How do you calculate molarity?

Definition

Molarity ($M$) is a measure of concentration that expresses the number of moles of solute dissolved in one liter of solution. It is calculated using the formula:

$$ M = \frac{n}{V} $$

where:

• $M$ = molarity (mol/L)
• $n$ = moles of solute (mol)
• $V$ = volume of solution (L)

---

Worked Example

Question:
What is the molarity of a solution prepared by dissolving 5.00 grams of NaCl in enough water to make 250 mL of solution?

Step 1: Calculate moles of NaCl

The molar mass of NaCl is:

$$ \text{NaCl: } 22.99,(\text{Na}) + 35.45,(\text{Cl}) = 58.44,\text{g/mol} $$

Number of moles:

$$ n = \frac{\text{mass}}{\text{molar mass}} = \frac{5.00,\text{g}}{58.44,\text{g/mol}} = 0.0856,\text{mol} $$

Step 2: Convert volume to liters

$$ 250,\text{mL} = 0.250,\text{L} $$

Step 3: Calculate molarity

$$ M = \frac{n}{V} = \frac{0.0856,\text{mol}}{0.250,\text{L}} = 0.342,\text{mol/L} $$

---

Takeaways

• Molarity ($M$) is calculated as moles of solute divided by liters of solution.
• Always convert mass to moles and volume to liters before calculating molarity.
• Molarity is expressed in units of mol/L.