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The '''heat of vaporization''', (<math>H_v</math> or <math>H_{vap}</math>) is the amount of thermal [[energy]] required to convert a  quantity of [[liquid]] into a [[vapor]]. It can be thought of as the energy required to break the
*Stoichiometry and Process Calculations By Narayanan, B. Lakshnikutty, K.V. Narayanan
intermolecular bonds within the liquid.
 
It is also often referred to as the '''latent heat of vaporization''' (<math>LH_v</math> or <math>L_v</math>) and the '''enthalpy of vaporization''' (<math>\Delta H_v</math> or <math>\Delta H_{vap}</math> or <math>\Delta_v H</math>) and is usually measured and reported at the [[temperature]] corresponding to the [[normal boiling point]] of the liquid. Sometimes reported values have been corrected to a temperature of 298 [[Kelvin|K]].
 
== Measurement units ==
 
Heat of vaporization values are usually reported in measurement units such as [[Joule|J]]/[[Mole (unit)|mol]] or kJ/mol and referred to as the '''''molar heat of vaporization''''', although J/g or kJ/[[Kilogram|kg]] are also often used. Older units such as k[[Calorie|cal]]/mol, cal/g, [[U.S. customary units|Btu]]/[[U.S. customary units|lb]] and others are still used sometimes.
 
{{Image|Heat of Vaporization.png|right|300px|Figure 1: Heats of vaporization versus temperature.<ref name=Dortmund>[http://www.ddbst.com/new/Default.htm Dortmund Data Bank Online Search]</ref>}}
== Temperature dependency ==
 
The heat of vaporization is not a constant. It is temperature dependent as shown in Figure 1 by the example graphs of temperature versus heat of vaporization for [[acetone]], [[benzene]], [[methanol]] and [[water]].
 
As shown by the example graphs, the heat of vaporization of a liquid at a given temperature (other than the normal boiling point temperature) may vary significantly from the value reported at the normal boiling point of the liquid.
 
== Estimating heat of vaporization values ==
 
Heats of vaporization can be measured calorimetrically and measured values are available from a number of sources.<ref name=Dortmund/><ref>{{cite book|author=Carl L. Yaws|title=Chemical properties Handbook|edition=1st Edition|publisher=McGraw-Hill|year=1998|id=ISBN 0-07--073401-1}}</ref><ref>{{cite book|author=Václav Svoboda and Henry V. Kehiaian|title=Enthalpies of Vaporization of Organic Compounds: A Critical Review and Data Compilation|edition=IUPAC Chemical Data Series 32|publisher=Blackwell Scientific|year=1985|id=ISBN 0-632-01529-2}}</ref><ref>{{cite book|author=Perry, R.H. and Green, D.W. (Editors)|title=Perry's Chemical Engineers' Handbook|edition=Eighth Edition|publisher=McGraw-Hill|year=2007|id=ISBN 0-07-142294-3}}</ref> However, data is not always available for certain liquids or at certain temperatures. In such cases, estimation of heats of vaporization can be made by any of a large number of different methods. Four of the commonly used methods are discussed in the following sections.
 
=== Using the Clausius-Clapeyron equation ===
 
This integrated form of the [[Clausius-Clapeyron equation]] can be used to provide a good approximation of the heat of vaporization for many pure liquids:<ref name=Vidal>{{cite book|author=Jean Vidal|title=Thermodynamics: Applications in Chemical Engineering and the Petroleum Industry|edition=|publisher=Editions Technip|year=2003|id=ISBN 2-7108-0800-5}} (Equation 2.10, page 38)</ref><ref name=Faghri>{{cite book|author=Amir Faghri and Yuwen Zhang|title=Transport Phenomena in Multiphase Systems|edition=1st Edition|publisher=Academic Press|year=2006|id=ISBN 0-12-370610-6}} (Equation 2.168, Chapter 2)</ref>
 
:'''(1)''' &nbsp; &nbsp; <math>\log_e \left( \frac{\; p_2}{p_1} \right) = \frac{\;H_v}{R} \left( \frac{1}{T_2} - \frac{1}{T_1} \right)</math>
 
which can be re-arranged to obtain:
 
