Transcription of Gibbs Phase Rule: f = c - Colby College
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Gibbs Phase Rule: f = c - Colby College
Colby College Gibbs Phase Rule: f = c p + 2 f = Intensive Degrees of freedom = variance Number of intensive variables that can be changed independently without disturbing the number of phases in equilibrium p = number of phases gas, homogeneous liquid phases , homogeneous solid phases c = components Minimum number of independent constituents Case I. No chemical reactions: c = constituents Example 1: start with methanol and water 2 components Case II With chemical reactions: Example 2: start with NaH2PO4 in water -- Ka2 Ka3 H2PO4- HPO42- + H+ PO43- + H+ Constituents: Na+, H+, H2PO4-, HPO42-, PO43-, H2O but only 2 components -- NaH2PO4 and H2O. Example 3: start with NaH2PO4 and Na2 HPO4 in water -- Same constituents: Na+, H+, H2PO4-, HPO42-, PO43-, H2O but now 3 components -- NaH2PO4, Na2 HPO4, and H2O. Need to know: T, P, yA, yB, xA, xB total intensive variables = c p + 2 But yA + yB = 1 xA + xB = 1 Get p such equations, one for each Phase : Independent variables = c p + 2 p But, chemical potential is everywhere equal: A(xA) = A(g) B(xB) = B(g) Get p 1 for each component Get c( p 1) such equations: Independent variables = c p + 2 p c( p 1) f = c p + 2 A & B liquid A(g) A(xA) = B(xB) = B(g) xA + xB =1 A & B vapor yA + yB =1 f ' = c p
Colby College Gibbs Phase Rule: f = c – p + 2 f = Intensive Degrees of freedom = variance Number of intensive variables that can be changed independently without
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