How to calculate boiling point elevation?

You multiply three values together: the van't Hoff factor of the solute, the boiling point elevation constant for the solvent, and the molal concentration of the solution. This product gives you the increase in degrees. Adding this value to the boiling point of the pure solvent will give you the temperature at which the solution boils. For 0.5 moles per kilogram of sugar in water, you would multiply 1 by 0.512 and then again by 0.5, giving a result of 0.256 degrees Celsius. Therefore, water with this concentration of sugar will boil at 100.256 degrees Celsius.

What is the boiling point elevation constant for water?

It is 0.512 °C kg/mol. Sometimes it is also given as 0.512 K kg/mol since a degree Celsius and a Kelvin have the same size. This value means that if you dissolve one mole of stuff in a kilogram of water, the boiling point will increase by about half a degree. This value was not chosen arbitrarily but is determined from the boiling point of water, its molar mass, and the energy required to vaporize water. The derivation was shown above.

Why is kilograms of solvent used in molarity instead of liters of solution?

The reason for this is that the experiment involves heating. As the volume of a liquid expands when heated, the molar concentrations measured at room temperature are inaccurate once the boiling point is reached. The mass concentration does not change with temperature and therefore remains constant during measurement. Note that the denominator represents the solvent itself, rather than the solution after preparation.

Is the van't Hoff factor always an integer?

Only under ideal conditions. Sodium chloride should have a value of 2 but the usual measured values are closer to 1.9. This is because some sodium ions and chloride ions pair up and are counted as one unit rather than two units. The higher the concentration and charge of the ions, the greater the deviation. So calcium chloride deviates more from its ideal value of 3 than does sodium chloride from its ideal value of 2. The values for weak acids are slightly above 1 because only a fraction of the molecules dissociate.

Does salt reduce cooking time for spaghetti water?

No, it actually slightly delays the process. Even if you add a tablespoon of salt to four liters of water, the boiling point will only increase by about 0.08 °C which is such a small change that it's barely noticeable. Technically speaking, the water has to reach a slightly higher temperature in order to boil. Salt is mainly added for seasoning purposes.

How do you find molar mass using boiling point elevation?

The measured values of the boiling point elevation are divided by the product of the van't Hoff factor and the constant for the boiling point elevation to obtain the molar concentration. This is then multiplied by the number of kilograms of solvent to determine the amount, and finally the weighed mass is divided by this amount. The "Mode Five" device automatically performs these calculations. Use solvents with large constants, such as benzene or naphthalene, because temperature changes limit accuracy.

Boiling Point Elevation Calculator

Boiling point elevation

What do you want to work out?

Boiling point elevation

Molality from a measured elevation

Van't Hoff factor from a measured elevation

Ebullioscopic constant from a measured elevation

Molar mass of an unknown solute

Solvent

What does the solute do in solution?

How are you giving the concentration?

Enter the molality directly

Work it out from masses

Molality, b (mol/kg)

Boiling point elevation (C degrees)

Boiling point of the solution (C)

Pick the solvent, say what the solute does in solution, then give the concentration. The calculator returns the rise in boiling point and where the solution actually boils.

Boiling point elevation (C degrees)

Boiling point of the solution: °C
Boiling point of the pure solvent: °C
Elevation in Fahrenheit degrees

Molality in play (mol/kg)
Van't Hoff factor in play
Ebullioscopic constant in play (C kg/mol)

The dissolved particles push the boiling point up by 0.256 C degrees, so this solution boils at 100.256°C instead of 100°C.

Curve and solvent comparison

Show how the elevation grows with molality

Plot the straight line the equation predicts, next to the same solvent with a nonelectrolyte solute.

Show the solvent comparison table

The same solution strength poured into each of the twelve preset solvents.

Your solution strength and solute type applied to each preset solvent
Solvent	Kb (C kg/mol)	Boils at (C)	Elevation (C degrees)	Solution boils at (C)
Water	0.512	100	0.256	100.256
Ethanol	1.22	78.37	0.61	78.98
Methanol	0.83	64.7	0.415	65.115
Benzene	2.53	80.09	1.265	81.355
Chloroform	3.63	61.2	1.815	63.015
Acetic acid	3.07	118.1	1.535	119.635
Acetone	1.71	56.05	0.855	56.905
Carbon tetrachloride	5.03	76.72	2.515	79.235
Cyclohexane	2.79	80.74	1.395	82.135
Diethyl ether	2.02	34.55	1.01	35.56
Phenol	3.04	181.75	1.52	183.27
Naphthalene	5.8	217.9	2.9	220.8

Any substance that dissolves in a liquid raises the boiling point of that liquid. Sugar or salt dissolved in water, or grit left on roads after snow has melted, require slightly higher temperatures for the solvent to evaporate.

