What Is the Boiling Point Formula and How Is It Derived
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 Explained with Equation and Applications
1. What is the formula for boiling point elevation?
The formula for boiling point elevation is ΔTb = iKbm, where ΔTb is the increase in boiling point.
- ΔTb = Tb(solution) − Tb(pure solvent)
- i = van’t Hoff factor (number of particles formed in solution)
- Kb = ebullioscopic constant of the solvent (°C·kg·mol-1)
- m = molality of the solution (mol/kg)
2. What is the Clausius–Clapeyron equation for boiling point?
The Clausius–Clapeyron equation is ln(P2/P1) = −ΔHvap/R (1/T2 − 1/T1), which relates vapor pressure and temperature.
- P1, P2 = vapor pressures
- T1, T2 = absolute temperatures (K)
- ΔHvap = enthalpy of vaporization (J/mol)
- R = gas constant (8.314 J·mol-1·K-1)
3. How do you calculate the boiling point of a solution?
The boiling point of a solution is calculated using Tb(solution) = Tb(pure solvent) + iKbm.
- Step 1: Calculate molality (m) = moles of solute / kg of solvent.
- Step 2: Determine the van’t Hoff factor (i).
- Step 3: Multiply iKbm to get ΔTb.
- Step 4: Add ΔTb to the normal boiling point.
4. What is the normal boiling point formula?
The normal boiling point is the temperature at which a liquid’s vapor pressure equals 1 atm (101.325 kPa). It can be estimated using the Clausius–Clapeyron equation when ΔHvap and vapor pressure data are known.
- At boiling: Vapor pressure = External pressure
- Normal boiling point: External pressure = 1 atm
5. What does ΔTb mean in the boiling point formula?
In the boiling point formula, ΔTb means the increase in boiling temperature caused by dissolving a solute.
- ΔTb = Tb(solution) − Tb(pure solvent)
- It is measured in °C or K.
- It depends on the number of dissolved particles.
6. What is the value and unit of Kb in the boiling point formula?
The Kb value is the ebullioscopic constant of a solvent and has units of °C·kg·mol-1.
- It is specific to each solvent.
- For water, Kb = 0.512 °C·kg·mol-1.
- Higher Kb means greater boiling point change per molal concentration.
7. Why does adding a solute increase the boiling point?
Adding a non-volatile solute increases the boiling point because it lowers the solvent’s vapor pressure.
- Solute particles reduce the number of solvent molecules escaping into vapor.
- A higher temperature is needed for vapor pressure to reach external pressure.
- This results in boiling point elevation.
8. What is the van’t Hoff factor (i) in the boiling point equation?
The van’t Hoff factor (i) is the number of particles a solute forms in solution.
- For non-electrolytes like glucose: i = 1.
- For NaCl: i ≈ 2 (Na+ and Cl-).
- For CaCl2: i ≈ 3 (Ca2+ and 2Cl-).
9. How does pressure affect boiling point?
Boiling point increases with increasing external pressure and decreases with decreasing pressure.
- Boiling occurs when vapor pressure = external pressure.
- At high altitude (low pressure), liquids boil at lower temperatures.
- Pressure cookers raise boiling point by increasing pressure.
10. Can you give an example calculation using the boiling point elevation formula?
Yes, the boiling point elevation can be calculated using ΔTb = iKbm.
- Example: 1 mol of glucose (i = 1) dissolved in 1 kg of water.
- m = 1 mol/kg
- Kb for water = 0.512 °C·kg·mol-1
- ΔTb = (1)(0.512)(1) = 0.512°C
