Question

The elevation in boiling point is given by the formula $$\Delta x \quad K_{h} \times \frac{\mathfrak{w}}{m} \times \frac{1}{W}$$ where \(K_{b}\) is called (a) boiling point constant (b) ebullioscopic constant (c) molal elevation constant (d) all of these

Short answer

The name given to the constant \(K_{b}\) in the given boiling point elevation formula is all of these - 'boiling point constant', 'ebullioscopic constant', and 'molal elevation constant'.

Step-by-step solution

Understand the concepts

First, understand the meaning of the parameters in the boiling point elevation formula. The formula itself is used in physics and chemistry to calculate the change in the boiling point of a solution upon addition of a non-volatile solute. Here, \(K_{b}\) is a proportionality constant that depends on the particular solvent.

Analysis of each option

Let's analyze each given option. Boiling point constant, ebullioscopic constant, and molal elevation constant are all different terms used for the term \(K_{b}\) in various contexts.

Final assessment

As all the options are different names of the constant \(K_{b}\), we can conclude that option (d) 'all of these' is accurate.

Key concepts

Colligative Properties

Colligative properties are a category of properties in chemistry that depend on the number of particles in a solution rather than the type of particle. They are unique because they only care about the quantity, not the identity. This concept is fundamental when studying solutions and their behavior.

One of the most remarkable colligative properties is the boiling point elevation. When you dissolve a non-volatile solute in a liquid, the boiling point of the resulting solution will be higher than the pure solvent. This happens because the solute particles disrupt the solvent's ability to evaporate, requiring more energy (and thus, temperature) to boil.

The application of this knowledge is vast, ranging from culinary techniques, like boiling pasta in saltwater, to industrial processes, such as the production of antifreeze. Understanding colligative properties helps in grasping how solutions behave under various conditions and can be crucial for predicting outcomes in both experimental and real-world scenarios.

Ebullioscopic Constant

The ebullioscopic constant, denoted as \(K_b\), is a critical constant in understanding boiling point elevation. It's a proportionality factor that quantifies how much the boiling point of a liquid solvent will increase when a solute is added. Not to be confused with simplistic constants, the ebullioscopic constant is specific to each solvent due to their distinct properties.

For example, water has a different \(K_b\) compared to alcohol, meaning that the same amount of solute will cause different degrees of boiling point elevation in each solvent. This constant is vital for accurate calculations in laboratories and industries. For instance, it's used to determine molecular masses by measuring the change in the boiling point of a solution when a known amount of solute is dissolved.

Non-Volatile Solute

A non-volatile solute is a substance that does not readily vaporize into a gas under existing conditions. When a non-volatile solute is dissolved in a solvent, it affects the solution’s boiling point without contributing particles to the vapor phase. This distinct characteristic plays a significant role in boiling point elevation.

Because these solutes do not evaporate, they disrupt the normal escape of solvent molecules during boiling, directly influencing the colligative property of boiling point elevation. The presence of a non-volatile solute raises the boiling point because it lowers the vapor pressure of the solution, making it harder for the solvent to evaporate and consequently requiring more heat to reach the boiling point.

Non-volatile solutes are prevalent in everyday life and in various industries. They're found in salt solutions, sweetened beverages where sugar is the solute, and in antifreeze, where ethylene glycol is added to water to lower the freezing point and elevate the boiling point, thus ensuring a car's engine functions optimally in different temperatures.