Experimentally determined molar mass is always lower than the true value in case of:
Strong electrolytes
Understanding Abnormal Molar Mass and Colligative Properties
Colligative properties of solutions, such as osmotic pressure, boiling point elevation, freezing point depression, and vapor pressure lowering, depend only on the number of solute particles in a given amount of solvent, not on the identity of the solute.
When we use these colligative properties to experimentally determine the molar mass of a solute, we typically assume that the solute particles are individual molecules and do not interact with each other (ideal behavior). However, if the solute dissociates into multiple ions or associates to form larger particles, the actual number of particles in the solution will be different from the number of molecules added. This leads to an abnormal molar mass calculation.
Effect of Dissociation and Association on Experimental Molar Mass
The Van't Hoff factor (\(i\)) is used to account for the number of particles a solute produces in solution. It is defined as:
\( i = \frac{\text{Actual number of particles in solution}}{\text{Number of formula units initially dissolved}} \)
- For a non-electrolyte, \(i = 1\) (e.g., glucose, urea).
- For a solute that dissociates into \(n\) ions, the theoretical \(i = n\) (e.g., NaCl dissociates into Na\(^+\) and Cl\(^-\), so \(n=2\), ideal \(i=2\)).
- For a solute that associates to form particles of size \(n\) (e.g., dimerization, \(n=2\)), the theoretical \(i = 1/n\) (e.g., two molecules form one dimer, \(i = 1/2\)).
Colligative properties are proportional to the number of particles, and thus proportional to \(i\). For example, the freezing point depression is given by:
\( \Delta T_f = i K_f m \)
Where \(K_f\) is the cryoscopic constant and \(m\) is the molality of the solution. Molality is defined as moles of solute per kilogram of solvent. Moles of solute can be expressed as mass of solute divided by molar mass (\(n = \frac{w_B}{M_B}\)). So, molality \(m = \frac{w_B/M_B}{w_A}\), where \(w_B\) is mass of solute and \(w_A\) is mass of solvent.
Thus, \( \Delta T_f = i K_f \frac{w_B}{M_B^{\text{true}} w_A} \)
When we experimentally measure \(\Delta T_f\) and calculate the molar mass (\(M_B^{\text{exp}}\)) assuming no dissociation or association (i.e., assuming \(i=1\)), we use the formula:
\( \Delta T_f^{\text{measured}} = 1 \cdot K_f \frac{w_B}{M_B^{\text{exp}} w_A} \)
Since \(\Delta T_f^{\text{measured}} = i K_f \frac{w_B}{M_B^{\text{true}} w_A}\), we can equate the two expressions:
\( i K_f \frac{w_B}{M_B^{\text{true}} w_A} = K_f \frac{w_B}{M_B^{\text{exp}} w_A} \)
Cancelling \(K_f\), \(w_B\), and \(w_A\) (assuming they are the same for both true and experimental scenarios), we get:
\( \frac{i}{M_B^{\text{true}}} = \frac{1}{M_B^{\text{exp}}} \)
Rearranging this gives the relationship between experimental and true molar mass:
\( M_B^{\text{exp}} = \frac{M_B^{\text{true}}}{i} \)
From this relationship:
- If \(i > 1\) (dissociation), then \(M_B^{\text{exp}} < M_B^{\text{true}}\). The experimental molar mass is lower than the true value.
- If \(i < 1\) (association), then \(M_B^{\text{exp}} > M_B^{\text{true}}\). The experimental molar mass is higher than the true value.
- If \(i = 1\) (non-electrolyte), then \(M_B^{\text{exp}} = M_B^{\text{true}}\) (assuming ideal behavior).
Analyzing the Options
Let's examine each option based on the effect on the number of particles and the value of \(i\):
- Strong electrolytes: These substances dissociate almost completely into ions when dissolved in a suitable solvent (like water). Examples include NaCl, KCl, Na\( _2 \)SO\( _4 \). For NaCl, \(i\) is close to 2 (dissociates into Na\(^+\) and Cl\(^-\)). For Na\( _2 \)SO\( _4 \), \(i\) is close to 3 (dissociates into 2 Na\(^+\) and 1 SO\( _4^{2-} \)). Since \(i > 1\), the experimental molar mass calculated from colligative properties will be lower than the true molar mass. Strong electrolytes exhibit the most significant and predictable dissociation among the options involving ionization.
- Weak electrolytes: These substances only partially dissociate into ions. Examples include acetic acid (CH\( _3 \)COOH), ammonia (NH\( _3 \)). The degree of dissociation depends on concentration. So, \(1 < i < \text{theoretical maximum}\) (the theoretical maximum is the number of particles if it were a strong electrolyte). Since \(i > 1\), the experimental molar mass will be lower than the true molar mass. However, the question asks when it is *always* lower; strong electrolytes *always* exhibit significant dissociation leading to a lower experimental molar mass in standard colligative property experiments, while the effect is less pronounced and concentration-dependent for weak electrolytes.
- Non-electrolytes: These substances do not dissociate or associate in solution. Examples include sugar (sucrose, glucose), urea. For non-electrolytes, \(i = 1\). Therefore, the experimental molar mass determined using colligative properties should ideally be equal to the true molar mass.
