Asolution contains 45 grams of nitrogen gas and 40 grams of argon. what is the mole fraction of argon in this solution?

 0.38 

You first calculate the total moles by dividing the grams by molecular weight: 
45 g N2 / 28.02 g/mol = 1.6 mol N2 
40 g Ar / 39.95 g/mol = 1.0 mol 

Then you divide the moles of Ar by the total number of moles: 
1.0 / (1.6 + 1.0) = 0.38 mol fraction

The mass has escaped into a gas which you can not see so the law stays true.