An Introduction to Boiling Point
The temperature at which the vapour pressure of a liquid and the pressure surrounding the liquid are in equilibrium, also the process by which the liquid converts itself into its vapour form is called its boiling point.
The boiling point can differ in a wide range such as boiling point of water is 100°C(2.2°F) at sea level, but at 1,905m (6,250ft) altitude, the boiling point is 93.4°C(200.1°F)
On the other hand, the normal boiling point (i.e, atmospheric boiling point or the atmospheric boiling point) is the point where the vapour pressure of liquid stays in equilibrium with the defined atmospheric pressure at sea level i.e, 1 ATM(atmospheric pressure).
Boiling Point Elevation Formula
One of the important properties of any solution is the boiling point elevation. The elevation in boiling point formula indicates that an increase in the boiling point can be calculated by the use of boiling point elevation and the molality and constant of the solution. The vapour of any solvent can decrease when a solute is added. And by this, some of the solvent molecules can be replaced by a solute. A high temperature is required to match the atmospheric pressure and the vapour pressure.
Formula:
The general formula to calculate the boiling point is:
\[K_b = \frac{RT_b 2M}{\Delta H_v}\]
Where R is the denotation of the universal gas constant
Tb is the denotation of the boiling temperature
[ln K]M — denotes the molar mass of the solvent
Another formula that can be utilised to calculate the elevation in boiling point can be written as:
\[T_b = \begin{bmatrix} \frac{1}{T_0} - \frac{R}{\Delta H_{Vap}} ln(\frac{P}{P_0}) \end{bmatrix}^{-1}\]
Variables
The formula of boiling points has the following variables:
Tb — Denotation of the boiling point temperature.
Po— Denotation of the pressure at boiling point.
To— Denotation of boiling temperature
R — Denotation of the universal gas constant
P — denotation of the vapour pressure of the liquid
∆Hvap — denotation of the Heat of vapourization
While considering a solution, when the boiling point of a liquid (a solvent) is higher than the pure solvent, then the phenomenon is termed as boiling point elevation.
Some of the basic examples of the boiling point elevation can be described as; when salt (non-volatile solute) is added to water (pure solvent), the boiling point can be measured accurately using an ebullioscopic measurement.
Boiling Point Equation
We all know that water boils at 100 degrees at 1 atm pressure but if we add a little amount of salt to it, then an interesting thing happens, it increases the boiling point of the solution. This is proven by researchers that adding a solute in a solution changes its form and results in an elevation in the boiling point. Both the amount of the change and the present boiling point are proportional to each other. The addition of a solution decreases the vapour pressure of the given solvent.
This change happens due to the displacement of the solvent molecules. This formula for elevation in boiling point hence proves that few of the solvent molecules that are present on the surface of the liquid solution are replaced by the solvent that is both non-electrolyte and electrolyte. If the amount of the solvent molecules on a surface is lowered then less evaporation can occur. To balance the vapour and make it equal to the ambient pressure, a higher boiling point is observed.
How to find the Boiling Point of a Solution?
The boiling point of a solution can be found by the following steps of the formula of elevation in boiling point:
^Tb = 1000*Kb*wM*W
where, “is the weight of the solute”, “is the molar mass of the solute and “W” is the weight of the solvent in grams.
^Tb = 1000 *Kb*wM*W
1.1 = 1000 *2.53 *10M*200
As a result of adding solvent to a solute, the vapour pressure of the individual solvent becomes less than the vapour pressure above the pure solvent present. This increases the boiling point of the solvent and it will be needed to treat at a higher temperature to make vapour pressure equal to the external pressure.
Hence the boiling point of the solution changes as the concentration of that particular solute in the solution changes its form.
Boiling Point Elevation Equation: Non-Volatile Solutes
The boiling point of a solvent above any solution changes its form and becomes greater than the boiling point of the solvent irrespective of non-volatile or volatile solute. But to maintain its simplicity, only the non-volatile solute shall be considered over here.
The formula is:
^T = Kbm
Where:
^T is the change in the boiling point of the solvent,
Kb is the molal boiling point elevation constant, and
M is the molal concentration of the solute in the solution.
The molal boiling point elevation constant, Kb, has a specific value depending on the identity of the solution.
