Boiling Point: Difference between revisions
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==The Main Idea== | ==The Main Idea== | ||
The boiling point of a liquid is the temperature at which its vapor pressure becomes equal to the external pressure around it, allowing the liquid to transition into vapor. Because vapor pressure depends on temperature, the boiling point changes when pressure changes. At high external pressure, a liquid boils at a higher temperature; at low external pressure (such as at high altitudes or in a partial vacuum), the boiling point is lower. | |||
Boiling point also varies from substance to substance, since different liquids have different intermolecular forces and vapor pressure curves. These principles are important for chemistry, cooking, engineering, distillation, and everyday processes involving heat transfer. | |||
===A Mathematical Model=== | ===A Mathematical Model=== | ||
Two major equations help model boiling point behavior: the Clausius–Clapeyron equation and the boiling point elevation equation. | |||
---- | |||
'''Clausius–Clapeyron Equation''' | |||
This equation is used when the vapor pressure at one temperature and the heat of vaporization are known, and the goal is to determine the boiling point at a different pressure. | |||
[[File:ClausiusClapeyron.png|center|400px]] | |||
''Constants in the equation:'' | |||
* '''T<sub>B</sub>''' – boiling temperature at pressure P | |||
* '''T<sub>0</sub>''' – reference temperature corresponding to pressure P<sub>0</sub> | |||
* '''R''' – ideal gas constant (8.314 J·mol<sup>−1</sup>·K<sup>−1</sup>) | |||
* '''P''' – vapor pressure at desired boiling conditions | |||
* '''P<sub>0</sub>''' – vapor pressure at reference conditions | |||
* '''ΔH<sub>vap</sub>''' – heat of vaporization | |||
---- | |||
''' | '''Boiling Point Elevation Equation''' | ||
This describes how adding a solute to a solvent increases its boiling point: | |||
''' | '''ΔT<sub>b</sub> = K<sub>b</sub> · b<sub>B</sub>''' | ||
''' | ''Where:'' | ||
''' | * '''ΔT<sub>b</sub>''' – boiling point elevation (T<sub>b,solution</sub> − T<sub>b,solvent</sub>) | ||
* '''K<sub>b</sub>''' – [[Ebullioscopic constant]] | |||
* '''b<sub>B</sub>''' – molality of solute particles, b<sub>B</sub> = b<sub>solute</sub> · i | |||
* '''i''' – van't Hoff factor (number of dissolved particles produced per solute molecule) | |||
These equations model how temperature, pressure, and solute concentration affect boiling point. | |||
===A Computational Model=== | |||
A computational model for boiling point elevation begins by defining relevant constants: | |||
* K<sub>b</sub> = ebullioscopic constant | |||
* b<sub>solute</sub> = molality of the solute | |||
* i = van’t Hoff factor | |||
* b<sub>B</sub> = b<sub>solute</sub> · i | |||
Then compute: | |||
'''ΔT<sub>b</sub> = K<sub>b</sub> · b<sub>B</sub>''' | |||
A program can simulate increasing solute concentration and produce a temperature–concentration graph showing how boiling point rises. | |||
==Examples== | |||
Below are structured examples following the Physics Book template. | |||
===Simple=== | |||
A 1.0 m NaCl solution (i = 2) is prepared in water with K<sub>b</sub> = 0.512 K·kg/mol. | |||
=== | ΔT<sub>b</sub> = (0.512)(1.0)(2) = 1.024°C | ||
T<sub>b</sub> = 100°C + 1.024°C = 101.024°C | |||
===Middling=== | |||
K<sub> | A substance has vapor pressure P<sub>0</sub> = 0.80 atm at T<sub>0</sub> = 360 K. | ||
Find T<sub>B</sub> at pressure P = 1.00 atm using Clausius–Clapeyron and ΔH<sub>vap</sub> = 32,000 J/mol. | |||
<math> | |||
\ln\left(\frac{1.00}{0.80}\right) | |||
= -\frac{32000}{8.314}\left(\frac{1}{T_B} - \frac{1}{360}\right) | |||
</math> | |||
Solving gives T<sub>B</sub> ≈ 372 K. | |||
===Difficult=== | |||
A liquid has P<sub>1</sub> = 0.50 atm at T<sub>1</sub> = 300 K and P<sub>2</sub> = 1.20 atm at T<sub>2</sub>. | |||
