Boyle's Law and Charle's law can be combined into a single equation
V= constant x T/P
constant is independent of temperature and pressure but oes not depdend on the amount of gas.For one mole,the constant will have a specific value,which we will denote as R.The molar volume Vm is
Vm =R x T/P
According to the avogadro law the molar volume at a specific value of T and P is a constant independent of the nature of the gas and this implies that R is a constant of proportionality relating molar volume of a gas to T/P.
The preceeding equation can be written for n moles of gas by multiplying both sides by n.
nVm = nRT/P or PV=nRT
The equation whichc combines all of the gas laws,is called the ideal gas law.
Lets see one example :
Answer the equation asked in the chapter opening;how many grams of oxygen are there in a 50.0 L tank at 21 oc when the oxygen pressure is 15.7 atm.
Answer: P= 15.7 atm
V = 50.0 l
T = 21oc + 273 k = 294 K
n = ?
Solving the ideal gas law for n given,
n = PV/RT
n = 15.7 atm x 50.0 L /0.0821 L.atm/(K.mol) x 294 = 32.5 mol
now converting moles ot mass of o2
32.5 mol x32.0 O2/1 mol O2 = 1.04 x 10^3 g O2