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Basic Application
There are several different applications of the boiling point elevation which are enlisted below:
The most appropriate and the only major application of this factor is, it is highly used to measure the degree of dissociation or the molar mass of the solute.
Anti freezing process
Sugar refining process
Measurement of molar mass
Cooking
Limitations
Though boiling point has made a major impact in the growing ages. It also has some points of limitations too. These limitations can be described as
It is difficult to superheat and thus getting a precise calculation is difficult. This limitation is somehow overcome by the invention of the Beckmann thermometer up to some extend.
Moreover, determining the freezing point is much easier and thus more preferable as this type of measurement is highly precise. The cryoscopic constant is used to determine the freezing point.
Though adding particles to the solvent brings its temperature equal to the boiling point, this is because the addition hinders the interaction between the particles of solvent.
In the year 1741, Anders Celsius defined the scale of the temperature of boiling and boiling point of elevation as a colligative property. It happens in both types of solute i.e, electrolyte as well as non-electrolyte. In thermodynamics terms, the boiling point of elevation is isentropic and is measured in terms of either vapour pressure or the chemical potential of a solvent. Boiling point elevation and freezing point depression work in the same phenomenon. Though, the magnitude of both phenomena differs.
FAQs on Boiling Point Formula
1. What is the formula for calculating the elevation in boiling point?
The formula to calculate the elevation in the boiling point of a solution is given by the expression: ΔT_b = K_b × m. Here, the formula calculates the increase in the boiling point, not the final boiling point itself. The final boiling point is the sum of the original solvent's boiling point and this elevation.
2. What do the terms in the boiling point elevation formula (ΔT_b = K_b × m) represent?
Each term in the boiling point elevation formula has a specific meaning:
- ΔT_b represents the elevation in boiling point, which is the amount by which the boiling temperature increases.
- K_b is the Ebullioscopic Constant, or the molal boiling point elevation constant. This value is specific to the solvent used (e.g., water, benzene).
- m stands for the molality of the solution, which is the number of moles of solute dissolved per kilogram of solvent.
3. Why does adding a non-volatile solute, like salt, to water increase its boiling point?
Adding a non-volatile solute to a pure solvent lowers the solution's vapour pressure. This happens because the solute particles occupy space at the liquid's surface, reducing the rate at which solvent molecules can escape into the gas phase. Since boiling occurs when the vapour pressure equals the surrounding atmospheric pressure, the solution must be heated to a higher temperature to reach that required vapour pressure. This results in an elevated boiling point.
4. What is the main difference between boiling and evaporation?
The key difference lies in the mechanism and conditions. Boiling is a bulk phenomenon that occurs throughout the entire volume of a liquid at a specific temperature (the boiling point), where bubbles of vapour form within the liquid. In contrast, evaporation is a surface phenomenon that can occur at any temperature, where only molecules at the liquid's surface gain enough energy to escape into the gas phase.
5. How can the boiling point formula be used to find the molar mass of an unknown solute?
You can determine the molar mass of a non-volatile solute by rearranging the boiling point elevation formula. The steps are:
- Measure the boiling point elevation (ΔT_b) experimentally.
- Expand the molality (m) term in the formula: m = (moles of solute) / (mass of solvent in kg).
- Substitute 'moles of solute' with (given mass of solute, w₂) / (molar mass of solute, M₂).
- The rearranged formula becomes: M₂ = (K_b × w₂ × 1000) / (ΔT_b × w₁), where w₁ is the mass of the solvent in grams. By plugging in the known values, you can solve for M₂.
6. What is the Ebullioscopic Constant (K_b) and what does it depend on?
The Ebullioscopic Constant (K_b) is a physical constant that represents the increase in boiling point for a 1 molal solution of a non-volatile solute. Its value is a unique property of the solvent and does not depend on the nature of the solute dissolved in it. For example, the K_b for water is 0.512 °C·kg/mol, regardless of whether sugar or salt is the solute.
7. How does atmospheric pressure affect a liquid's boiling point?
A liquid's boiling point is directly affected by the external atmospheric pressure. Boiling begins when the liquid's internal vapour pressure equals the external pressure. Therefore:
- At high altitudes, where atmospheric pressure is lower, water boils at a temperature below 100°C.
- In a pressure cooker, where the pressure is artificially increased, water boils at a temperature above 100°C, allowing food to cook faster.
