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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}.

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 H
_{2}O (18), Benzene C_{6}H_{6}(78), Sodium hydroxide NaOH (40), Hydrogen chloride HCl (36.5), Sulphuric acid H_{2}SO_{4}(98), potassium hydroxide KOH (56), Acetic acid (60), Sodium carbonate Na_{2}CO_{3}(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, 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 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 (X_{B}) =?**Solution:**

#### Example – 04:

- 0.8 M solution of H2SO4 has a density of 1.06 g/cm
^{3}. calculate molality and mole fraction **Given:**M = 0.8 M, d = 1.06 g/cm^{3}.**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:**

#### 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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