Concentration Terms & Solutions
The core of quantitative chemistry. Master Molarity, Molality, Normality, mixing laws, and interconversion shortcuts to drastically improve your numerical speed.
Module Focus
A solution is a homogeneous mixture of two or more components. The component present in the largest quantity is the solvent, and the others are solutes. To quantify how much solute is in a solvent, we use Concentration Terms. In NEET, you must seamlessly convert between these terms, calculate final concentrations upon mixing, and apply them directly in chapters like Electrochemistry, Kinetics, and Solutions.
1. Temperature Dependence (The Ultimate Segregation)
Before memorizing formulas, you must categorize concentration terms based on their response to temperature changes. This concept alone is tested frequently as a standalone theoretical question in NEET.
Liquids expand when heated and contract when cooled. Therefore, any concentration term that includes the Volume ($V$) of the solution in its formula will change with temperature.
- Molarity ($M$)
- Normality ($N$)
- Formality ($F$)
- Percentage by Volume ($\% v/v$)
- Percentage Weight by Volume ($\% w/v$)
Mass does not change with temperature. Therefore, terms that exclusively use the Mass ($w$) or Moles ($n$) of the solute and solvent remain constant regardless of temperature changes.
- Molality ($m$) - Preferred standard for precision
- Mole Fraction ($X$)
- Percentage by Mass ($\% w/w$)
- Parts Per Million ($\text{ppm w/w}$)
2. The "Big Three" Concentration Terms
I. Molarity ($M$)
Defined as the number of moles of solute present in exactly 1 Litre (1000 mL) of the solution.
$M = \frac{W_{\text{solute}} \times 1000}{M_{\text{solute}} \times V_{mL}}$
Where $W_{\text{solute}}$ is weight of solute, $M_{\text{solute}}$ is molar mass of solute, and $V_{mL}$ is volume in mL.
- Dilution Law: When you add water, moles of solute remain constant. $\Rightarrow \mathbf{M_1 V_1 = M_2 V_2}$
- Mixing Similar Solutions: Mixing two solutions of the same substance. $\Rightarrow \mathbf{M_{mix} = \frac{M_1 V_1 + M_2 V_2}{V_1 + V_2}}$
II. Molality ($m$)
Defined as the number of moles of solute present in 1 kg (1000 g) of the solvent. Notice that this is the only major term that divides by the solvent, not the solution.
$m = \frac{W_{\text{solute}} \times 1000}{M_{\text{solute}} \times W_{\text{solvent (g)}}}$
III. Normality ($N$)
Defined as the number of gram equivalents of solute present in 1 Litre of the solution. It is heavily used in titration and volumetric analysis.
$\text{Gram Equivalents} = \frac{\text{Given Mass}}{\text{Equivalent Weight}} = \frac{W_{\text{solute}}}{E_{\text{solute}}}$
$N = \frac{W_{\text{solute}} \times 1000}{E_{\text{solute}} \times V_{mL}}$
Equivalent weight is the Molar Mass ($M$) divided by the valency factor (n-factor). $\Rightarrow \mathbf{E = \frac{M}{n_f}}$
- For Acids: $n_f$ = Basicity (number of replaceable $H^+$ ions). Example: $H_2SO_4 \rightarrow n_f = 2$. $H_3PO_3 \rightarrow n_f = 2$ (Exception!)
- For Bases: $n_f$ = Acidity (number of replaceable $OH^-$ ions). Example: $Al(OH)_3 \rightarrow n_f = 3$.
- For Salts: $n_f$ = Total positive or negative charge on ions. Example: $Al_2(SO_4)_3 \rightarrow n_f = 2 \times 3 = 6$.
- For Redox: $n_f$ = Change in oxidation number per molecule. Example: $KMnO_4$ in acidic medium changes from +7 to +2 $\Rightarrow n_f = 5$.
3. Mole Fraction and Percentage Terms
Mole Fraction ($X$): The ratio of the number of moles of a particular component to the total number of moles in the solution. It is unitless.
$X_{\text{solvent}} = \frac{n_{\text{solvent}}}{n_{\text{solvent}} + n_{\text{solute}}} \quad \text{and} \quad X_{\text{solute}} = \frac{n_{\text{solute}}}{n_{\text{solvent}} + n_{\text{solute}}}$
$\mathbf{X_{\text{solvent}} + X_{\text{solute}} = 1}$
Percentage and Parts Per Million (ppm):
$\% w/w = \left(\frac{W_{\text{solute}}}{W_{\text{solution}}}\right) \times 100$
$\% w/v = \left(\frac{W_{\text{solute}}}{V_{\text{solution in mL}}}\right) \times 100$
$\text{ppm} = \left(\frac{\text{Mass of Solute}}{\text{Total Mass of Solution}}\right) \times 10^6$
4. Direct Interconversion Formulas (Time Savers)
In NEET, you do not have 3 minutes to derive relations from scratch. Memorize these direct shortcuts. Let $d$ = density of solution in g/mL, $M$ = Molarity, $m$ = Molality, $M_{\text{solute}}$ = Molar mass of solute, $M_{\text{solvent}}$ = Molar mass of solvent.
1. Molarity to Molality (Requires density):
2. $\% w/w$ to Molarity (Requires density):
3. Mole Fraction to Molality (Independent of density):
5. Mixing Acids and Bases (Neutralization)
When you mix an acid and a base, they neutralize each other. To find the resulting nature and concentration of the mixture, you MUST use Normality (or Milliequivalents), not just Molarity.
Let $N_{\text{acid}}V_{\text{acid}}$ be the equivalents of Acid, and $N_{\text{base}}V_{\text{base}}$ be the equivalents of Base.
- If $N_{\text{acid}}V_{\text{acid}} > N_{\text{base}}V_{\text{base}}$, the resulting solution is Acidic.
Resulting Normality: $\mathbf{N_{mix} = \frac{N_{\text{acid}}V_{\text{acid}} - N_{\text{base}}V_{\text{base}}}{V_{\text{acid}} + V_{\text{base}}}}$ - If $N_{\text{base}}V_{\text{base}} > N_{\text{acid}}V_{\text{acid}}$, the resulting solution is Basic.
Resulting Normality: $\mathbf{N_{mix} = \frac{N_{\text{base}}V_{\text{base}} - N_{\text{acid}}V_{\text{acid}}}{V_{\text{acid}} + V_{\text{base}}}}$ - If $N_{\text{acid}}V_{\text{acid}} = N_{\text{base}}V_{\text{base}}$, the solution is Neutral.
Always remember: $N = M \times n\text{-factor}$. Convert Molarity to Normality before subtracting!
NEET Grand Test: Concentration Terms
15 High-Order Thinking Questions testing interconversions, n-factor logic, and application.
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