{"id":24539,"date":"2025-06-18T16:04:19","date_gmt":"2025-06-18T16:04:19","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=24539"},"modified":"2025-06-18T16:04:21","modified_gmt":"2025-06-18T16:04:21","slug":"antoine-coefficients-p-in-mmhg-t-in-k-log-to-base-e","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/antoine-coefficients-p-in-mmhg-t-in-k-log-to-base-e\/","title":{"rendered":"Antoine coefficients (P in mmHg; T in K, log to base e)"},"content":{"rendered":"\n

Antoine coefficients (P in mmHg; T in K, log to base e): Methanol: A = 18.588, B = 3626.6, C = -34.29 Water: A = 18.304, B = 3816.4, C = -46.13 Ethanol: A = 18.9119, B = 3803.98, C = -41.68 Margules parameters: Methanol-Water: Awm = 0.6174, Amw = 0.7279 Ethanol-Water: Awe = 0.7917, Aew = 0.6366 1. a) Calculate the Henry’s Law constant for dilute methanol in water at atmosphere: i) assuming ideal solution behavior ii) using the Margules Coefficients provided to account for the non-ideality of the solution Compare your answers with the value roughly obtained from the gradient in the X-y diagram below: b) Now repeat part a) but this time to determine the Henry’s Law constant for dilute water in methanol at p=1 atm. Again, compare your results to the constant roughly obtained from the X-y diagram: x-y diagram for methanol-water at atm 1 1 L Xm (mole fraction of methanol in liquid)<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Solution for Henry\u2019s Law Constant Calculations<\/strong><\/h3>\n\n\n\n

Part (a) \u2013 Dilute Methanol in Water at 1 atm<\/strong><\/h4>\n\n\n\n
(i) Assuming Ideal Solution Behavior<\/strong><\/h5>\n\n\n\n

Henry\u2019s Law states that the equilibrium partial pressure of a solute gas over a liquid is proportional to its mole fraction:<\/p>\n\n\n\n

P=H\u22c5xP = H \\cdot x<\/p>\n\n\n\n

where HH is the Henry\u2019s Law constant and xx is the mole fraction in the liquid phase.<\/p>\n\n\n\n

For methanol:<\/p>\n\n\n\n

ln\u2061P=A\u2212BT+C\\ln P = A – \\frac{B}{T + C}<\/p>\n\n\n\n

Using Antoine constants for methanol, the vapor pressure at a given temperature TT can be calculated. Assuming ideal solution behavior:<\/p>\n\n\n\n

Pmethanol=xmethanolPmethanol0P_{\\text{methanol}} = x_{\\text{methanol}} P^0_{\\text{methanol}}<\/p>\n\n\n\n

At infinite dilution (xmethanol\u21920x_{\\text{methanol}} \\to 0), Henry\u2019s Law constant is approximately the pure component vapor pressure.<\/p>\n\n\n\n

(ii) Using Margules Coefficients<\/strong><\/h5>\n\n\n\n

The non-ideal behavior is accounted for using the Margules activity coefficient expression:<\/p>\n\n\n\n

ln\u2061\u03b3methanol=Awmxwater2+Amwxmethanol2\\ln \\gamma_{\\text{methanol}} = Awm x_{\\text{water}}^2 + Amw x_{\\text{methanol}}^2<\/p>\n\n\n\n

At infinite dilution (xmethanol\u21920x_{\\text{methanol}} \\to 0), the activity coefficient simplifies to:<\/p>\n\n\n\n

\u03b3methanol=eAwm\\gamma_{\\text{methanol}} = e^{Awm}<\/p>\n\n\n\n

Thus, the corrected Henry\u2019s Law constant is:<\/p>\n\n\n\n

Hmethanol=\u03b3methanolPmethanol0H_{\\text{methanol}} = \\gamma_{\\text{methanol}} P^0_{\\text{methanol}}<\/p>\n\n\n\n

Part (b) \u2013 Dilute Water in Methanol at 1 atm<\/strong><\/h4>\n\n\n\n
(i) Ideal Solution Assumption<\/strong><\/h5>\n\n\n\n

Applying the same method, the vapor pressure of water is used to find:<\/p>\n\n\n\n

Pwater=xwaterPwater0P_{\\text{water}} = x_{\\text{water}} P^0_{\\text{water}}<\/p>\n\n\n\n

At infinite dilution, Henry\u2019s Law constant for water is:<\/p>\n\n\n\n

Hwater\u2248Pwater0H_{\\text{water}} \\approx P^0_{\\text{water}}<\/p>\n\n\n\n

(ii) Using Margules Coefficients<\/strong><\/h5>\n\n\n\n

For water in methanol:<\/p>\n\n\n\n

ln\u2061\u03b3water=Aewxmethanol2+Awexwater2\\ln \\gamma_{\\text{water}} = Aew x_{\\text{methanol}}^2 + Awe x_{\\text{water}}^2<\/p>\n\n\n\n

At infinite dilution (xwater\u21920x_{\\text{water}} \\to 0):<\/p>\n\n\n\n

\u03b3water=eAew\\gamma_{\\text{water}} = e^{Aew}<\/p>\n\n\n\n

Thus, Henry\u2019s Law constant is:<\/p>\n\n\n\n

Hwater=\u03b3waterPwater0H_{\\text{water}} = \\gamma_{\\text{water}} P^0_{\\text{water}}<\/p>\n\n\n\n

Comparison with X-Y Diagram<\/strong><\/h3>\n\n\n\n

The Henry\u2019s Law constants derived should be compared against values obtained from the slope of the vapor-liquid equilibrium curve. Deviations indicate the importance of including Margules corrections to account for real solution behavior.<\/p>\n\n\n\n

\"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

Antoine coefficients (P in mmHg; T in K, log to base e): Methanol: A = 18.588, B = 3626.6, C = -34.29 Water: A = 18.304, B = 3816.4, C = -46.13 Ethanol: A = 18.9119, B = 3803.98, C = -41.68 Margules parameters: Methanol-Water: Awm = 0.6174, Amw = 0.7279 Ethanol-Water: Awe = 0.7917, […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-24539","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/24539","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=24539"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/24539\/revisions"}],"predecessor-version":[{"id":24547,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/24539\/revisions\/24547"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=24539"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=24539"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=24539"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}