{"id":220,"date":"2020-07-02T13:02:09","date_gmt":"2020-07-02T13:02:09","guid":{"rendered":"https:\/\/libraryresources.nse.org.ng\/chbe220\/chapter\/phase-equilibrium-chapter-review\/"},"modified":"2026-03-16T13:51:54","modified_gmt":"2026-03-16T13:51:54","slug":"phase-equilibrium-chapter-review","status":"publish","type":"chapter","link":"https:\/\/libraryresources.nse.org.ng\/chbe220\/chapter\/phase-equilibrium-chapter-review\/","title":{"raw":"Phase Equilibrium Chapter Review","rendered":"Phase Equilibrium Chapter Review"},"content":{"raw":"<h2>Important Equations<\/h2>\n<table class=\"grid\" style=\"border-collapse: collapse;width: 100%;height: 210px\" border=\"0\">\n<tbody>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">Pressure definition<\/td>\n<td style=\"width: 50%;height: 15px;text-align: center\">[latex]P=\\frac{F}{A}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">Calculating pressure using a manometer<\/td>\n<td style=\"width: 50%;height: 15px;text-align: center\">[latex]P=P_{ref}+\\rho g(h_{ref}-h)[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">Converting gauge\/absolute pressure<\/td>\n<td style=\"width: 50%;height: 15px;text-align: center\">[latex]\\text{gauge pressure}=\\text{absolute pressure}-\\text{atmospheric pressure}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">Temperature conversions<\/td>\n<td style=\"width: 50%;height: 15px;text-align: center\">\n<p style=\"text-align: left\">Celsius to Kelvin:<span style=\"font-family: inherit;font-size: inherit\">[latex]T (K) = T (\u00b0C) + 273.15[\/latex]<\/span><\/p>\n<p style=\"text-align: left\">Fahrenheit to Rankine: [latex]T (\u00b0R) = T (\u00b0F) + 459.67[\/latex]<\/p>\n<p style=\"text-align: left\">Kelvin to Rankine:<\/p>\n<p style=\"text-align: left\"><span style=\"font-family: inherit;font-size: inherit\">[latex]T (\u00b0R) = 1.8\u00b7T (K)[\/latex]<\/span><\/p>\n<p style=\"text-align: left\">Celsius to Fahrenheit: <span style=\"font-family: inherit;font-size: inherit\">[latex]T (\u00b0F) = 1.8\u00b7T (\u00b0C) + 32[\/latex]<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px;text-align: left\">Reduced properties<\/td>\n<td style=\"width: 50%;height: 15px\">\n<p style=\"text-align: center\">[latex]T_{r}=\\frac{T}{T_c}[\/latex]<\/p>\n<p style=\"text-align: center\">[latex]P_{r}=\\frac{P}{P_c}[\/latex]<\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">Gibb's Phase Rule<\/td>\n<td style=\"width: 50%;height: 15px;text-align: center\">[latex]DF=2+c-\\pi-r[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">Ideal Gas Law<\/td>\n<td style=\"width: 50%;height: 15px\">\n<p style=\"text-align: center\">[latex]PV=nRT[\/latex]<\/p>\n<p style=\"text-align: center\">[latex]P\\hat{V}=RT[\/latex]<\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">Dalton's Law<\/td>\n<td style=\"width: 50%;height: 15px\">\n<p style=\"text-align: center\">[latex]P=\\sum^n_{i}p_{i}[\/latex]<\/p>\n<p style=\"text-align: center\">[latex]p_{A}=y_{A}P[\/latex]<\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">Amgat's Law<\/td>\n<td style=\"width: 50%;height: 15px\">\n<p style=\"text-align: center\">[latex]V=\\sum^n_{i}v_{i}[\/latex]<\/p>\n<p style=\"text-align: center\">[latex]v_{A}=y_{A}V[\/latex]<\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">Relating ideal gas properties<\/td>\n<td style=\"width: 50%;height: 15px;text-align: center\">[latex]R=\\frac{V_s\u00b7P_s}{n\u00b7T_s}=\\frac{V\u00b7P}{n\u00b7T}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">Compressibility Factor<\/td>\n<td style=\"width: 50%;height: 15px;text-align: center\">[latex]\\frac{PV}{RT}=Z[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">Antoine Equation<\/td>\n<td style=\"width: 50%;height: 15px;text-align: center\">[latex]log_{10}(p^*)=A-\\frac{B}{T+C}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">Raoult's Law<\/td>\n<td style=\"width: 50%;height: 15px;text-align: center\">[latex]p_{i}=y_{i}\u00b7P=x_{i}\u00b7p_i^*(T)[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">Henry's Law<\/td>\n<td style=\"width: 50%;height: 15px;text-align: center\">[latex]p_{i}=y_{i}\u00b7P=\\frac{x_{i}}{H_{i}(T)}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Terms to know<\/h2>\nThe original version of this chapter contained H5P content. You may want to remove or replace this element.","rendered":"<h2>Important Equations<\/h2>\n<table class=\"grid\" style=\"border-collapse: collapse;width: 100%;height: 210px\">\n<tbody>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">Pressure definition<\/td>\n<td style=\"width: 50%;height: 15px;text-align: center\">[latex]P=\\frac{F}{A}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">Calculating pressure using a manometer<\/td>\n<td style=\"width: 50%;height: 15px;text-align: center\">[latex]P=P_{ref}+\\rho g(h_{ref}-h)[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">Converting gauge\/absolute pressure<\/td>\n<td