Assume ΔH<sub>vap</sub> is constant. | |||
Use the two-point Clausius–Clapeyron form: | |||
= | <math> | ||
\ln\left(\frac{1.20}{0.50}\right) | |||
= -\frac{\Delta H_{vap}}{R}\left(\frac{1}{T_2} - \frac{1}{300}\right) | |||
</math> | |||
Solving yields T<sub>2</sub> ≈ 345 K. | |||
More practice problems can be found here: | |||
[http://www.chemteam.info/Solutions/BP-elevation-probs1-to-10.html Boiling Point Elevation] | [http://www.chemteam.info/Solutions/BP-elevation-probs1-to-10.html Boiling Point Elevation] | ||
==Connectedness== | ==Connectedness== | ||
Boiling point | Boiling point is crucial in real-world applications: | ||
* **Cooking:** Adding salt slightly raises boiling point (though only by a small amount). | |||
* **Chemical engineering:** Boiling and vaporization are central to distillation, separation, and refining. | |||
* **Food and sugar processing:** Syrup concentration changes boiling temperature, which indicates sugar content. | |||
* **Environmental science:** Atmospheric pressure variations affect evaporation and boiling. | |||
This topic connects strongly to chemistry, thermodynamics, and material science. | |||
==History== | ==History== | ||
In 1741, Anders Celsius | In 1741, Anders Celsius proposed a temperature scale using the boiling and melting points of water. | ||
Earlier Greek scientists such as Philo and Hero of Alexandria described primitive thermometric principles and explored steam power concepts. | |||
Celsius | Celsius originally labeled the boiling point as 0° and freezing point as 100°, which was later reversed to form the modern Celsius scale. | ||
==See also== | |||
* [[Melting Point]] | |||
* [[Vapor Pressure]] | |||
* [[Clausius–Clapeyron Equation]] | |||
* [[Phase Diagram]] | |||
===Further reading=== | ===Further reading=== | ||
* [https://www.chem.purdue.edu/gchelp/liquids/boil.html Boiling – Purdue Chemistry] | |||
* [http://www.britannica.com/science/boiling-point Boiling Point – Britannica] | |||
[https://www.chem.purdue.edu/gchelp/liquids/boil.html Boiling] | |||
[http://www.britannica.com/science/boiling-point Boiling Point] | |||
===External links=== | ===External links=== | ||
[https://en.wikipedia.org/wiki/Boiling_point] | * [https://en.wikipedia.org/wiki/Boiling_point Boiling Point – Wikipedia] | ||
==References== | ==References== | ||
[http://www.ehow.com/info_8344665_uses-boiling-point-elevation.html Uses of Boiling Point Elevation] | * [http://www.ehow.com/info_8344665_uses-boiling-point-elevation.html Uses of Boiling Point Elevation] | ||
* [http://www.chemteam.info/Solutions/BP-elevation.html Boiling Point Elevation Problems] | |||
[http://www.chemteam.info/Solutions/BP-elevation.html Boiling Point Elevation] | * [https://www.chem.tamu.edu/class/majors/tutorialnotefiles/intext.htm Chemistry Basics – TAMU] | ||
[https://www.chem.tamu.edu/class/majors/tutorialnotefiles/intext.htm Chemistry Basics] | * [http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch14/melting.php Melting/Freezing/Boiling Points – Purdue] | ||
[http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch14/melting.php Melting | * [http://didyouknow.org/celsius/ Boiling Point of Water] | ||
[http://didyouknow.org/celsius/ Boiling Point of Water] | |||
[[Category:Properties of Matter]] | [[Category:Properties of Matter]] | ||
Revision as of 21:47, 1 December 2025
Claimed by Chris Li (Fall 2025)
The Main Idea
The boiling point of a liquid is the temperature at which its vapor pressure becomes equal to the external pressure around it, allowing the liquid to transition into vapor. Because vapor pressure depends on temperature, the boiling point changes when pressure changes. At high external pressure, a liquid boils at a higher temperature; at low external pressure (such as at high altitudes or in a partial vacuum), the boiling point is lower.
