Molarity ($M$)
The Most Common Concentration Term | Basic Concepts of Chemistry
1. Definition & Formula
Molarity ($M$) is defined as the number of moles of solute dissolved in 1 Liter (or 1 $\text{dm}^3$) of the solution.
$$ M = \frac{\text{Moles of Solute ($n$)}}{\text{Volume of Solution in Liters ($V$)}} $$
Since $n = \frac{\text{Mass ($w$)}}{\text{Molar Mass ($M_{sol}$)}}$, the expanded formula is:
$$ M = \frac{w}{M_{sol} \times V_{(L)}} \quad \text{or} \quad M = \frac{w \times 1000}{M_{sol} \times V_{(mL)}} $$Unit: $mol/L$ or Molar ($M$).
2. Important Relations (Shortcuts)
A. From Percentage by Mass & Density
If a solution has $x\%$ solute by mass and density $d$ (g/mL):
$$ M = \frac{x \times d \times 10}{M_{solute}} $$
B. Molarity of Pure Water
Density of water $\approx 1$ g/mL $\Rightarrow 1000$ g in 1 Liter.
$$ M = \frac{1000}{18} = 55.55 \, M $$3. Dilution and Mixing Laws
A. Dilution Law
When water is added to a solution, the moles of solute remain constant.
$$ M_1 V_1 = M_2 V_2 $$(Before Dilution = After Dilution)
B. Mixing Law
When two non-reacting solutions of the same solute are mixed:
$$ M_{mix} = \frac{M_1 V_1 + M_2 V_2}{V_1 + V_2} $$4. Effect of Temperature
Key Concept: Since Volume ($V$) expands on heating, and Molarity ($M \propto 1/V$) is inversely proportional to volume, Molarity decreases as Temperature increases.
This is why Molality ($m$) is often preferred in thermodynamics, as it depends on mass (independent of temperature).
5. Common Concentration Terms
| Name | Molarity |
|---|---|
| Molar Solution | 1 M |
| Semimolar | M/2 or 0.5 M |
| Decimolar | M/10 or 0.1 M |
| Centimolar | M/100 or 0.01 M |
| Millimolar | M/1000 or 0.001 M |
Practice Quiz
Test your numerical skills on Molarity.
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