This calculator will calculate the amount of temperature increase required. When you enter the solvent, number of particles produced when dissolved and concentration of solution it gives the value of boiling point elevation and actual temperature at which the solution starts to boil.

Calculations can also be performed in the opposite direction. From a measured value of boiling point elevation you can determine either the mass concentration, van't Hoff factor, solvent's ebullioscopic constant or molar weight of compounds that cannot otherwise be identified.

What is boiling point elevation?

A liquid begins to boil when its vapor pressure is equal to the air pressure above it. When a nonvolatile solute is dissolved, some of the surface area of the liquid is occupied by particles that cannot evaporate, so fewer solvent molecules are able to escape and the vapor pressure is lowered.

In this case the pressure of the liquid is lower than the external pressure so the only way to do it would be to heat further. This is the principle and this effect is called a colligative property because it depends on the number of dissolved particles not what kind of particle they are.

If you dissolve one mole of sugar and one mole of urea in the same kilogram of water, the value for boiling point elevation is the same. The solvent only counts the particles and does not distinguish what they are made from. With a mole of sodium chloride, the boiling point elevation doubles but this is not because of any special properties of the chloride ion, it is because one unit of the chemical formula exists as two ions.

Formula for boiling point elevation:

The value of the boiling point elevation is proportional to concentration and the proportionality constant is determined by the solvent.

\Delta T_{b} = i \times K_{b} \times b

The solution then boils at the following temperature:

T_{b,\,solution} = T_{b,\,solvent} + \Delta T_{b}

Symbol	Meaning	Units	Typical value
dTb	Rise in boiling point	C degrees or K	a few tenths of a degree
i	Van't Hoff factor, particles per formula unit	none	1 for sugar, about 2 for NaCl
Kb	Ebullioscopic constant of the solvent	C kg/mol	0.512 for water
b	Molality of the solution	mol/kg	0.1 to 2
Tb,solvent	Boiling point of the pure solvent	C	100 for water at 1 atm

The value of the boiling point elevation is a difference between two temperatures so the numerical values are the same whether expressed in Celsius or Kelvin. If they were expressed in Fahrenheit, then the numerical values would be different. Since one degree Celsius is equal to 1.8 degrees Fahrenheit, rather than using the normal temperature conversion, it is multiplied by 1.8.

Example: "Salt dissolved in water".

One takes 10.0 g of sodium chloride and adds it to 250 g of water while stirring. As the molar mass of sodium chloride is 58.44 g/mol, the amount of substance in the sample is 0.1711 mol, calculated by dividing 10.0 by 58.44.

The mass concentration is calculated relative to the mass of solvent. As 250 g equals 0.250 kg, the mass concentration is 0.6845 mol/kg, calculated by dividing 0.1711 by 0.250.

b = \frac{10.0 \;/\; 58.44}{0.250} = 0.6845\ \mathrm{mol/kg}

Since sodium chloride dissociates into sodium and chloride ions, the ideal van 't Hoff factor is 2. The ebullioscopic constant of water is 0.512 °C kg/mol.

\Delta T_{b} = 2 \times 0.512 \times 0.6845 = 0.701\ \mathrm{C\ degrees}

This solution boils at 100.701 degrees Celsius, not 100 degrees Celsius. Even if you add two grams of salt to one hundred grams of water, the temperature only increases by about 0.7 degrees Celsius, which shows how small this effect is.

Why does adding salt to cooking water for spaghetti have little effect?

A tablespoon of salt is about 18 g and a large pot of water holds around 4 liters. The calculated molarity would be 0.077 mol/kg. Since the factor for salts that dissociate completely is 2, the boiling point elevation would be approximately 0.08 °C.

To achieve a change that cannot be ignored would require about ten times as much salt to be added, but long before then the water becomes unpalatable. Adding salt to the pot is for taste and not a physical effect.

Salt water shows this from a different perspective. When 35 g of salt is dissolved in 1 kg of water the molar concentration of all ions will be about 1.2 mol/kg and the boiling point elevation will be approximately 0.6 °C. The boiling point of salt water will be around 100.6 °C, not exactly two degrees as often quoted.

Molality vs. Molarity

Molality is the number of moles of solute per kilogram of solvent. Molarity is the number of moles of solute per liter of solution. The difference is that molality stays constant with mass of solvent, while volume changes with temperature and mass remains constant.

A 1.00 molar solution is 1.00 molar at 20 °C but no longer 1.00 molar once the liquid expands at 100 °C. A 1.00 mol/kg solution has a molality of 1.00 mol/kg at any temperature, which is an important property for experiments using hot plates.

