Determination of Molecular Masses — Revision Notes

⚡ 30-Second Revision

Colligative Properties: — Depend on number of solute particles, not nature.
RLVP: — $\frac{P^0 - P_s}{P^0} = i X_B$. $M_B = \frac{W_B M_A}{W_A} \left( \frac{P^0}{i(P^0 - P_s)} \right)$ (for dilute solution).
EBP: — $\Delta T_b = i K_b m$. $M_B = \frac{i K_b W_B \times 1000}{\Delta T_b W_A (\text{in g})}$.
DFP: — $\Delta T_f = i K_f m$. $M_B = \frac{i K_f W_B \times 1000}{\Delta T_f W_A (\text{in g})}$.
Osmotic Pressure: — $\Pi = i C R T$. $M_B = \frac{i W_B R T}{\Pi V (\text{in L})}$.
Van't Hoff Factor ($i$): — $i=1$ (non-electrolyte), $i>1$ (dissociation), $i<1$ (association).
Units: — $T$ in Kelvin, $V$ in Liters, $W_A$ in kg (for $m$) or g (with $imes 1000$). $R = 0.0821,\text{L atm mol}^{-1}\text{K}^{-1}$ or $8.314,\text{J mol}^{-1}\text{K}^{-1}$.
Preference: — Osmotic pressure for macromolecules (large $\Pi$, room temp).

2-Minute Revision

Molecular mass determination for non-volatile solutes relies on colligative properties: relative lowering of vapor pressure, elevation in boiling point, depression in freezing point, and osmotic pressure.

These properties are directly proportional to the number of solute particles. To calculate molecular mass ($M_B$), we rearrange the respective formulas. For example, from osmotic pressure, $M_B = \frac{i W_B R T}{\Pi V}$.

The van't Hoff factor ($i$) is crucial; it's 1 for non-electrolytes, greater than 1 for dissociating electrolytes (like NaCl, $i=2$; CaCl$_2$, $i=3$), and less than 1 for associating solutes. Osmotic pressure is the preferred method for macromolecules (proteins, polymers) because it produces a large, easily measurable effect even at low concentrations and can be measured at room temperature, preserving sensitive biological samples.

Always ensure consistent units: temperature in Kelvin, volume in liters, and mass of solvent in kilograms for molality-based calculations or grams with a factor of 1000. Remember that these methods are most accurate for dilute, non-volatile solutions.

5-Minute Revision

To determine the molecular mass of an unknown non-volatile solute, we harness colligative properties, which are solution properties dependent solely on the number of solute particles. The four key properties are relative lowering of vapor pressure (RLVP), elevation in boiling point ($\Delta T_b$), depression in freezing point ($\Delta T_f$), and osmotic pressure ($\Pi$). Each can be mathematically related to the solute's concentration, and thus, its molecular mass ($M_B$).

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RLVP: — $\frac{P^0 - P_s}{P^0} = i X_B$. For dilute solutions, $X_B \approx \frac{n_B}{n_A} = \frac{W_B/M_B}{W_A/M_A}$. Rearranging gives $M_B = \frac{W_B M_A}{W_A} \left( \frac{P^0}{i(P^0 - P_s)} \right)$. This is less practical due to small changes.

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EBP: — $\Delta T_b = i K_b m$. Since $m = \frac{W_B/M_B}{W_A(\text{kg})} = \frac{W_B \times 1000}{M_B \times W_A(\text{g})}$, we get $M_B = \frac{i K_b W_B \times 1000}{\Delta T_b W_A(\text{g})}$. Requires heating, unsuitable for sensitive samples.

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DFP: — $\Delta T_f = i K_f m$. Similarly, $M_B = \frac{i K_f W_B \times 1000}{\Delta T_f W_A(\text{g})}$. Requires cooling, also unsuitable for sensitive samples.

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Osmotic Pressure: — $\Pi = i C R T$. Since $C = \frac{n_B}{V(\text{L})} = \frac{W_B/M_B}{V(\text{L})}$, we derive $M_B = \frac{i W_B R T}{\Pi V(\text{L})}$. This is the most preferred method for macromolecules due to its high sensitivity (large $\Pi$ even at low $C$) and measurement at room temperature.

**Van't Hoff Factor ($i$):** This factor corrects for the actual number of particles in solution. For non-electrolytes (e.g., glucose, urea), $i=1$. For strong electrolytes (e.g., NaCl, $ext{K}_2\text{SO}_4$), $i$ equals the number of ions produced (e.g., NaCl $o$ 2, $ext{K}_2\text{SO}_4 \to$ 3). For weak electrolytes, $i = 1 + (n-1)\alpha$, where $\alpha$ is the degree of dissociation. If solutes associate (e.g., ethanoic acid in benzene), $i<1$.

