A 30.00% (by mass) solution of #HNO_3# in water has a density of 1.18 g/cm^3 at 20°C. What is the molarity of #HNO_3# in the solution?

1 Answer
anor277
Apr 22, 2017

We are given that #"Mass of nitric acid"/"Mass of solution"xx100%# #=# #30.00%#.

Explanation:

Now #"Concentration"="Moles of solute"/"Volume of solution"#.

How do we turn one t'other? Well, we need the density of the solution, which you have supplied, #rho=1.18*g*cm^-3#, and some tedious 'rithmetic................

So we work with a #1*L# volume of solution, i.e. #10^3*cm^3#.

#"Moles of solute"=(30.00%xx10^3*cancel(cm^3)xx1.180*cancelg*cancel(cm^-3))/(63.01*cancelg*mol^-1)#

#=5.62*mol#

But this molar quantity was dissolved in a #1L# volume of solvent.....

#"Concentration"=(5.62*mol)/(1*L)=5.62*mol*L^-1#.

Now I happen to know that conc. nitric acid, which is commercially supplied as a #68%(w/w)# solution, has a molar concentration of approx. #15*mol*L^-1#, so the value we calculated is reasonably consistent. You should keep doing these types of problems; it's all too easy to get bewildered and make an error.

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