Boiling Point Formula

Dhristi JEE 2022-24

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: 

  1. ^T is the change in the boiling point of the solvent,

  2. Kb is the molal boiling point elevation constant, and

  3. 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.

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FAQs (Frequently Asked Questions)

1. How boiling point of elevation is required to calculate the molar mass of a solute?

In case, we avoid the intermolecular forces present between the H2O molecules, then the relation between the molar mass and boiling point of elevation shares an inverse relationship. The higher the molar mass will be, the lower will the boiling point of elevation and vice versa. So, to calculate the molar mass with the help of the boiling point of elevation, one should determine the moles of unknown (solute) from the molality of the solution and the mass of the solvent (in kg) used to make the solution.

2. Do alcohols have a higher boiling point?

Yes, alcohols have a much higher boiling point than other molecules which contain equal molecular mass which is equal to alcohol. This phenomenon takes place due to the presence of intermolecular hydrogen bonds of alcohol which are rather strong and are hard to break, increasing to the boiling point.

3. What is the difference between boiling point and evaporation?

The natural phenomenon in which the liquid form changes itself into a gaseous form is termed evaporation. On the other hand, to perform the boiling process, the liquid needs to be heated up to convert into vapour. Evaporation is a natural Process whereas boiling is an unnatural process.

4. Can water evaporate below 100°C?

Between the H2O molecules present in water, there's an intermolecular hydrogen bonding force present which makes the H2O molecules attract towards each other.  These bonds are generally weak and the molecules of H2O mostly go whizzing around with enough energy to break free of their neighbours which can be done well below 100°C.

5. Why is boiling faster than evaporation?

Evaporation leads to the cooling of the liquid where boiling doesn't undergo this cooling process. Moreover, the boiling process involves the movement of molecules much faster than evaporation. This is why the boiling process is much faster than that of the evaporation process.

6. Why does Boiling Point Elevation occur?

The boiling point of any liquid is its temperature in which the vapour pressure is equal to the pressure of the surrounding environment. Any non-volatile substance does not undergo evaporation readily and they have a low vapour pressure. Addition of the non-volatile solute to solvent results in lowering the vapour pressure of the solution. Hence, a larger amount of solute should be supplied to the solution to make it boil. This increase in the boiling temperature results in the elevation of the boiling point.

7. How Does Molality Affect the Boiling Point?

The boiling point of a solvent increases whenever a non-volatile substance is dissolved in it. It is said that the higher the concentration, the higher is the boiling point. This acts as a dissolved solute and crowds out other solvent molecules at its surface. It is difficult for the solvent molecules to escape into the gas phase if the concentration of the solute is high although, the rate of the condensation from gas to liquid form is not affected. So the solvent molecules need a higher temperature to escape the boiling at atmospheric pressure.

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