Question

Is molality or molarity dependent on temperature? Explain your answer. Why is molality, and not molarity, used in the equations describing freezing-point depression and boiling-point elevation?

Short answer

Molality is independent of temperature, as it depends only on the mass of the solute and solvent, while molarity is dependent on temperature since it relies on the volume of the solution, which may change with temperature. In equations describing freezing-point depression and boiling-point elevation, molality is used because these colligative properties depend on the concentration of solute particles, and it's essential to use a concentration measure that is independent of temperature. This ensures accurate calculations without the influence of temperature changes on the solution's concentration.

Step-by-step solution

Define Molality and Molarity

Molality (m) is defined as the number of moles of solute (solute particles) per kilogram of solvent (mass of solvent). It is written as: \[m = \frac{moles\, of\, solute}{kg\, of\, solvent}\] Molarity (M) is defined as the number of moles of solute per liter of solution. It is written as: \[M = \frac{moles\, of\, solute}{L\, of\, solution}\]

Temperature Dependence

Molality depends only on the mass of the solute and solvent, and doesn't have any relation to volume or temperature. Thus, molality is independent of temperature. On the other hand, molarity depends on the volume of the solution, which might be affected by temperature since the volume of a liquid can change with temperature. Thus, molarity is dependent on temperature.

Relation to Freezing-Point Depression and Boiling-Point Elevation

Freezing-point depression (∆Tf) and boiling-point elevation (∆Tb) depend on the concentration of the solute particles in the solution. These colligative properties can be described by the equations: \[\Delta Tf = K_f \cdot m \cdot i\] \[\Delta Tb = K_b \cdot m \cdot i\] Here, Kf and Kb are the cryoscopic and ebullioscopic constants for a particular solvent, m is the molality, and i is the van 't Hoff factor (the number of dissociated particles per formula unit in the solution). As the colligative properties depend only on the concentration of the solute particles and not on their chemical nature, it's important to use a concentration measure that is independent of temperature. This is because the colligative properties describe changes in properties of the solvent due to the presence of solute particles, and the dependence on temperature might affect the changes in these properties. Since molality is independent of temperature, it is used in these equations rather than molarity, which is dependent on temperature. Therefore, molality allows for the calculation of freezing-point depression and boiling-point elevation without any influence of temperature changes on the concentration of the solution.

Key concepts

Molality

When discussing colligative properties like freezing-point depression and boiling-point elevation, the concept of molality is crucial. Molality measures the concentration of a solution based on the mass of the solvent. This makes it unique compared to other concentration measures such as molarity.
Molality is calculated using the formula:

• \( m = \frac{moles\, of\, solute}{kg\, of\, solvent} \)

One significant advantage of molality is that it remains unaffected by changes in temperature. This is because it depends solely on the mass of the solvent, not on its volume.
Since temperature variations do not impact the mass, molality provides a stable and reliable measure that is particularly useful in calculations involving temperature-sensitive processes like colligative properties.
The constancy of molality with temperature is why it is chosen over other units like molarity when calculating changes such as freezing-point depression or boiling-point elevation.

Molarity

Molarity is another way to express the concentration of a solution, but it is fundamentally different from molality. It measures concentration based on the volume of the solution. The formula for molarity is:

• \( M = \frac{moles\, of\, solute}{L\, of\, solution} \)

This means that molarity will change when the temperature of the solution changes, because the volume of liquids expands or contracts with temperature fluctuations.
Temperature impacts molarity in the following ways:

• As temperature increases, the volume of the solution may expand, leading to a decrease in molarity.
• Conversely, a decrease in temperature may cause contraction, increasing molarity.

Due to these variations, molarity is not ideal for calculations regarding colligative properties, which require concentration measures that are consistent regardless of temperature change. Thus, while molarity is widely used in various chemistry applications because it is intuitive, its temperature dependence can be a limitation in specific scientific calculations.

Temperature Dependence

The dependence of concentration measures on temperature is particularly important when discussing colligative properties. These properties are physical changes in solutions that depend solely on the number of solute particles and not on their identities. They include phenomena like:

• Freezing-point depression
• Boiling-point elevation
• Osmotic pressure

For these calculations, it's imperative to have a unit of measurement that remains constant under varying temperatures. This ensures accuracy and reliability in predicting how the solution will behave under different conditions.
Molality fits this requirement perfectly as it remains independent of temperature changes. It focuses on mass rather than volume, making it immune to the expansions or contractions of the solvent that are induced by temperature fluctuations.
Using molality for colligative property equations is advisable as it provides unchanging concentration metrics. This consistency ensures that the measures of changes within the solution, such as shifts in boiling or freezing points, are solely due to the concentration of particles and not altered by temperature-driven volume changes. Consequently, molality provides more precise and reliable results in experiments and applications involving colligative properties.