Another point that is easily overlooked when calculating molarity has to do with the denominator. When calculating molality only the mass of the solvent itself is taken into account, not the mass of the resulting solution. If 10 g of salt are dissolved in 250 g of water, then the resulting solution will have a mass of 260 g, but for purposes of calculating molality we use 250.

van't Hoff factor

This factor indicates how many particles are produced from one unit of the chemical formula when dissolved. For solids that dissolve as intact molecules, this factor is 1. Ionic solids dissociate and the number of particles formed depends on the chemical formula.

Solute	Dissociation	Ideal i
Sucrose, urea, glycerol	none, stays molecular	1
NaCl, KCl, KBr, NaNO3	2 ions	2
CaCl2, MgCl2, Na2SO4	3 ions	3
AlCl3, K3PO4, FeCl3	4 ions	4
Acetic acid in water	partial, weak acid	just above 1

These whole numbers are ideal values, and they are not achieved in real solutions. Ions with opposite charges remain close enough to each other for some time and move as pairs. These pairs are counted as a single particle.

In dilute solutions the reading for sodium chloride is close to 1.9 rather than 2.0. The more concentrated the solution becomes, the greater this difference will be. For calcium chloride, which contains divalent cations, the deviation is even more pronounced. You can verify this yourself by determining the factor in mode three.

Where does the constant for boiling point elevation come from?

Kb is not an arbitrary number plucked from a table. It's derived according to thermodynamics from three properties of the solvent: its boiling temperature, the mass of one mole of the solvent and the energy required to vaporize the solvent.

K_{b} = \frac{R\,T_{b}^{2}\,M}{\Delta H_{vap}}

For water: R is 8.314 J/(mol K), Tb is 373.15 K, M is 0.01802 kg/mol and the enthalpy of vaporization is 40660 J/mol. Multiplying and dividing gives 0.513 C kg/mol, and the difference from the table value of 0.512 is only due to rounding errors.

This relationship explains the trend shown in the following table: solvents with high boiling points and good evaporation rates have large constant values. This is why naphthalene (5.8) has a sensitivity more than ten times that of water.

Solvent	Kb (C kg/mol)	Boiling point (C)
Water	0.512	100.00
Methanol	0.83	64.70
Ethanol	1.22	78.37
Acetone	1.71	56.05
Diethyl ether	2.02	34.55
Benzene	2.53	80.09
Cyclohexane	2.79	80.74
Phenol	3.04	181.75
Acetic acid	3.07	118.10
Chloroform	3.63	61.20
Carbon tetrachloride	5.03	76.72
Naphthalene	5.80	217.90

Because of this high sensitivity, chemists select a solvent for use in volumetric methods that is both soluble by the sample and has the highest constant value. The larger the constant value, the greater the temperature change caused by the same amount of unknown substance, and the larger the change, the more accurately it can be measured.

Determination of molar mass by boiling point elevation method

Reversing this equation gives an analytical technique. One weighs an unknown substance, dissolves it in a known amount of solvent and measures the increase in boiling point, from which the molar mass can be calculated.

M = \frac{i \times K_{b} \times m_{solute}}{\Delta T_{b} \times m_{solvent,\,kg}}

For example, if 2.50 g of an unknown nonelectrolyte compound is dissolved in 50.0 g of benzene and the freezing point depression is 1.30 °C, then the molar mass can be computed as follows. The constant for benzene is 5.12 °C·kg/mol. Thus, the molality is 1.30/5.12 = 0.254 mol/kg. In 0.0500 kg of benzene, this corresponds to 0.02569 mol. Dividing 2.50 g by 0.02569 mol gives a molar mass of 97.3 g/mol.

The problem is accuracy; in water the change in boiling point per kilogram and mole is only about half a degree. So even if an ordinary thermometer is accurate to one tenth of a degree, the number of significant figures you get is at most two. For this reason teaching equipment often has devices for measuring freezing points instead. The freezing-point depression constant for water is 1.86, which is more than three times the boiling-point elevation constant, while that for camphor is 37.7.

The assumption that an unknown substance is a nonelectrolyte is also made for the reason that this method requires it. If one assumes that the unknown substance does not ionize, then the calculated molar mass will be exactly by the amount determined by any overlooked factor.

Area where the model is no longer correctly applicable:

This equation is an approximation and its derivation assumes that the solution is sufficiently dilute and that the solute particles do not interact with each other. It works well for concentrations below about 0.5 mol/kg, but deviations begin to occur at around 2 mol/kg. This is because the number of effective particles depends on the concentration, which is caused by ion association and solvation shells.

It is also assumed that the solute is non-volatile. Ethanol dissolved in water does not lower the vapor pressure of the water but adds its own vapor pressure. So for a mixture of two liquids, this equation cannot be used, instead Raoult's law and the distillation curve must be used.

