Problem 27 - A Complete Resource Book in Chemistry for JEE Main

Question

Increasing the temperature of an aqueous solution will cause (a) decrease in molality (b) decrease in molarity (c) decrease in mole fraction (d) decrease in \% (w/w)

Step-by-Step Solution

Answer

Increasing temperature decreases molarity.

Step 1: Understanding Solution Terms

We need to assess how temperature affects molality, molarity, mole fraction, and \(\%\) (w/w). Molality (m) is based on the mass of the solvent, which doesn't change with temperature. Molarity (M) depends on volume, which expands with heat. Mole fraction involves ratios of moles, unaffected by expansion. \(\%\) (w/w) is mass-based, like molality.

Step 2: Effect on Molarity

As temperature increases, the volume of the solution also increases (due to expansion). Since molarity (M) is defined as moles of solute per liter of solution, an increase in volume results in a decrease in molarity.

Step 3: Effect on Molality

Molality is based on the mass of the solvent and the moles of solute. Since mass does not change with temperature, molality remains constant with temperature changes.

Step 4: Effect on Mole Fraction

Mole fraction is the ratio of the moles of a component to the total moles in the solution. It does not depend on the volume or mass and thus remains unchanged with temperature.

Step 5: Effect on Percentage (w/w)

The \(\%\) (w/w) refers to the mass percentage of solute in the total mass of solution. As mass does not change with temperature, \(\%\) (w/w) remains constant.

Key Concepts

Molarity

Molarity is a concept that helps us understand how concentrated a solution is by focusing on the number of moles of solute in a given volume of solution. Specifically, molarity (M) is calculated by dividing the moles of solute by the volume of solution in liters:

• Formula: \( M = \frac{\text{moles of solute}}{\text{liters of solution}} \)

When the temperature of a solution increases, the liquid components can expand, increasing the overall volume of the solution. Since molarity takes into account the volume of the solution, any increase in temperature can cause a decrease in concentration, because while the number of moles remains constant, the volume denominator increases. This is why a higher temperature results in a lower molarity.

Molality

Molality is another measure of concentration, representing the number of moles of solute per kilogram of solvent, instead of per volume:

• Formula: \( m = \frac{\text{moles of solute}}{\text{kilograms of solvent}} \)

A key feature of molality is its reliance on the mass of the solvent, which remains constant irrespective of temperature variations. Because mass does not change with temperature, molality also remains unaffected. This is particularly useful in scenarios requiring temperature-dependent reactions, providing a stable concentration measurement even when external conditions fluctuate.

Mole Fraction

The mole fraction is a way of expressing the proportion of a component in a solution, calculated by dividing the number of moles of the component by the total number of moles in the solution:

• Formula: \( X_i = \frac{\text{moles of component}}{\text{total moles of all components}} \)

The mole fraction is a dimensionless quantity, meaning it lacks any units, as it is purely a ratio. An important property of the mole fraction is that it remains constant regardless of temperature changes. This is because temperature affects volume and possibly phase states but not the ratio of moles in the solution. Thus, whether it gets hotter or colder, the mole fraction stays the same.

Percentage Weight by Weight (w/w)

Percentage weight by weight, often noted as % (w/w), describes the mass percentage of a solute within the mass of the total solution:

• Formula: \( \text{% (w/w)} = \left(\frac{\text{mass of solute}}{\text{total mass of solution}}\right) \times 100 \)

Like molality, the % (w/w) measurement is unaffected by changes in temperature because it is based on mass, and mass remains constant regardless of temperature fluctuations. This constancy is beneficial in analytical chemistry, where precise and consistent concentration measurements are necessary despite external environmental changes. Understanding the effect of temperature helps maintain accuracy in chemical processes that rely on specific concentration values.