- Dimers: This refers to association of solute molecules, where two molecules combine to form a single larger particle (a dimer). For example, carboxylic acids can form dimers in non-polar solvents through hydrogen bonding. If two molecules form one dimer, \(i = 1/2 = 0.5\). Since \(i < 1\), the experimental molar mass calculated will be higher than the true molar mass of the individual molecule.
Based on this analysis, the experimentally determined molar mass is always lower than the true value in the case of strong electrolytes due to their complete or near-complete dissociation, leading to a Van't Hoff factor \(i > 1\).
Summary Table
| Substance Type | Behavior in Solution | Effect on Number of Particles | Van't Hoff Factor (\(i\)) | Experimental Molar Mass \( M_B^{\text{exp}} = \frac{M_B^{\text{true}}}{i} \) |
|---|---|---|---|---|
| Strong Electrolytes | Dissociation (almost complete) | Increases significantly | \(i > 1\) (close to theoretical maximum) | \(M_B^{\text{exp}} < M_B^{\text{true}}\) (lower) |
| Weak Electrolytes | Dissociation (partial) | Increases | \(1 < i < \text{theoretical max}\) | \(M_B^{\text{exp}} < M_B^{\text{true}}\) (lower, less so than strong electrolytes) |
| Non-electrolytes | No Dissociation/Association | Stays the same | \(i = 1\) | \(M_B^{\text{exp}} = M_B^{\text{true}}\) (ideally) |
| Dimers (Association) | Association | Decreases | \(i < 1\) (e.g., \(i=0.5\) for dimerization) | \(M_B^{\text{exp}} > M_B^{\text{true}}\) (higher) |
Therefore, strong electrolytes are the substances for which the experimentally determined molar mass is consistently and significantly lower than the true value due to the increase in the number of particles in solution caused by dissociation.
Revision Table: Molar Mass Determination Concepts
| Concept | Description | Relevance to Molar Mass |
|---|---|---|
| Colligative Properties | Properties of solutions that depend only on the ratio of the number of solute particles to the number of solvent particles, not on the identity of the solute. | Used experimentally (e.g., \(\Delta T_f\), \(\Delta T_b\), \(\pi\), \(\Delta P\)) to determine molar mass. |
| Abnormal Molar Mass | Experimental molar mass differs from the theoretical or true molar mass due to dissociation or association of solute particles. | Occurs when the number of particles in solution is not equal to the number of molecules added. |
| Van't Hoff Factor (\(i\)) | Correction factor for colligative properties to account for dissociation or association; ratio of actual particles to added formula units. | Directly relates experimental molar mass to true molar mass: \( M_{\text{exp}} = M_{\text{true}} / i \). |
| Dissociation | Solute breaks into multiple particles (ions) when dissolved. \(i > 1\). | Leads to lower experimental molar mass (\(M_{\text{exp}} < M_{\text{true}}\)). |
| Association | Solute molecules combine to form larger particles when dissolved. \(i < 1\). | Leads to higher experimental molar mass (\(M_{\text{exp}} > M_{\text{true}}\)). |
Additional Information: Factors Affecting Van't Hoff Factor
While the ideal Van't Hoff factor (\(i_{\text{ideal}}\)) is the theoretical number of particles per formula unit upon complete dissociation, the actual Van't Hoff factor (\(i_{\text{actual}}\)) can be slightly different from the ideal value due to interionic attractions in the solution, especially at higher concentrations. For strong electrolytes, \(i_{\text{actual}}\) is usually slightly less than \(i_{\text{ideal}}\) due to ion pairing, but it is still significantly greater than 1. The question implies a scenario where the abnormal molar mass effect (lower than true value) is observed, which is characteristic of solutes with \(i > 1\). Strong electrolytes are the primary examples where this effect is prominent and expected.
For weak electrolytes, the degree of dissociation, and thus the actual \(i\) value (\(1 < i_{\text{actual}} < i_{\text{ideal}}\)), varies with concentration and temperature. At infinite dilution, weak electrolytes would approach ideal dissociation, but at typical experimental concentrations, their \(i\) is between 1 and the value for a strong electrolyte.
Non-electrolytes, ideally, have \(i=1\), and their experimental molar mass matches the true value (assuming ideal solution behavior). Association leads to \(i < 1\).
Therefore, strong electrolytes provide the clearest example where the increase in particle number due to dissociation leads to an experimentally determined molar mass that is lower than the true value.
Important Questions from p-block Elements
Second most abundant element in alloy misch metal is:
Match List-I with List-II:
List-I List-II (A) Gel (I) Hair cream (B) Foam (II) Dust (C) Emulsion (III) Cheese (D) Aerosol (IV) Whipped cream Choose the correct answer from the options given below:
Rate of a reaction changes from 2.48 × 10⁻³ mol⁻¹ sec⁻¹ to 4.96 × 10⁻³ mol⁻¹ sec⁻¹ when concentration of reactant is changed from 0.6 M to 2.4 M respectively, the order of reaction is:
Degree of dissociation, when molar conductivity of X at its concentration C is 24.14 and its limiting molar conductivity is 48.28 will be:
A divalent ion of 'V' (Atomic no. 23) in aqueous solution is:
