Short Cuts For Numerical Problems on Solutions

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These methods can only be used in competitive exams only.

Direct Formulae for Calculations:

Where M = molarity in mol L-1 or M

m = molality in mol kg-1 or m

a = % by mass of solute



d = density of solution in g/mL or g cm-3.

MB = Molecular mass of solute in grams

MA = Molecular mass of solvent in grams

Note: When using these formulae, take care that the quantities are in prescribed units



Molecular masses of certain substances in grams:

  • Water H2O (18), Benzene C6H6 (78), Sodium hydroxide NaOH (40), Hydrogen chloride HCl (36.5), Sulphuric acid H2SO4 (98), potassium hydroxide KOH (56), Acetic acid (60), Sodium carbonate Na2CO3 (116),

Example – 01:

  • The density of a solution containing 13 % by mass of sulphuric acid is 1.09 g/mL. Calculate molarity and normality of the solution
  • Given: a = 13, d = 1.09 g/mL
  • To Find: Molarity (M) =? and Normality (N) =?
  • Solution:

n = Molecular mass/equivalent mass = 98 g/49 g = 2

Normality = molarity x n = 1.446 x 2 = 2.892 N

Example – 02:

  • The density of 2.03 M solution of acetic acid (molecular mass = 60) in water is 1.017 g/mL. Calculate molality of solution
  • Given: M = 2.03, MB = 60 g mol-1, d = 1.017 g/mL
  • To Find: Molality (m) = ?
  • Solution:

molality = m = 1/0.4410 = 2.268 molal



Example – 03:

  • The density of a 10.0% by mass of KCl solution in water is 1.06 g/mL. Calculate the molality, molarity and mole fraction of KCl.
  • Given: a = 10, d = 1.06 g/mL
  • To Find: Molarity (M) =?, molality (m) =?, mole fraction (XB) =?
  • Solution:

Example – 04:

  • 0.8 M solution of H2SO4 has a density of 1.06 g/cm3. calculate molality and mole fraction
  • Given: M = 0.8 M, d = 1.06 g/cm3.
  • To Find: Molality (m) =?, mole fraction (XB) =?
  • Solution:

molality = m = 1/1.227 = 0.814 molal

0.814 x 18 x (1 – XB) = 1000 XB



14.652 – 14.652 XB = 1000 XB

1014.652 XB = 14.652

XB = 14.652/1014.652  = 0.014

Example – 05:

  • A 6.90 M solution of KOH in water contains 30% by mass of KOH. Calculate the density of solution.
  • Given: M = 6.90 M, a = 30
  • To Find: density of solution = d = ?
  • Solution:

Example – 06:

  • An aqueous solution of NaOH is marked 10% (w/w). The density of the solution is 1.070 g cm-3. Calculate molality, molarity and mole fraction of NaOH in water. Given Na = 23, H =1 , O = 16
  • Given: a = 10, d =  1.070 g cm-3,
  • To Find: mole fraction =? molarity = ? and molality =?
  • Solution:



Example – 07:

  • Calculate the mole fraction of solute in its 2 molal aqueous solution.
  • Given: molality = 2 molal
  • To Find: Mole fraction =?
  • Solution:

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