style=\"width: 50%;height: 15px;text-align: center\">[latex]\\text{gauge pressure}=\\text{absolute pressure}-\\text{atmospheric pressure}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">Temperature conversions<\/td>\n<td style=\"width: 50%;height: 15px;text-align: center\">\n<p style=\"text-align: left\">Celsius to Kelvin:<span style=\"font-family: inherit;font-size: inherit\">[latex]T (K) = T (\u00b0C) + 273.15[\/latex]<\/span><\/p>\n<p style=\"text-align: left\">Fahrenheit to Rankine: [latex]T (\u00b0R) = T (\u00b0F) + 459.67[\/latex]<\/p>\n<p style=\"text-align: left\">Kelvin to Rankine:<\/p>\n<p style=\"text-align: left\"><span style=\"font-family: inherit;font-size: inherit\">[latex]T (\u00b0R) = 1.8\u00b7T (K)[\/latex]<\/span><\/p>\n<p style=\"text-align: left\">Celsius to Fahrenheit: <span style=\"font-family: inherit;font-size: inherit\">[latex]T (\u00b0F) = 1.8\u00b7T (\u00b0C) + 32[\/latex]<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px;text-align: left\">Reduced properties<\/td>\n<td style=\"width: 50%;height: 15px\">\n<p style=\"text-align: center\">[latex]T_{r}=\\frac{T}{T_c}[\/latex]<\/p>\n<p style=\"text-align: center\">[latex]P_{r}=\\frac{P}{P_c}[\/latex]<\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">Gibb&#8217;s Phase Rule<\/td>\n<td style=\"width: 50%;height: 15px;text-align: center\">[latex]DF=2+c-\\pi-r[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">Ideal Gas Law<\/td>\n<td style=\"width: 50%;height: 15px\">\n<p style=\"text-align: center\">[latex]PV=nRT[\/latex]<\/p>\n<p style=\"text-align: center\">[latex]P\\hat{V}=RT[\/latex]<\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">Dalton&#8217;s Law<\/td>\n<td style=\"width: 50%;height: 15px\">\n<p style=\"text-align: center\">[latex]P=\\sum^n_{i}p_{i}[\/latex]<\/p>\n<p style=\"text-align: center\">[latex]p_{A}=y_{A}P[\/latex]<\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">Amgat&#8217;s Law<\/td>\n<td style=\"width: 50%;height: 15px\">\n<p style=\"text-align: center\">[latex]V=\\sum^n_{i}v_{i}[\/latex]<\/p>\n<p style=\"text-align: center\">[latex]v_{A}=y_{A}V[\/latex]<\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">Relating ideal gas properties<\/td>\n<td style=\"width: 50%;height: 15px;text-align: center\">[latex]R=\\frac{V_s\u00b7P_s}{n\u00b7T_s}=\\frac{V\u00b7P}{n\u00b7T}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">Compressibility Factor<\/td>\n<td style=\"width: 50%;height: 15px;text-align: center\">[latex]\\frac{PV}{RT}=Z[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">Antoine Equation<\/td>\n<td style=\"width: 50%;height: 15px;text-align: center\">[latex]log_{10}(p^*)=A-\\frac{B}{T+C}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">Raoult&#8217;s Law<\/td>\n<td style=\"width: 50%;height: 15px;text-align: center\">[latex]p_{i}=y_{i}\u00b7P=x_{i}\u00b7p_i^*(T)[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">Henry&#8217;s Law<\/td>\n<td style=\"width: 50%;height: 15px;text-align: center\">[latex]p_{i}=y_{i}\u00b7P=\\frac{x_{i}}{H_{i}(T)}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Terms to know<\/h2>\n<p>The original version of this chapter contained H5P content. You may want to remove or replace this element.<\/p>\n","protected":false},"author":1,"menu_order":11,"template":"","meta":{"pb_show_title":"","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-220","chapter","type-chapter","status-publish","hentry"],"part":154,"_links":{"self":[{"href":"https:\/\/libraryresources.nse.org.ng\/chbe220\/wp-json\/pressbooks\/v2\/chapters\/220","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/libraryresources.nse.org.ng\/chbe220\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/libraryresources.nse.org.ng\/chbe220\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/libraryresources.nse.org.ng\/chbe220\/wp-json\/wp\/v2\/users\/1"}],"version-history":[{"count":1,"href":"https:\/\/libraryresources.nse.org.ng\/chbe220\/wp-json\/pressbooks\/v2\/chapters\/220\/revisions"}],"predecessor-version":[{"id":221,"href":"https:\/\/libraryresources.nse.org.ng\/chbe220\/wp-json\/pressbooks\/v2\/chapters\/220\/revisions\/221"}],"part":[{"href":"https:\/\/libraryresources.nse.org.ng\/chbe220\/wp-json\/pressbooks\/v2\/parts\/154"}],"metadata":[{"href":"https:\/\/libraryresources.nse.org.ng\/chbe220\/wp-json\/pressbooks\/v2\/chapters\/220\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/libraryresources.nse.org.ng\/chbe220\/wp-json\/wp\/v2\/media?parent=220"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/libraryresources.nse.org.ng\/chbe220\/wp-json\/pressbooks\/v2\/chapter-type?post=220"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/libraryresources.nse.org.ng\/chbe220\/wp-json\/wp\/v2\/contributor?post=220"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/libraryresources.nse.org.ng\/chbe220\/wp-json\/wp\/v2\/license?post=220"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}