:'''(2)''' &nbsp; &nbsp; <math>H_v = R\cdot \log_e \left( \frac{\; p_2}{p_1} \right) \left(\frac{\; T_1 \cdot T_2}{T_2 - T_1}\right)</math>
 
:{|border="0" cellpadding="2"
|-
|align=right|where:
|-
|align=right|<font style="vertical-align:-10%;"><math>H_v</math></font>
|align=left|= Heat of vaporization, in [[Joule|J]]/[[Mole (unit)|mol]]
|-
|align=right|<math>R</math>
|align=left|= 8.3144 = [[Universal gas constant]], in J/([[Kelvin|K]] <math>\cdot</math> mol)
|-
|align=right|<font style="vertical-align:+10%;"><math>log_e</math></font>
|align=left|= [[Logarithm]] on base <math>e</math>
|-
|align=right|<font style="vertical-align:-20%;"><math>p_1</math></font>
|align=left|= The liquid's [[vapor pressure]] at <math>T_1</math>, in [[Pressure|atm]]
|-
|align=right|<font style="vertical-align:-20%;"><math>p_2</math></font>
|align=left|= The liquid's vapor pressure at <math>T_2</math>, in atm
|-
|align=right|<math>T_1</math>
|align=left|= Temperature, in K
|-
|align=right|<math>T_2</math>
|align=left|= Temperature, in K
|}
 
{| border="0" width="485" align="right" cellpadding="0" cellspacing="0" style="wrap=no"
|
{| class = "wikitable" align="right"
|+ Table 1: Heat of vaporization, normal boiling point<br />and critical temperature and pressure of various liquids <ref name=Smith>{{cite book|author=J.M. Smith, H.C. Van Ness and M.M. Abbot|title=Introduction to Chemical Engineering Thermodynamics|edition=7th Edition|publisher=McGraw-Hill|year=2004|id=ISBN 0-07-310445-0}}</ref><ref>{{cite book|author=Robert C. Weast (Editor)|title=Perry's Chemical Engineers' Handbook|edition=56th Edition|publisher=CRC Press|year=1976|id=ISBN 0-87819-455-X}}</ref>
|-
!rowspan=2|Name
!rowspan=2|Formula
!colspan=2|H<sub>v</sub>!!colspan=2|T<sub>n</sub>!!colspan=2|T<sub>c</sub>!!colspan=2 |p<sub>c</sub>
|-
!colspan=2|( J/mol )
!( °C )!!( K )
!colspan=2|( K )
!colspan=2|( atm )
|- align="center"
|[[Acetic acid]]||C<sub>2</sub>H<sub>4</sub>O<sub>2</sub>||colspan=2|23,700||117.9||391.1||colspan=2|594.8|| colspan=2|57.1
|- align="center"
| [[Acetone]]||C<sub>3</sub>H<sub>6</sub>O||colspan=2|29,100||56.2||329.4||colspan=2|508.7||colspan=2|47.0
|- align="center"
|[[Benzene]]||C<sub>6</sub>H<sub>6</sub>||colspan=2|30,720||80.0||353.2||colspan=2|562.1||colspan=2|48.6
|- align="center"
|[[Butane]]||C<sub>4</sub>H<sub>10</sub>||colspan=2|22,440||– 0.5||272.7||colspan=2|425.2||colspan=2|37.5
|- align="center"
|[[Carbon tetrachloride]]||CCl<sub>4</sub>||colspan=2|29,820||76.6||349.8||colspan=2|556.3||colspan=2|45.0
|- align="center"
|[[Chloroform]]||CHCl<sub>3</sub>||colspan=2|29,240||61.1||334.3||colspan=2|536.2||colspan=2|54.0
|- align="center"
|[[Cyclopentane]]||C<sub>5</sub>H<sub>10</sub>||colspan=2|27,300||49.2||322.4||colspan=2|511.8||colspan=2|44.6
|- align="center"
|[[Ethanol]]||C<sub>2</sub>H<sub>6</sub>O||colspan=2|38,560||78.2||351.4||colspan=2|516.2||colspan=2|63.0
|- align="center"
|[[Hexane]]||C<sub>6</sub>H<sub>14</sub>||colspan=2|28.850||68.7||341.9||colspan=2|507.4||colspan=2|29.9
|- align="center"
|[[Methanol]]||CH<sub>4</sub>O||colspan=2|35,210||64.7||337.9||colspan=2|513.2||colspan=2|78.5
|- align="center"
|[[Water]]||H<sub>2</sub>0||colspan=2|40,660||100||373.2||colspan=2|647.3||colspan=2|218.3
|-
|colspan=10|<small>Notes:<br />
:(1) H<sub>v</sub> = heat of vaporization at the normal boiling point<br />
:(2) T<sub>n</sub> = normal boiling point<br />
:(3) T<sub>c</sub> = critical temperature<br/>
:(4) p<sub>c</sub> = absolute critical pressure</small>
|}
|}
 
