Ideal gas law


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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