Molarity Equation

What is molarity?

Molarity (M) = Moles of solute/Litres of solution

Where, solute is the substance dissolved, solvent is the substance where the solute is dissolved (usually water) and the solution is the combination of both solute and solvent.

Molarity Equation examples:

Example 1. Find the Molarity of a solution where 1.56 moles of sugar is dissolved in 2.79 L of solution?

Answer: Molarity (M) = Moles of solute / Litres of solution
               Molarity (M) = 1.56 moles of sugar / 2.79 L of solution
                                   = 0.559 moles/L

Example 2. How many grams of NaCl will be needed to make 1.70 Litres of an aqueous 0.650 M solution?

Answer: The moles of solute (NaCl) should be rearranged, the moles of solute can be converted into grams.

Moles of solute = Molarity (moles/L) × L of solution
                         = 0.650 (moles/L) × 1.70 L
                         = 1.105 moles

Now, by using the molar mass of NaCl, convert the moles of solute into grams.

Na = 22.99 g/mol
Cl = 35.45 g/mol
NaCl = 22.99 + 35.45 g/mol
Grams of NaCl = 1.105 moles × 58.44 gms/mole
                         = 64.57 gms

The molarity equation can also be calculated by:

Moles = molarity × litres

Molarity = moles/litres

Litres = moles / molarity

Another schematic diagram to explain Molarity:

Some other methods to calculate molarity:

1. Calculate Molarity with Moles and Volume:
   Molarity = moles of solute/litres of solution
   Example: Find the molarity of a solution containing 0.67mol NaCl in 3.7 Litres?
   
   
   
   Moles= 0.67 mol NaCl
   Volume = 3.7 L
   Molarity = 0.67mol / 3.7L
                 = 0.181 M NaCl

2. Calculate Molarity with Mass and Volume:
   Example: Find the molarity of a solution by dissolving 2.8 g of KMnO₄ in 4.3 liters of water?
   Mass = 2.8 g KMnO₄
   Volume = 5.2 L
   Here, you have to find the molar mass of the solute using the periodic table of elememts.

   Molar mass of K = 39.1 g
   Molar mass of Mn = 54.9 g
   Molar mass of O = 16.0 g
   Total molar mass = K + Mn + O + O + O + O = 39.1 + 54.9 + 16 + 16 + 16 + 16 = 158.0 g
   = 2.8 g × 1 mol / 158g (convert grams into moles)
   = 0.0177 mol
   Now, we can calculate the molarity:
   = 0.0177 mol / 4.3 L
   = 0.00411
   = 0.004 M KMnO₄

3. Calculate Molarity with Moles and Millilitres:
   Example: Find the molarity of a solution containing 2.3 moles CaCl₂ in 2985 milliliters?
   Moles = 2.3 mol CaCl₂
   Volume = 2985mL
   Convert mL into litres
   = 2985mL × 1 / 1000mL
   = 2.985 L
   Now, calculate the molarity:
   = moles of solute/litres of solution
   = 2.3mol / 2.985L
   = 0.7705
   = 0.770 M CaCl₂