The primary Clausius-Clapeyron equation is exact. However, the above integrated form of the equation is not exact because it is necessary to make these assumptions in order to perform the integration:<ref name=Vidal/><ref name=Faghri/>
 
* The [[molar volume]] of the liquid phase is negligible compared to the molar volume of the vapor phase
* The vapor phase behaves like an [[ideal gas]]
* The heat of vaporization is constant over the temperature range as defined by '''''T<sub>1</sub>''''' and '''''T<sub>2</sub>'''''
 
As an example of using the Clausius-Clapeyron equation, given that the vapor pressure of benzene is 1 atm at 353 K and 2 atm at 377 K, benzene's heat of vaporization is obtained as 32,390 J/mol within that temperature range.
 
=== Using Riedel's equation ===
 
Riedel proposed an empirical equation for estimating a liquid's heat of vaporization at its normal boiling point.<ref>L. Riedel, ''Chem. Ing. Tech.'', 26, pp. 679-683, 1954</ref> The equation may be expressed as:<ref name=Smith/><ref name=Schaum>{{cite book|author=M.M. Abbott and H.C. Van Ness|title=Schaum's Outline of Thermodynamics With Chemical Applications|edition=2nd Edition|publisher=McGraw-Hill|year=1989|id=ISBN 0-07-000042-5}}</ref>
 
:'''(3)''' &nbsp; &nbsp; <math>H_v = \frac{1.092\, R\, T_n\, (\log_e p_c -\, 1.013)}{0.930 - (T_n/T_c)}</math>
 
:{|border="0" cellpadding="2"
|-
|align=right|where:
|-
|align=right|<font style="vertical-align:-10%;"><math>H_v</math></font>
|align=left|= Heat of vaporization, in J/mol
|-
|align=right|<math>R</math>
|align=left|= 8.3144 = [[Universal gas constant]], in J/(K <math>\cdot</math> mol)
|-
|align=right|<math>T_n</math>
|align=left|= The liquid's normal boiling point, in K
|-
|align=right|<math>T_c</math>
|align=left|= The liquid's critical temperature, in K
|-
|align=right|<font style="vertical-align:+10%;"><math>log_e</math></font>
|align=left|= Logarithm on base <math>e</math>
|-
|align=right|<math>p_c</math>
|align=left|= The liquid's critical pressure at <math>T_n</math>, in [[bar]] <ref>1 bar = 0.98692 atm</ref>
|}
 
For an empirical expression, equation (3) is surprisingly accurate and its error rarely exceeds 5 %. For example, using water data (see Table 1) of T<sub>n</sub> = 373.2 K, <br />T<sub>c</sub> = 647.3 K and P<sub>c</sub> = 221.2 bar (218.3 atm), the heat of vaporization is obtained as 42,060 J/mol. That is within 3 percent of the 40,660 J/mol in Table 1.
 
