Boyle's, Charles' and Avogadro's results on the different state variables of a gas, can be combined into one "equation of state” known as the ideal gas equation, PV = nRT, where R = 8.514 J/mol-K. Consider the following situation.
A mixture of hydrogen and oxygen has volume 2000 cm3, temperature 300 K, pressure 100 kPa and mass 0.76 gms. Calculate the masses of hydrogen and oxygen in the mixture.
0.12 gms; 0.64 gms
Suppose there are n1 moles of hydrogen and n2 moles of oxygen in the mixture. The pressure of the mixture will be -
P=(n1RTV)+(n2RTV)=(n1+n2)RTV
⇒100×103Pa=(n1+n2)×[(8.3 JK−1 mol−1)(300 K)200×10−6m−3]
⇒(n1+n2)=0.08 mol .....(i)
The mass of the mixture is -
(n1×2 gms/mol)+(n2×32 gms/mol)=0.76 gms
⇒(n1+16n2)=0.38 mol. ...(ii)
From (i) and (ii),
n1=0.06 mol and n2=0.02 mol
The mass of hydrogen = 0.06×2 gms=0.12 gms, and the mass of oxygen = 0.02×32 gms=0.64 gms.