Example: $1.0,\text{g}$ of a non-electrolyte in $100,\text{mL}$ water at $27^circ\text{C}$ has $\Pi = 0.821,\text{atm}$. Find $M_B$. ($R=0.0821,\text{L atm mol}^{-1}\text{K}^{-1}$) $T = 27+273 = 300,\text{K}$, $V = 0.1,\text{L}$, $W_B = 1.0,\text{g}$, $i=1$. $M_B = \frac{1 \times 1.0 \times 0.0821 \times 300}{0.821 \times 0.1} = \frac{24.63}{0.0821} = 300,\text{g/mol}$.

Always remember unit consistency and the correct application of $i$ for accurate results.

Prelims Revision Notes

Determination of Molecular Masses using Colligative Properties

1. Core Principle: Colligative properties depend *only* on the number of solute particles, not their identity. By measuring a colligative property, we can determine the molar concentration of the solute, and thus its molecular mass ($M_B$). Applicable only for non-volatile solutes.

2. Van't Hoff Factor ($i$):

* Non-electrolytes (e.g., urea, glucose): $i=1$. * Strong Electrolytes (complete dissociation): $i = \text{number of ions produced per formula unit}$. * NaCl $o \text{Na}^+ + \text{Cl}^-$, so $i=2$.

* $ext{CaCl}_2 \to \text{Ca}^{2+} + 2\text{Cl}^-$, so $i=3$. * $ext{K}_2\text{SO}_4 \to 2\text{K}^+ + \text{SO}_4^{2-}$, so $i=3$. * Weak Electrolytes (partial dissociation): $i = 1 + (n-1)\alpha$, where $n$ is the theoretical number of ions and $\alpha$ is the degree of dissociation.

* Association (e.g., ethanoic acid in benzene forming dimers): $i < 1$. If 'n' molecules associate to form one, $i = 1/n$.

3. Formulas for Molecular Mass ($M_B$):

* Relative Lowering of Vapor Pressure (RLVP): $\frac{P^0 - P_s}{P^0} = i X_B \approx i \frac{n_B}{n_A} = i \frac{W_B/M_B}{W_A/M_A}$ (for dilute solutions) $M_B = \frac{i W_B M_A}{W_A} \left( \frac{P^0}{P^0 - P_s} \right)$ (less practical) * Elevation in Boiling Point (EBP): $\Delta T_b = i K_b m$ $M_B = \frac{i K_b W_B \times 1000}{\Delta T_b W_A (\text{in g})}$ * Depression in Freezing Point (DFP): $\Delta T_f = i K_f m$ $M_B = \frac{i K_f W_B \times 1000}{\Delta T_f W_A (\text{in g})}$ * **Osmotic Pressure ($Pi$):** $\Pi = i C R T$ $M_B = \frac{i W_B R T}{\Pi V (\text{in L})}$

4. Key Constants & Units:

* $R$ (Gas Constant): $0.0821,\text{L atm mol}^{-1}\text{K}^{-1}$ (if $Pi$ in atm, $V$ in L) or $8.314,\text{J mol}^{-1}\text{K}^{-1}$ (if $Pi$ in Pa, $V$ in $ext{m}^3$). * $T$ (Temperature): Always in Kelvin ($^circ ext{C} + 273.

15$). *$K_b$(Ebullioscopic constant) and$K_f$(Cryoscopic constant): Units are$ ext{K kg mol}^{-1}$. *$W_A$(Mass of solvent): Use in kg for molality ($m$), or in grams with a factor of 1000 in the numerator for$M_B$ formulas.

* $V$ (Volume of solution): Always in Liters for osmotic pressure calculations.

5. Preferred Method for Macromolecules:

* Osmotic Pressure is preferred for polymers, proteins, etc. * Reasons: * Produces a large, easily measurable pressure even at very low concentrations (high $M_B$ means low $C$). * Can be measured at room temperature, preventing denaturation of sensitive biological samples. * Directly relates to molarity ($C$), which is convenient. * Other properties yield very small, hard-to-measure changes for macromolecules and often require extreme temperatures.

6. Common Mistakes to Avoid:

* Incorrect unit conversions (T to K, mL to L, g to kg). * Forgetting or miscalculating the van't Hoff factor ($i$). * Confusing $W_A$ (mass of solvent) with $V$ (volume of solution). * Using the wrong value of $R$ for given units of $\Pi$ and $V$.

Vyyuha Quick Recall

To find Molecular mass, remember Osmotic Pressure is Best for Polymers: My Old Professor Believes Pi = iCRT (Pi = iCRT is the key formula for osmotic pressure, which is best for polymers).