{| border="0" width="158" align="right" cellpadding="0" cellspacing="0" style="wrap=no"
|
{| class = "wikitable" align="right"
|+ Table 2: Application<br />of Trouton's rule
|-
!Name
!H<sub>v</sub> <math>\scriptstyle/</math> T<sub>n</sub>
|- align="center"
|Acetone||90.6
|- align="center"
|Benzene||87.3
|- align="center"
|Butane||82.3
|- align="center"
|Cyclohexane||84.8
|- align="center"
|Octane||87.3
|}
|}
 
=== Using Trouton's rule ===
 
Troutons's rule, dating back to 1883,<ref>F.T. Trouton, ''Nature'', 27, p. 292, 1883</ref><ref>F.T. Trouton, ''Phil. Mag.'', 18, pp.54-57, 1884</ref> is a relation between a liquid's heat of vaporization and it's normal boiling point <math>T_n</math>.<ref name=Vidal/><ref name=Faghri/><ref name=Roy>{{cite book|author=Bimalendu Narayan Roy|title=Fundamentals of Classical and Statistical Thermodynamics|edition=|publisher=John Wiley & Sons|year=2002|id=ISBN 0-470-84316-0}}</ref> It provides a good approximation of the heat of vaporization at the normal boiling point of many pure substances, and it may be expressed as:
 
:'''(4)''' &nbsp; &nbsp; <math>\frac{H_v}{T_n} \approx 87\;\, \mathrm{to}\;\, 88</math>
 
Table 2 provides some examples of the application of Trouton's rule.
 
Trouton's rule fails for liquids with boiling points below 150 K. It also fails for water, alcohols, amines and liquid ammonia.<ref name=Roy/>
 
=== Using Watson's equation ===
 
Given the heat of vaporization of a liquid at any temperature, its heat of vaporization at another temperature may be estimated by using the Watson equation:<ref name=Vidal/><ref name=Smith/><ref>K.M. Watson, Thermodynamics of the Liquid States, Generalized Prediction of Properties, ''Ind. Eng. Chem.'', 35, pp.398-406, 1943</ref>
 
:'''(5)''' &nbsp; &nbsp; <math>\frac{H_{v2}}{H_{v1}} = \left[\frac{1 - (T_2/T_c)}{1 - (T_1/T_c)}\right]^{0.38}</math>
 
which can be re-arranged to obtain:
 
:'''(6)''' &nbsp; &nbsp; <math>\frac{H_{v2}}{H_{v1}} = \left(\frac{T_c - T_2}{T_c - T_1}\right)^{0.38}</math>
 
:{|border="0" cellpadding="2"
|-
|align=right|where:
|-
|align=right|<font style="vertical-align:-10%;"><math>H_{v1}</math></font>
|align=left|= Heat of vaporization of the liquid at <math>T_1</math>, in J/mol
|-
|align=right|<font style="vertical-align:-10%;"><math>H_{v2}</math></font>
|align=left|= Heat of vaporization of the liquid at <math>T_2</math>, in J/mol
|-
|align=right|<math>T_1</math>
|align=left|= Temperature, in K
|-
|align=right|<math>T_2</math>
|align=left|= Temperature, in K
|-
|align=right|<math>T_c</math>
|align=left|= Critical temperature of the liquid, in K
|}
 
Watson's equation has achieved wide acceptance and is simple and reliable.
 
==References==
{{reflist}}
 
 
___________________________
 
Stoichiometry and Process Calculations By Narayanan, B. Lakshnikutty, K.V. Narayanan
*Standard handbook of petroleum and natural gas engineering By William C. Lyons, Joseph Zaba
*Standard handbook of petroleum and natural gas engineering By William C. Lyons, Joseph Zaba
*Chemical property estimation: theory and application By Edward J. Baum
*Chemical property estimation: theory and application By Edward J. Baum

Revision as of 20:36, 10 September 2009

  • Stoichiometry and Process Calculations By Narayanan, B. Lakshnikutty, K.V. Narayanan
  • Standard handbook of petroleum and natural gas engineering By William C. Lyons, Joseph Zaba
  • Chemical property estimation: theory and application By Edward J. Baum
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