After all, everything here is relative to 1 atm. If you take water from a pot up a mountain, the boiling point of pure solvent will decrease, and so will the boiling point of the solution. The value of the elevation in boiling point itself changes little, but the temperature at which that value is added changes.

These results are for reference information only. They are intended for educational, experimental, and general curiosity purposes only. Constants can vary slightly from source to source, and non-ideal behavior in real solutions may cause deviations. For important applications always use measured data.

Frequently asked questions

How to calculate boiling point elevation?: You multiply three values together: the van't Hoff factor of the solute, the boiling point elevation constant for the solvent, and the molal concentration of the solution. This product gives you the increase in degrees. Adding this value to the boiling point of the pure solvent will give you the temperature at which the solution boils. For 0.5 moles per kilogram of sugar in water, you would multiply 1 by 0.512 and then again by 0.5, giving a result of 0.256 degrees Celsius. Therefore, water with this concentration of sugar will boil at 100.256 degrees Celsius.
What is the boiling point elevation constant for water?: It is 0.512 °C kg/mol. Sometimes it is also given as 0.512 K kg/mol since a degree Celsius and a Kelvin have the same size. This value means that if you dissolve one mole of stuff in a kilogram of water, the boiling point will increase by about half a degree. This value was not chosen arbitrarily but is determined from the boiling point of water, its molar mass, and the energy required to vaporize water. The derivation was shown above.
Why is kilograms of solvent used in molarity instead of liters of solution?: The reason for this is that the experiment involves heating. As the volume of a liquid expands when heated, the molar concentrations measured at room temperature are inaccurate once the boiling point is reached. The mass concentration does not change with temperature and therefore remains constant during measurement. Note that the denominator represents the solvent itself, rather than the solution after preparation.
Is the van't Hoff factor always an integer?: Only under ideal conditions. Sodium chloride should have a value of 2 but the usual measured values are closer to 1.9. This is because some sodium ions and chloride ions pair up and are counted as one unit rather than two units. The higher the concentration and charge of the ions, the greater the deviation. So calcium chloride deviates more from its ideal value of 3 than does sodium chloride from its ideal value of 2. The values for weak acids are slightly above 1 because only a fraction of the molecules dissociate.
Does salt reduce cooking time for spaghetti water?: No, it actually slightly delays the process. Even if you add a tablespoon of salt to four liters of water, the boiling point will only increase by about 0.08 °C which is such a small change that it's barely noticeable. Technically speaking, the water has to reach a slightly higher temperature in order to boil. Salt is mainly added for seasoning purposes.
How do you find molar mass using boiling point elevation?: The measured values of the boiling point elevation are divided by the product of the van't Hoff factor and the constant for the boiling point elevation to obtain the molar concentration. This is then multiplied by the number of kilograms of solvent to determine the amount, and finally the weighed mass is divided by this amount. The "Mode Five" device automatically performs these calculations. Use solvents with large constants, such as benzene or naphthalene, because temperature changes limit accuracy.

Related calculators

Boiling Point CalculatorFind the boiling point of water and other substances at any pressure with the Clausius-Clapeyron relation, solve for the pressure needed to hit a target temperature, derive the heat of vaporisation from two measured points, or work from an altitude.

Arrhenius Equation CalculatorSolve the Arrhenius equation k = A*exp(-Ea/RT) for any variable, or find the activation energy from a rate constant measured at two temperatures. Per mole or per molecule, with an Arrhenius plot.

Brine CalculatorWork out the salt for any brine, on the water, the total weight or the food alone, or run it backwards from the salt you already used. Includes spoon measures by salt brand, brining times by thickness and the density, molarity, salinometer degree and freezing point of the solution.

Atomic Mass CalculatorFind the average atomic mass of an element from its isotopes and their abundances, work out a missing percent abundance from a known average, or get the mass number of a single atom from its protons and neutrons.

Avogadro's Number CalculatorConvert between moles, mass, molar mass, and the number of atoms, molecules, or ions using Avogadro's number.

Buffer Capacity CalculatorWork out a buffer's capacity beta three ways: from pKa, total concentration and pH with the Van Slyke equation, from a measured pH change, or straight from the weak acid and conjugate base concentrations.

Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

IUPAC Gold Book: ebullioscopic constant
Formal definition of Kb and its relation to the solvent's properties.
LibreTexts Chemistry: Boiling Point Elevation
Derivation of the colligative relationship and worked examples.
NIST Chemistry WebBook
Reference boiling points and enthalpies of vaporisation for the preset solvents.
Wikipedia: Boiling-point elevation
Overview of the effect, the constants table and the ebullioscopy method.
Wikipedia: Van 't Hoff factor
Ideal versus measured factors and the role of ion pairing.