Boiling point also varies from substance to substance, since different liquids have different intermolecular forces and vapor pressure curves. These principles are important for chemistry, cooking, engineering, distillation, and everyday processes involving heat transfer.
A Mathematical Model
Two major equations help model boiling point behavior: the Clausius–Clapeyron equation and the boiling point elevation equation.
Clausius–Clapeyron Equation
This equation is used when the vapor pressure at one temperature and the heat of vaporization are known, and the goal is to determine the boiling point at a different pressure.
Constants in the equation:
- TB – boiling temperature at pressure P
- T0 – reference temperature corresponding to pressure P0
- R – ideal gas constant (8.314 J·mol−1·K−1)
- P – vapor pressure at desired boiling conditions
- P0 – vapor pressure at reference conditions
- ΔHvap – heat of vaporization
Boiling Point Elevation Equation
This describes how adding a solute to a solvent increases its boiling point:
ΔTb = Kb · bB
Where:
- ΔTb – boiling point elevation (Tb,solution − Tb,solvent)
- Kb – Ebullioscopic constant
- bB – molality of solute particles, bB = bsolute · i
- i – van't Hoff factor (number of dissolved particles produced per solute molecule)
These equations model how temperature, pressure, and solute concentration affect boiling point.
A Computational Model
A computational model for boiling point elevation begins by defining relevant constants:
- Kb = ebullioscopic constant
- bsolute = molality of the solute
- i = van’t Hoff factor
- bB = bsolute · i
Then compute:
ΔTb = Kb · bB
A program can simulate increasing solute concentration and produce a temperature–concentration graph showing how boiling point rises.
Examples
Below are structured examples following the Physics Book template.
Simple
A 1.0 m NaCl solution (i = 2) is prepared in water with Kb = 0.512 K·kg/mol.
ΔTb = (0.512)(1.0)(2) = 1.024°C Tb = 100°C + 1.024°C = 101.024°C
Middling
A substance has vapor pressure P0 = 0.80 atm at T0 = 360 K. Find TB at pressure P = 1.00 atm using Clausius–Clapeyron and ΔHvap = 32,000 J/mol.
[math]\displaystyle{ \ln\left(\frac{1.00}{0.80}\right) = -\frac{32000}{8.314}\left(\frac{1}{T_B} - \frac{1}{360}\right) }[/math]
Solving gives TB ≈ 372 K.
Difficult
A liquid has P1 = 0.50 atm at T1 = 300 K and P2 = 1.20 atm at T2. Assume ΔHvap is constant.
Use the two-point Clausius–Clapeyron form:
[math]\displaystyle{ \ln\left(\frac{1.20}{0.50}\right) = -\frac{\Delta H_{vap}}{R}\left(\frac{1}{T_2} - \frac{1}{300}\right) }[/math]
Solving yields T2 ≈ 345 K.
More practice problems can be found here: Boiling Point Elevation
Connectedness
Boiling point is crucial in real-world applications:
- **Cooking:** Adding salt slightly raises boiling point (though only by a small amount).
- **Chemical engineering:** Boiling and vaporization are central to distillation, separation, and refining.
- **Food and sugar processing:** Syrup concentration changes boiling temperature, which indicates sugar content.
- **Environmental science:** Atmospheric pressure variations affect evaporation and boiling.
This topic connects strongly to chemistry, thermodynamics, and material science.
History
In 1741, Anders Celsius proposed a temperature scale using the boiling and melting points of water. Earlier Greek scientists such as Philo and Hero of Alexandria described primitive thermometric principles and explored steam power concepts. Celsius originally labeled the boiling point as 0° and freezing point as 100°, which was later reversed to form the modern Celsius scale.