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Q1.3 (iii):
Define the following terms: (iii) Molarity

Solution :

1. Formal Definition of Molarity

Molarity ($M$) is defined as the number of moles of a solute dissolved per liter of the total solution. It is a temperature-dependent unit of concentration, as the volume of the solution fluctuates with variations in temperature [Per the principle of thermal expansion].

2. Mathematical Formulation

The molarity of a solution is represented by the following mathematical expression:

$M = \frac{n_{solute}}{V_{solution(L)}}$

Where:

  • $n_{solute}$ = Number of moles of the solute.
  • $V_{solution(L)}$ = Volume of the total solution measured in liters ($L$).

3. Derivation from Mass and Molar Mass

Given that the number of moles ($n$) is calculated by the ratio of the given mass of the substance ($w$) to its molar mass ($M_m$), we substitute this into the primary equation:

$M = \frac{w_B}{M_{m(B)} \times V_{solution(L)}}$

If the volume is provided in milliliters ($mL$), the conversion factor is applied to normalize the units to liters:

$M = \frac{w_B \times 1000}{M_{m(B)} \times V_{solution(mL)}}$

4. Conceptual Visualization

The following diagram represents the transition from a pure solute to a solution of defined molarity.

Solute ($n$ moles) Solution ($V = 1 L$) Dissolve

5. Dimensional Analysis

Parameter Unit
Numerator ($n$) $mol$
Denominator ($V$) $L$
Molarity ($M$) $mol \cdot L^{-1}$ or $M$ (Molar)

Final Solution: Molarity is the concentration unit representing the moles of solute per liter of solution, denoted as $M = \frac{n}{V(L)}$. It is highly sensitive to temperature changes due to the liquid expansion coefficient of the solvent.


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