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)

Short answer

Increasing temperature decreases molarity. Hence, the correct answer is (b).

Step-by-step solution

Understanding Temperature Effect on Solutions

When temperature increases, the volume of a solution, which is typically expressed in liters, can expand due to the increase in kinetic energy of the molecules.

Effect on Molality

Molality \(m\) is defined as the number of moles of solute per kilogram of solvent. Since mass does not change with temperature, increasing temperature will not affect molality. Therefore, option (a) is incorrect.

Effect on Molarity

Molarity \(M\) is defined as the number of moles of solute per liter of solution. As temperature increases, the volume of the solution may increase, leading to a decrease in molarity. Therefore, option (b) is correct.

Effect on Mole Fraction

Mole fraction depends on the ratio of moles of solute to the total number of moles in solution. This ratio is not affected by a change in temperature, hence, option (c) is incorrect.

Effect on % (w/w)

Percentage weight/weight \(% (w/w)\) is calculated as the mass of solute divided by the total mass of the solution, multiplied by 100. Since mass is unaffected by temperature change, \% (w/w) remains constant. Therefore, option (d) is incorrect.

Key concepts

Effect on Molarity

The concept of molarity is fundamental when studying how temperature affects solutions. Molarity, represented as \( M \), measures the concentration of a solution. It tells us the number of moles of solute per liter of solution. A key fact to remember is that molarity changes if the volume of the solution changes.
When temperature increases, the kinetic energy of molecules within the solution also increases. This addition of energy can cause the liquid to expand, resulting in more significant space between molecules. When this happens, the overall volume of the solution increases. However, the quantity of solute remains the same, but because the volume is larger, the concentration decreases.
Thus, higher temperatures can lead to a decrease in molarity. It’s crucial to note that although the volume and therefore the overall concentration changes, the actual amount of solute in terms of moles is unaffected. Understanding this distinction is vital for analyzing reactions and processes that depend on precise concentrations.

Effect on Molality

Molality is another way to express the concentration of a solution and is denoted by \( m \). Unlike molarity, molality is defined by the number of moles of solute per kilogram of solvent. This distinction makes molality particularly interesting because it is independent of temperature changes.
Why is that? Heat affects the volume but not the mass of substances. Even if the temperature increases causing the solution to expand, the actual weight of the solvent remains constant. Therefore, the quotient of moles of solute to kilograms of solvent remains the same no matter the temperature.
This property of molality is especially useful for calculations in situations where temperature fluctuates, such as in chemical reactions conducted at varying temperatures. By relying on molality, chemists can ensure that they have a stable and accurate measure of concentration unaffected by thermal changes.

Effect on Mole Fraction

The mole fraction of a component in a solution is a way to express its concentration. It is defined as the number of moles of a particular substance divided by the total number of moles in the solution. The remarkable feature of this concentration measure is its invariance with temperature changes.
Since the mole fraction relies only on the ratio of moles, neither the expansion of the solution volume nor the increase in molecular spacing affects it. An increase in temperature may change the volume, but it does not affect the actual count of moles.
For instance, if a solution consists of 2 moles of solute and 8 moles of solvent, the mole fraction of the solute is \( \frac{2}{10} \). This ratio remains the same unless moles of solute or solvent are added or removed, regardless of how the solution's volume might change with temperature. This makes mole fraction a dependable unit for maintaining a stable view of component ratios in solutions across varying conditions.