Problem 1 - Chemistry in 30 days

Question

Out of molarity \((F)\), molality \((m)\), formality \((F)\) and mole fraction \((x)\), those independent of temperature are (a) \(M, m\) (b) \(\bar{F}, x\) (c) \(m, x\) (d) \(M x\)

Step-by-Step Solution

Answer

The correct answer is (c) \(m, x\) because they are independent of temperature.

Step 1: Understand the Definitions

To solve this problem, we need to understand the definitions of each term. Molarity \(M\) is the number of moles of solute per liter of solution. Molality \(m\) is the number of moles of solute per kilogram of solvent. Formality \(F\) is similar to molarity but used for ionic compounds and refers to the moles of a compound dissolved per liter of solution. Mole fraction \(x\) is the ratio of moles of a component to the total moles of all components in the mixture.

Step 2: Analyze the Influence of Temperature

Molarity and formality depend on temperature because they involve the volume of the solution, which can change with temperature. Molality and mole fraction, however, do not depend on the volume of the solution but rather on its mass or specific ratios, which remain constant with temperature changes.

Step 3: Identify Temperature-Independent terms

Based on the influence of temperature, molality \(m\) and mole fraction \(x\) are independent of temperature because they are calculated based on mass or ratios rather than the volume of the solution.

Key Concepts

Molarity

Molarity (M) is a way to express the concentration of a solution by calculating how many moles of solute are present in one liter of solution. It's one of the most common measures for concentration used in chemistry because it's straightforward and directly related to the volume.
However, molarity has a peculiarity—it changes with temperature. This is because the volume of a liquid can expand or contract when heated or cooled, which affects the concentration.

To calculate molarity, use the formula: \[ M = \frac{n}{V} \]where:

• \( n \) is the number of moles of solute
• \( V \) is the volume of the solution in liters

In practice, when temperature fluctuations are a concern, chemists might prefer other measures like molality, which depend only on the mass and are unaffected by temperature changes. But in a controlled environment where temperature remains constant, molarity is a convenient and effective method to express solution concentration.

Molality

Molality (m) measures the concentration of a solute in a solution, but unlike molarity, it is expressed as the number of moles of solute per kilogram of solvent. Because it depends on mass, molality is not influenced by temperature changes.
This makes it especially useful in experiments where temperature variations are significant, or when precise data is crucial.

Here's how you can calculate molality: \[ m = \frac{n}{m_{\text{solvent}}} \]where:

• \( n \) is the number of moles of solute
• \( m_{\text{solvent}} \) is the mass of the solvent in kilograms

Molality provides a stable measure for solution concentration across different temperatures. It is particularly reliable for calculations involving colligative properties, such as boiling point elevation and freezing point depression, since these properties depend on the number of solute particles in a given mass of solvent.

Mole Fraction

Mole fraction is a concept that deals with the ratio of the moles of a component to the total moles in the mixture. It is a dimensionless number because it is a ratio and hence, provides a straightforward comparison. Importantly, it does not vary with temperature, making it very useful in many chemical calculations.
The mole fraction is especially relevant in gas mixtures and solutions where precise composition is needed. It's calculated using this formula:
\[ x = \frac{n_{\text{component}}}{n_{\text{total}}} \]where:

• \( n_{\text{component}} \) is the number of moles of the specific component
• \( n_{\text{total}} \) is the total number of moles in the mixture

This fraction gives a clear picture of each component's contribution to the overall mixture. The sum of mole fractions for all components in a solution will always be equal to 1, providing a balance and check for your calculations.
Mole fraction is pivotal in calculating partial pressures in gas mixtures and is also used in the Raoult’s Law applications for ideal solutions.