Short-cut Methods For Calculating Concentration of Solutions

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In this article, we shall study short-cut methods to calculate molality, molarity, etc.

These methods can only be used in competitive exams only.

Direct Formulae to Calculate Molality and Molarity:

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.

M_B = Molecular mass of solute in grams

M_A = 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),

Numerical Problems to Calculate Molality and Molarity:

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, M_B = 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 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 (X_B) =?

Solution:

Ans: Molarity 1.42 M, Molality = 1.491 m, Mole fraction = 0.0261

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 (X_B) =?

Solution:

molality = m = 1/1.227 = 0.814 molal

0.814 x 18 x (1 – X_B) = 1000 X_B

14.652 – 14.652 X_B = 1000 X_B

1014.652 X_B = 14.652

X_B = 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:

Ans: Density of solution = 1.288 g/mL

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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Science > Chemistry > Solutions and Their Colligative Properties > Short-cut Methods For Calculating Concentration of Solutions