is determined by utilizing a variation of the ideal gas law where density and molar mass replace moles and volume.
The original ideal gas law uses the formula PV = nRT, the density version of the ideal gas law is PM = dRT, where P is pressure measured in atmospheres (atm), T is temperature measured in kelvin (K), R is the ideal gas law constant 0.0821 a t m ( L ) m o l ( K ) just as in the original formula, but M is now the molar mass ( g mo l ) and d is the density ( g L ).
By rearranging the formula to P M R T = d the units of atm, mol and K will cancel and the value will be left with the g L units for density.