Question

Molarity of H₂SO₄ is 18 M. Its density is 1.8 g/ml. Hence molality is
(a) 36
(b) 200
(c) 500
(d) 18

Answer 1

molality = (moles of solute) / (kilograms of solvent)  

(molality is denoted by a lower case m)  

First, pick an arbitrary amount of solution that will make the calculations easier, say 1.00L. Since the concentration of the solution is 18.0 mol/L and the density is 1.8 g/ml (or 1.8 kg/ L), 1.00 Liter of the solution contains 18.0 mol (1765 g) of H2SO4 and has a mass of 1.8 grams:  

1.  

Moles of H2SO4 in 1.0L soln= (18.0 mol/L)x(1.00L) = 18 mol  

2.  

Mass of H2SO4 in 1.0 L soln=(18 mol)x(98.1g/mol) = 1765 g  

(molar mass of sulfuric acid is 98.1g/mol)  

3.  

Mass of 1.0L soln = (1.00L) x (1.8kg/L) = 1.8 kg  

4.  

Mass of H20 in 1.0L soln =(1.8kg) - (1.765 kg)=0.035 kg H2O  

5.  

Since 0.035 kg of water has 18 mol of H2SO4 dissolved in it, 1.00 kg of water would have 514 mol dissolved in it:  

1.00kg H20 x (18 mol H2SO4 / 0.035 kg H20) =  

= 514 mol H2SO4 (kg cancel)  

So, finally, sorry this was so long, but the answer closest to the exact calculation is  

C. 500 mol H2SO4 per kilogram of water.