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The amount of solute dissolved in the solvents, and the solution formed can all be expressed in terms of concentrations. There are different ways in which the concentration is estimated such as molarity, molality, formality, percent composition and many more.

To find the Molality the required information is

- Moles of the solute used to form a solution.
- Amount of the solvent expressed in kilograms.

Here the moles of the solute = 5 moles.

The amount of the solvent = 2000 grams.

Expressing the solvent in Kilograms = 2000/1000 = 2Kg.

Hence using the formula for calculating Molality gives:

Simplifying the calculation, Molality = 2.5 m.

Here, the amount of the solvent = 1.5 Kg.

Molality of the solvent used = 0.3 m.

Hence rearranging the Molality formula for calculating the moles of the solute:

This gives Moles of solute = 0.3 x 1.5 = 4.5 moles of Feo.

Here, the number of moles of the solute = 0.24.

The molality of the solution = 0.48 m.

Hence rearranging the molality formula for calculating the mass of the solvent gives:

The amount of the solvent = 1/2Kg = 0.5 Kg.

Mass of solute = 20 grams.

Molar mass or molecular weight of KCl = Atomic mass unit of (K + Cl)

= 39.0983 + 35.453 = 74.5513 g/mol

= 74.6 g/mol (approx.)

Moles of KCl = 20/74.6 = 0.27 moles.

Amount of solvent in Kg = 400/1000 = 0.4 Kg.

Using the molality formula:

Therefore, molality of the given solution = 0.27/0.4 = 0.675 m

Given is the mass of Sodium Carbonate = 15 grams.

The number of moles of Na

The Molar mass of Sodium Carbonate Na

Refer the periodic table for the atomic mass unit for Na, C and O.

Molar mass of Na

= 105.98844 g/mol = 106 g/mol (approx.)

Moles of Sodium Carbonate Na

Using the Molality formula

Hence the molality = 0.14/0.25 = 0.56 m

The formula used to calculate the Molarity of a solution is:

Another very useful measuring unit used while solving questions related to concentrations is density. Density of a given solution is mass of the substance per unit volume. The units for expressing density are g/ml. The formula for calculating density is:

Following are very unique and useful solved examples involving molality and molarity.

The molality of the solution = 0.56m.

This implies 0.56 moles of a solute NaCl is dissolved in 1 kg of the solvent.

Moles of NaCl = 0.56;

Molar mass of NaCl = Atomic weight of (Na + Cl) = (22.989770 + 34.453)

= 58.44277 g/mol = 58.44g/mol (approx.)

Using the moles formula, mass of NaCl dissolved = 0.56 x 58.44 = 32.73 gm (approx.)

Mass of solution = Mass of Solute + Mass of Solvent

= 32.73 grams + 1000 grams = 1032.73 grams

Density of the solution given = 1.8g/ml.

Using the density formula .

Volume of the solution = 1.8 x 1032.73 = 1858.91 ml = 1.85891 L = 1.86 L (approx.).

Using the molarity formula:

Therefore, Molarity of the solution = 0.56/1.86 = 0.30 M

The molality of the solution = 1.2m.

This implies 1.2 moles of a solute KI is dissolved in 1 kg of the solvent.

Moles of KI = 1.2;

Molar mass of KI = Atomic weight of (K + I) = (39.0983 + 126.90447)

= 166.00277 g/mol = 166.00g/mol (approx.)

Using the moles formula, mass of KI dissolved = 1.2 x 166.00 = 199.20 gm

Mass of solution = Mass of Solute + Mass of Solvent

= 199.20 grams + 1000 grams = 1199.20 grams

Density of the solution given = 2.5g/ml.

Using the density formula .

Volume of the solution = 2.5 x 1199.20 = 2998 ml = 2.998 L.

Using the molarity formula:

Therefore, Molarity of the solution = 1.2/2.998 = 0.40 M