What is Molarity?
In chemistry, molarity (M) is the standard unit of concentration. It describes how crowded the solute particles are inside a liquid solution:
- •Solute: The substance being dissolved (e.g., salt, sugar, acid).
- •Solvent: The liquid doing the dissolving (usually water).
- •Solution: The total combined mixture of solute + solvent.
The Molarity Triangle Formula
Watch the Units!
Volume must ALWAYS be in Liters (L). If a problem states 250 mL, you must divide by 1,000 first:
250 mL ÷ 1000 = 0.250 L.
Worked Example 1: Direct Moles and Milliliters
Problem:
A chemist dissolves 0.75 moles of potassium chloride (KCl) into enough water to make 250 mL of solution.
What is the molarity of the solution?
Step 1: Check moles of solute
Moles (n) = 0.75 mol (already in moles).
Step 2: Convert volume to Liters
Step 3: Apply the Molarity formula (M = nV)
The concentration of the solution is 3.0 M (pronounced "3.0 Molar").
Worked Example 2: Starting from Grams (Grams to Moles to Molarity)
On most chemistry tests, you will be given grams of a chemical instead of moles. You must convert grams to moles using the substance's molar mass first!
Problem:
You dissolve 29.22 g of sodium chloride (NaCl) in water to create a total volume of 500 mL.
What is the molarity? (Molar mass of NaCl = 58.44 g/mol).
Step 1: Convert grams of NaCl to moles
Step 2: Convert 500 mL to Liters
Step 3: Calculate Molarity
The solution is 1.0 M.
Dilution Calculations: M_1 V_1 = M_2 V_2
When you add pure water to a concentrated solution (a stock solution), the number of moles of solute stays exactly the same—only the volume changes!
- •M_1 = Initial concentration
- •V_1 = Initial volume
- •M_2 = Final diluted concentration
- •V_2 = Final total volume
Quick Dilution Example:
What volume of 12 M HCl stock acid is needed to prepare 600 mL of 2.0 M HCl?
M_1 V_1 = M_2 V_2
(12) × V_1 = (2.0) × (600)
12 V_1 = 1200 ⟹ V_1 = 100 mL
You need 100 mL of stock acid diluted up to 600 mL!
Molarity Summary Cheat Sheet
| Formula | To Find | What to Multiply / Divide |
|---|---|---|
| M = nV | Molarity | Moles divided by Liters |
| n = M × V | Moles | Molarity times Liters |
| V = nM | Volume | Moles divided by Molarity |
| M_1 V_1 = M_2 V_2 | Dilution | Conserve moles across volumes |
Safety Pro-Tip in the Lab:
Always add Acid to Water (A&W), never water to acid! Adding water to concentrated acid can cause intense boiling and dangerous splattering.