Molarity (M)

It is a concentration measurement used in chemistry to describe the amount of solute (substance being dissolved) in a given volume of solvent (usually a liquid). It is defined as the number of moles of solute dissolved per liter of solution. Molarity is a widely used unit in chemical calculations and is denoted by the symbol "M."

Mathematically, the molarity (M) of a solution is calculated using the following formula:

M = n / V

Where:

  • M = Molarity of the solution (in moles per liter, mol/L or M)
  • n = Number of moles of solute
  • V = Volume of the solvent in liters

Let's delve into some numerical problems to better understand molarity.

Numerical Problems:

Problem 1:

Calculate the molarity of a solution that contains 0.5 moles of sodium chloride (NaCl) dissolved in 0.2 liters of water.

Solution: M = n / V M = 0.5 moles / 0.2 L M = 2.5 M

The molarity of the solution is 2.5 M.

Problem 2:

What volume of a 0.8 M hydrochloric acid (HCl) solution contains 0.4 moles of HCl?

Solution: V = n / M V = 0.4 moles / 0.8 M V = 0.5 L

The volume of the HCl solution required is 0.5 liters.

Problem 3:

Dilution is the process of adding solvent to a solution to decrease its concentration. If you dilute 250 mL of a 6 M hydrochloric acid (HCl) solution to a final volume of 1.5 L, what is the molarity of the diluted solution?

Solution: M1V1 = M2V2

M2 = M1V1 / V2 M2 = 6 M * 0.25 L / 1.5 L M2 = 1 M

The molarity of the diluted HCl solution is 1 M.

Problem 4:

You want to prepare 500 mL of a 2.5 M sulfuric acid (H2SO4) solution. How many moles of H2SO4 are needed to make this solution?

Solution: n = MV n = 2.5 M * 0.5 L n = 1.25 moles

You need 1.25 moles of H2SO4 to prepare the solution.

Practice problems

  1. Calculate the molarity of a solution that contains 0.3 moles of potassium chloride (KCl) dissolved in 0.4 liters of water.

  2. What volume of a 1.2 M sulfuric acid (H2SO4) solution contains 0.6 moles of H2SO4?

  3. You want to dilute 150 mL of a 3.5 M hydrochloric acid (HCl) solution to a final volume of 0.8 L. What is the molarity of the diluted solution?

  4. Calculate the molarity of a solution prepared by dissolving 0.25 moles of glucose (C6H12O6) in enough water to make a final volume of 0.5 liters.

  5. What volume of a 2.8 M sodium hydroxide (NaOH) solution contains 0.7 moles of NaOH?

  6. Dilute 200 mL of a 5.0 M nitric acid (HNO3) solution to a final volume of 1.2 L. Calculate the molarity of the diluted solution.

  7. You have 0.4 moles of magnesium sulfate (MgSO4) and want to prepare a solution with a molarity of 1.5 M. What volume of solution should you make?

  8. Calculate the molarity of a solution prepared by dissolving 0.15 moles of potassium nitrate (KNO3) in enough water to make a final volume of 250 mL.

  9. What volume of a 2.0 M hydrochloric acid (HCl) solution contains 0.8 moles of HCl?

  10. Dilute 300 mL of a 4.2 M sodium hydroxide (NaOH) solution to a final volume of 1.5 L. Calculate the molarity of the diluted solution.