Concentration Calculation Examples | Molarity

In this tutorial, we study about molarity and molality theories of solutions and solve questions to get better understand.

Definition of concentration

Solvent, solute, solution definition

What is solvent?

The component is present in greater amount

What is the solute?

The component is present in lesser amount.

What is solution?

The mixture of solvent and solute

In this tutorial we try to study the molarity and molality of solutions.

Molarity of a solution

The number of moles of the solute dissolved per unit volume of the solution is the definition of molarity. Units can be mol dm^-3 or mol m^-3.

Molarity equation

Molarity units

Molarity can be expressed in different units.

• mol dm^-3 : mostly used
• mol l^-
• kmol m^-3

How to calculate concentration in mol dm^-3 ?

In the units, there are mol and dm^-3. They tells us about amount and volume respectively. Therefore we have to find the dissolved amount and volume of the solution to calculate concentration in mol dm^-3.

Examples about molarity values

• If 1 dm³ aqueous solution contains 0.45 mol of HCl, molarity of HCl is 0.45 mol dm^-3. Otherwise, we can describe this is as, 0.45 mol of HCl is dissolved 1 dm³ of the total solution.
• If 10 dm³ aqueous solution contains 0.98 mol of HNO₃, molarity of HNO₃ is 0.098 mol dm^-3.

Sometimes we use '[ solute ]' to represent concentration of solute. As an example, to represent concentration of aqueous HCl, we can use [HCl_(aq)]

Example: [HNO_3(aq)] = 0.1 mol dm^-3

Calculating molarity of solutions

Before calculating molarity of solutions, you should have an idea about following parametres.

• Calculating molar mass when relative atomic masses are known
• Relationship of molar mass (M), mass (m) and amount (n): n = m/M

Calculate molarity - Example 1

5.85 g of NaCl is dissolved in 500cm³ of distilled water. Calculate the molarity of NaCl mol dm^-3. ( Na = 23 , Cl = 38.5 )

Answer

Dissolved amount (moles) and totoal volume of the solution are required to calculate the concentration according to the molarity equation. In this example, total solution volume is given as a data. Therefore we have to find the dissolved NaCl amount.

Find the amount of moles of dissolved NaCl

Mass of dissolved NaCl is given. Now we can find the NaCl amount using mass, molar mass and amount relationship. First molar mass of NaCl should be calculated.

Let's calculate the molar mass of NaCl

molar mass of NaCl = 23 *1 + 35.5*1

molar mass of NaCl = 58.5 g mol^-1

Amount = mass / molar mass

Dissolved NaCl amount = 5.85 g / 58.5 g mol^-1

Dissolved NaCl amount = 0.1 mol

Calculate the volume of total solution in dm³

1dm³ = 1000cm³

500cm³ = 500 * 10^-3 dm³ = 0.5dm³

Now, we know the volume of solution in dm³ and amount of moles of NaCl. So we can find molarity of NaCl now.

Molarity Equation

Substitute NaCl moles and volume of the solution.

Molarity of NaCl = 0.2 mol dm^-3

Example 2

You are advised to prepare 0.47 mol dm^-3 NaOH solution in the laboratory. Solid NaOH, distilled water and other lab facilities are supplied for you. If you have to prepare 25cm³ solution, calculate followings.

1. Required amount of moles of NaOH
2. Required NaOH mass

In this example, required molarity 0.47 mol dm^-3 and volume are given. When we know the molarity and volume, we can easily calculate the required amount of moles of NaOH using relationship of concentration, moles, and volume of solution. After calculating NaOH moles, required NaOH mass is calculated.

Calculate moles of NaOH

Calculate required mass of NaOH

Now we can use the relation of mass, molar mass and amount of moles to find required mass of NaOH.

Example 3

A mixture of Na₂CO₃ and K₂CO₃ is dissolved in distilled water upto 250 cm³. Dissolved mixture includes 10.6 g of Na₂CO₃ and 13.8 g of K₂CO₃.

1. Calculate amount of moles each Na₂CO₃ and K₂CO₃ compounds.
2. Express concentrations in mol dm^-3 of each Na₂CO₃ and K₂CO₃.
3. Calculate concentrations of CO₃^2- in the solution.

K=39 , Na=23 , O=16 , C=12

1.

Masses of Na₂CO₃ and K₂CO₃ are given as data. So we can find amount of Na₂CO₃ and K₂CO₃. In this example, We use 'M' to express molar mass as a symbol.

Find molar masses of Na₂CO₃

Find amount of Na₂CO₃

Find molar masses of K₂CO₃

Find amount of K₂CO₃

2.

Now we know the amount of moles of each Na₂CO₃ and K₂CO₃. Therefore molarity can be found now.

Find molarity

3.

CO₃^2- ions are given from both Na₂CO₃ and K₂CO₃ compounds. Both Na₂CO₃ and K₂CO₃ dissociate completely to ions in the water. Therefore total amount of CO₃^2- ions in the water equals to the sum of CO₃^2- given by Na₂CO₃ and CO₃^2- given by K₂CO₃. After calculating total CO₃^2-, molarity is calculated.

Example 4

You have to prepare a NaOH solution and its pH value should be 13. Total volume of the solution is 500 ml. Calculate the required mass of NaOH to prepare this solution at 25⁰C.

Calculate concentration of a pH known solution

Calculate pOH from pH by using the pH + pOH = 14 (at 25⁰C)
Then you can calculate the concentration of NaOH solution by pOH = -log₁₀[OH^-_(aq)] .
Then find the required moles of NaOH by the equation of C=n/v . Here C= concentration, n=required moles, v-volume of solution
Now weight is measured by multiplying n and molar mass.

Assumptions

The OH^- received from water dissociation is negligible when it compare with OH^- received from NaOH.

Calculate pOH from pH value

pH + pOH = 14
13 + pOH = 14
pOH = 1

Calculate concentration(mol dm^-3)of solution

Now we know the pOH of NaOH solution. Use the relation of pOH and OH^- concentration

pOH = -log₁₀[OH^-_(aq)]
1 = -log₁₀[OH^-_(aq)]
[OH^-_(aq)] = 0.1 mol dm^-3

Find the required moles(mol) of NaOH

Concentration, moles amount, and volume relation is used.

C = n/v
0.1 = n/0.5      [500ml = 0.5 dm³]
n = 0.05mol

Find the required weight(g)

Multiply required moles times molecular weight

m = mass
n = moles
M = molecular weight
n = m/M

m = M*n
m = 0.05 * 40
m = 2g

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