Determining the boiling point elevation calculates how much a liquid’s boiling temperature increases when a substance is dissolved in it. This phenomenon occurs when a non-volatile solute, like salt or sugar, is added to a pure solvent, such as water. The resulting solution will always boil at a higher temperature than the pure solvent. Boiling point elevation is categorized as a colligative property, meaning the extent of the temperature increase depends solely on the number of dissolved particles present, not on the chemical identity of those particles. Understanding this concept allows for precise predictions about the thermal behavior of various solutions.
The Mechanism Behind Boiling Point Elevation
The foundation for boiling point elevation lies in the lowering of vapor pressure that occurs when a solute is introduced into a solvent. Boiling is defined as the temperature at which a liquid’s vapor pressure equals the surrounding atmospheric pressure. In a pure solvent, all molecules on the surface contribute to the vapor pressure. When a non-volatile solute is added, solute particles block some surface area, reducing the rate at which solvent molecules escape into the gas phase. This lowers the solution’s overall vapor pressure. Because the vapor pressure is lower, the solution must be heated to a higher temperature to match the external atmospheric pressure and begin boiling. This additional required heat is the measured boiling point elevation.
Defining the Variables Used in Calculation
The calculation for boiling point elevation is governed by a straightforward equation, requiring a clear understanding of its three main variables.
The first variable is molality (\(m\)), a measure of concentration. Molality is defined as the moles of solute dissolved per kilogram of the solvent, which is distinct from molarity that uses liters of solution.
The second variable is the ebullioscopic constant (\(K_b\)), a fixed value specific to the solvent being used. This constant reflects the solvent’s inherent resistance to boiling point changes and is provided in tables. For water, the \(K_b\) value is approximately \(0.512^{\circ}\text{C}/\text{m}\).
The third variable is the van’t Hoff factor (\(i\)), which accounts for the dissociation of the solute particles. For molecular solutes like sugar, \(i\) is 1. For ionic compounds, such as sodium chloride (\(\text{NaCl}\)), \(i\) is approximately 2 because it dissociates into two ions (\(\text{Na}^+\) and \(\text{Cl}^-\)).
Step-by-Step Calculation Procedure
The total increase in boiling temperature (\(\Delta T_b\)) is calculated using the formula: \(\Delta T_b = i \cdot K_b \cdot m\). This calculation determines the difference between the solution’s new boiling point and the pure solvent’s original boiling point. To illustrate the process, consider an example where 58.44 grams of \(\text{NaCl}\) (table salt) are dissolved in 1.00 kilogram of water.
The first step is to determine the molality (\(m\)) of the solution by converting the grams of solute into moles. Since the molar mass of \(\text{NaCl}\) is \(58.44\text{ g}/\text{mol}\), dissolving \(58.44\text{ grams}\) results in exactly \(1.00\text{ mole}\) of \(\text{NaCl}\). Because the solute is dissolved in \(1.00\text{ kilogram}\) of solvent, the molality is calculated as \(1.00\text{ m}\).
The next step involves identifying the constant values for the van’t Hoff factor (\(i\)) and the ebullioscopic constant (\(K_b\)). Since \(\text{NaCl}\) is an ionic compound that dissociates into two particles, \(i\) is 2. The \(K_b\) for water is \(0.512^{\circ}\text{C}/\text{m}\).
These values are then substituted into the formula. The calculation is \(\Delta T_b = (2) \cdot (0.512^{\circ}\text{C}/\text{m}) \cdot (1.00\text{ m})\), which yields a \(\Delta T_b\) of \(1.024^{\circ}\text{C}\). This result represents the temperature increase above the pure solvent’s boiling point.
Finally, to find the solution’s new boiling temperature, the calculated \(\Delta T_b\) is added to the original boiling point of the pure solvent. The boiling point of pure water at standard atmospheric pressure is \(100.00^{\circ}\text{C}\). Therefore, the new boiling point for this saltwater solution is \(100.00^{\circ}\text{C} + 1.024^{\circ}\text{C}\), resulting in \(101.024^{\circ}\text{C}\).
Practical Applications of Boiling Point Elevation
The principles of boiling point elevation are applied in numerous everyday and industrial settings. A common example is the use of antifreeze, typically ethylene glycol, in car cooling systems. This substance is added to water not only to prevent the coolant from freezing in cold temperatures but also to raise its boiling point. A higher boiling point allows the engine to run at hotter temperatures without the coolant boiling over, which is necessary for efficient engine operation.
In the kitchen, adding salt to water for cooking pasta is a demonstration of boiling point elevation. Although the temperature increase from a pinch of salt is minimal, the water will reach a slightly higher temperature than \(100^{\circ}\text{C}\). Industrially, this principle is used in processes like sugar refining to monitor the concentration of sugar syrup by measuring its boiling temperature.