The Ambrose-Walton method
is a method for estimating the vapor pressure of pure substances. The method is based on the theorem of the coincident states and uses the critical temperature , the critical pressure and the acentric factor . It is a further development of the Lee-Kesler method .
Determining equations
![{\ displaystyle \ ln {\ frac {P} {P _ {\ mathrm {c}}}} = f ^ {(0)} + \ omega \ cdot f ^ {(1)} + {\ omega} ^ {2 } \ cdot f ^ {(2)}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ac7b177d60df9e8bc75b8d4924f641827f67dc0a)
![{\ displaystyle f ^ {(0)} = {\ frac {-5 {,} 97616 \ cdot \ tau +1 {,} 29874 \ cdot \ tau ^ {1 {,} 5} -0 {,} 60394 \ cdot \ tau ^ {2 {,} 5} -1 {,} 06841 \ cdot \ tau ^ {5}} {T _ {\ mathrm {r}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/26dcfa644d302950c4b2bc30a8fb668aa317613e)
![{\ displaystyle f ^ {(1)} = {\ frac {-5 {,} 03365 \ cdot \ tau +1 {,} 11505 \ cdot \ tau ^ {1 {,} 5} -5 {,} 41217 \ cdot \ tau ^ {2 {,} 5} -7 {,} 46628 \ cdot \ tau ^ {5}} {T _ {\ mathrm {r}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/562bdfb011e773198156305a71f94575576ba4ad)
![{\ displaystyle f ^ {(2)} = {\ frac {-0 {,} 64771 \ cdot \ tau +2 {,} 41539 \ cdot \ tau ^ {1 {,} 5} -4 {,} 26979 \ cdot \ tau ^ {2 {,} 5} +3 {,} 25259 \ cdot \ tau ^ {5}} {T _ {\ mathrm {r}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a7986137b641f94df512bc2ad8711546464377c4)
with and![{\ displaystyle \ quad T _ {\ mathrm {r}} = {\ frac {T} {T _ {\ mathrm {c}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0b386f4177827efcf665df06a596cf1cb5835eee)
: Absolute temperature
: Critical temperature
: Vapor pressure
: Critical pressure
: Acentric factor
Sample calculation
For acetone ( ) at a temperature of 329 Kelvin, the following calculation results :
![{\ displaystyle T _ {\ mathrm {c}} = 508 \, \ mathrm {K}, P _ {\ mathrm {c}} = 4700 \, \ mathrm {kPa}, \ omega = 0 {,} 309}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2435dd08eef3e0ea47aeaa0d2d309f91f2969410)
![T](https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0)
With and surrender
![{\ displaystyle T _ {\ mathrm {r}} = {\ frac {329 \, \ mathrm {K}} {508 \, \ mathrm {K}}} = 0 {,} 6476}](https://wikimedia.org/api/rest_v1/media/math/render/svg/434ed6a541e08a8bc74afa4f7ff6648a921f37bc)
![{\ displaystyle \ tau = 1-T _ {\ mathrm {r}} = 0 {,} 3524}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a69b42cf2cebc1d9c8ff22d909222de6a9da3c02)
![{\ displaystyle f ^ {(0)} = - 2 {,} 9097}](https://wikimedia.org/api/rest_v1/media/math/render/svg/03f7b46c5882b6f01519b2ddb3abbd7a4ba8cf39)
![{\ displaystyle f ^ {(1)} = - 3 {,} 0571}](https://wikimedia.org/api/rest_v1/media/math/render/svg/48aa3cdbfc511c36e6763aabfdb93ce80fcdb49c)
![{\ displaystyle f ^ {(2)} = - 0 {,} 0309}](https://wikimedia.org/api/rest_v1/media/math/render/svg/12503edf4d4550ce0f7edde01de256fe5fc6af9f)
![{\ displaystyle \ ln {\ frac {P} {P _ {\ mathrm {c}}}} = - 2 {,} 9097 + 0 {,} 309 \ cdot (-3 {,} 0571) +0 {,} 309 ^ {2} \ cdot (-0 {,} 0309) = - 3 {,} 8573}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6d58e48d3ec672496f6c34c2b357933a139e55b0)
![{\ displaystyle P = e ^ {- 3 {,} 8573} \ cdot 4700 \, \ mathrm {kPa} = 99 {,} 2870 \, \ mathrm {kPa}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e05900aeac2d09ee50eb2bef733a888f75329be4)
329 Kelvin is about the normal boiling point temperature of acetone, i.e. the point at which acetone becomes gaseous at normal pressure ( ).
![{\ displaystyle \ approx 101 \, \ mathrm {kPa}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0a4343904443b6024ca45939cdc12dac96668b1f)
literature
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↑
Ambrose D., Walton J., "Vapor Pressures up to Their Critical Temperatures of Normal Alkanes and 1-Alkanols", Pure Appl. Chem. , 61, 1395-1403, 1989
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↑
Lee BI, Kesler MG, "A Generalized Thermodynamic Correlation Based on Three-Parameter Corresponding States", AIChE J., 21 (3), 510-527, 1975