![\"\"](\"https:\/\/chemical-engineering-review.com\/en\/wp-content\/uploads\/sites\/2\/2022\/02\/Pxy1.png\")
<\/p>\r\nA graph that shows the relationship between liquid phase composition x, gas phase composition y, and pressure P for two components at a constant temperature is called a Pxy diagram.<\/p>\r\n
<\/p>\r\n
As shown in the above figure, the Pxy diagram is a graph in which the pressure P is plotted on the vertical axis and the liquid phase composition x and gas phase composition y are plotted on the horizontal axis.<\/p>\r\n
The upper line in the figure is called the boiling point curve, and it represents the pressure at which the mixture begins to evaporate.<\/p>\r\n
The lower line in the figure is called the dew point curve and represents the pressure at which the gas mixture begins to condense.<\/p>\r\n
In general, substances are more likely to condense into liquid when the pressure is high, and evaporate into gas when the pressure is low.<\/p>\r\n
Therefore, point A in the figure is above the boiling point curve, which is the liquid state.<\/p>\r\n
The pressure is reduced from point A, and when it reaches point B, the liquid begins to evaporate.<\/p>\r\n
This point B is the boiling point of the mixture at that pressure, temperature, and composition.<\/p>\r\n
When the pressure is further reduced to reach point C, a mixture of liquid and gas is formed.<\/p>\r\n
It follows the principle of leverage to determine what composition separates a liquid from a gas.<\/p>\r\n
In the above figure, the liquid phase composition is at point C’ and the gas phase composition is at point C”.<\/p>\r\n
When the pressure is further reduced to reach point D, the liquid is completely finished evaporating.<\/p>\r\n
This point D is the dew point of the mixture at that pressure, temperature, and composition.<\/p>\r\n
Since there is a close relationship between the pressure and the state of the mixture, especially in a system where the pressure is changing, check the trend on the Pxy diagram.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n
If the two-component system is an ideal solution that obeys Raoult’s law, the boiling point curve in the Pxy diagram will be a straight line.<\/p>\r\n
This is useful because you can determine if it is an ideal system just by the shape of the Pxy diagram.<\/p>\r\n
This relationship can be derived from Dalton’s law and Raoult’s law.<\/p>\r\n
By combining Dalton’s law and Raoult’s law, the following two equations can be established.<\/p>\r\n
$$Py_{A}=x_{A}P_{A}^{o}\u30fb\u30fb\u30fb(1)$$<\/p>\r\n
\r\n\r\n<\/p>\r\n
$$Py_{B}=x_{B}P_{B}^{o}\u30fb\u30fb\u30fb(2)$$<\/p>\r\n
where P is the total pressure, Po<\/sup> is the vapor pressure of pure substance for each component, y is the gas phase mole fraction of each component, x is the liquid phase mole fraction of each component.<\/p>\r\n Add Eq. (1) and (2) together side by side.<\/p>\r\n $$P(y_{A}+y_{B})=x_{A}P_{A}^{o}+x_{B}P_{B}^{o}$$<\/p>\r\n Here we use the relationship between the compositions of the two components in Eq. (3) and (4).<\/p>\r\n $$y_{A}+y_{B}=1\u30fb\u30fb\u30fb(3)$$<\/p>\r\n \r\n\r\n<\/p>\r\n $$x_{A}+x_{B}=1\u30fb\u30fb\u30fb(4)$$<\/p>\r\n <\/p>\r\n $$P=x_{A}P_{A}^{o}+P_{B}^{o}(1-x_{A})$$<\/p>\r\n \r\n\r\n<\/p>\r\n $$P=(P_{A}^{o}-P_{B}^{o})x_{A}+P_{B}^{o}\u30fb\u30fb\u30fb(5)$$<\/p>\r\n It can be transformed to Eq. (5).<\/p>\r\n Since the temperature is constant in the Pxy diagram and the formula for calculating vapor pressure, such as the Antoine equation, is a function of temperature, the vapor pressures PA<\/sub>o<\/sup> and PB<\/sub>o<\/sup> are constant in Eq. (5).<\/p>\r\n Therefore, Eq. (5) is a linear function of xA<\/sub> with respect to pressure P, and it is a straight line on the Pxy diagram.<\/p>","protected":false},"excerpt":{"rendered":" A graph that shows the relationship between liquid phase composition x, gas phase composition y, and pressure P for two components at a constant temperature is called a Pxy diagram.<\/p>\n","protected":false},"author":1,"featured_media":146,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8],"tags":[],"class_list":["post-122","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-distillation"],"_links":{"self":[{"href":"https:\/\/chemical-engineering-review.com\/en\/wp-json\/wp\/v2\/posts\/122","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/chemical-engineering-review.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/chemical-engineering-review.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/chemical-engineering-review.com\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/chemical-engineering-review.com\/en\/wp-json\/wp\/v2\/comments?post=122"}],"version-history":[{"count":4,"href":"https:\/\/chemical-engineering-review.com\/en\/wp-json\/wp\/v2\/posts\/122\/revisions"}],"predecessor-version":[{"id":147,"href":"https:\/\/chemical-engineering-review.com\/en\/wp-json\/wp\/v2\/posts\/122\/revisions\/147"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/chemical-engineering-review.com\/en\/wp-json\/wp\/v2\/media\/146"}],"wp:attachment":[{"href":"https:\/\/chemical-engineering-review.com\/en\/wp-json\/wp\/v2\/media?parent=122"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/chemical-engineering-review.com\/en\/wp-json\/wp\/v2\/categories?post=122"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/chemical-engineering-review.com\/en\/wp-json\/wp\/v2\/tags?post=122"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}