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Unformatted text preview: to the above relation and differentiating with respect to temperature, we get
d 1ln K p 2 dT H* 1T2 R uT 2 d 3 H* 1T2 4 R uT dT d 3 S* 1T 2 4 R u dT At constant pressure, the second T ds relation, T ds dh v dP, reduces to T ds dh. Also, T d(S*) d(H*) since S* and H* consist of entropy and enthalpy terms of the reactants and the products. Therefore, the last two terms in the above relation cancel, and it reduces to
d 1ln K p 2 dT H* 1T2 R uT
2 h R 1T2 R uT
2 (1617) where hR 1T2 is the enthalpy of reaction at temperature T. Notice that we dropped the superscript * (which indicates a constant pressure of 1 atm) from H(T), since the enthalpy of an ideal gas depends on temperature only and is independent of pressure. Equation 1617 is an expression of the variation of KP with temperature in terms of hR 1T2 , and it is known as the van't Hoff equation. To integrate it, we need to know how hR varies with T. For small temperature intervals, h R can be treated as a constant and Eq. 1617 can be integrated to yield
ln KP2 KP1 hR 1 a Ru T1 1 b T2
(1618) Chapter 16
This equation has two important implications. First, it provides a m...
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This note was uploaded on 06/15/2009 for the course MAE 3311 taught by Professor Hajisheik during the Summer '08 term at UT Arlington.
- Summer '08