Problem 24 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following changes with change in temperature? (a) mole fraction (b) formality (c) \(\%(\mathrm{w} / \mathrm{W})\) (d) molality

Step-by-Step Solution

Answer

Formality changes with temperature; others do not.

Step 1: Understanding Mole Fraction

Mole fraction is defined as the ratio of the moles of a component to the total moles of all components in the mixture. It is a dimensionless quantity and is independent of temperature because the ratio of moles doesn't change with temperature.

Step 2: Analyzing Formality

Formality is similar to molarity but often used in place of it when dealing with strong electrolytes that completely dissociate. Like molarity, it is temperature-dependent since it relies on the volume of the solution, and volume changes with temperature.

Step 3: Investigating Percentage by Weight

Percentage by weight, \(%( ext{w/W})\), is calculated as weight of the solute divided by the total weight of the solution times 100. This property is also independent of temperature because it is based solely on the mass, which doesn't change with temperature.

Step 4: Examining Molality

Molality is defined as the number of moles of solute per kilogram of solvent. Since molality depends solely on mass (not volume), it remains unaffected by changes in temperature.

Step 5: Conclusion from Analysis

Based on the analysis, only formality is dependent on temperature due to its reliance on volume, which changes with temperature.

Key Concepts

Mole Fraction

Mole fraction is a vital concept in chemistry representing the ratio of the moles of one component to the total moles in a mixture. It's a dimensionless figure, meaning it has no units. This is because you are dividing the number of moles of the component by the total moles, both of which are counted similarly. The beauty and simplicity of mole fraction lie in its independence from temperature, making it a consistent way to express concentrations.
Changes in temperature do not affect the number of particles in a solution or mixture since mole counts remain the same. Thus, the ratio of these components—moles of one component to the total moles—remains constant regardless of any temperature fluctuations, assuring that mole fraction remains a stable and reliable measurement for concentrations in chemistry.

Formality

Formality is similar to molarity; however, it is used less frequently. It is specifically handy for solutions of strong electrolytes that completely dissociate in solution. Formality is defined as the number of formal units (original ionic compounds before dissociation) per liter of solution.
One thing to keep in mind is that formality, like molarity, shows susceptibility to temperature changes. Since it uses volume as a basis for its calculation, and volume tends to expand or contract with temperature variations, the formality value will change with these temperature shifts. Therefore, when dealing with situations that involve temperature changes, the dependency of formality on volume should not be overlooked, as it impacts the concentration measurement.

Percentage by Weight

Percentage by weight (% w/W) is a straightforward method for describing how much of a solute is present in a solution. It's calculated using the formula:

• \( \text{Percentage by weight} \ = \ \frac{\text{weight of solute}}{\text{total weight of solution}} \times 100 \)

This form of concentration measure remains unaffected by temperature changes. The reason for this stability is that mass—whether of solute or the entire solution—doesn't change with temperature. Thus, when you calculate a percentage by weight, you are relying solely on these constant mass values, ensuring a stable concentration measurement regardless of temperature fluctuations.
This makes it a useful metric when a temperature-invariant concentration expression is necessary.

Molality

Molality is crucial because it, too, is independent of temperature changes, due in part to its reliance on the mass of the solvent rather than its volume. Defined as the number of moles of solute per kilogram of solvent, molality provides a temperature-stable way to express concentration:

• \( \text{Molality} = \ \frac{\text{moles of solute}}{\text{kilograms of solvent}} \)

Since both the moles of solute and kilograms of solvent remain unaffected by variations in temperature, molality is consistently unchanged in such conditions.
Its temperature independence makes it quite practical in experiments and applications where the conditions are not tightly controlled, ensuring reliability even when temperatures fluctuate across a wide range.