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handout18 - 5.4 Chemical Equilibrium In Mole Fractions and...

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5.4 Chemical Equilibrium In Mole Fractions and Molarity REMINDER: In section 4-14, we derived an expression for K P , the thermodynamic equilibrium constant, in terms of partial pressures (Eq. 4.210): K P = i " P eq i P 0 # ν i . (5.25) It is often more convenient to express this in terms of mole fractions or molarity, particularly when we are dealing with reactions in solution. AIM: Derive alternative expressions for the thermodynamic equilibrium constant. We will have partial pressures: K P mole fraction: K X fi molarity: K C Mole Fractions REMINDER: If we have a mixture of I different substances, consisting of n i moles of substance i , the mole fraction of species i is x i = n i I j = 1 n j . (5.26) The partial pressure of substance i is then P i = x i P and at 5–16
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equilibrium we can write K P = i " P eq i P 0 # ν i (5.27) = i " x eq i P P 0 # ν i (5.28) = i h x eq i i ν i ! P P 0 i ν i (5.29) = K X P P 0 i ν i , (5.30) where x eq i is the mole fraction at equilibrium. Molarity REMINDER: Molarity is defined as c i = n i V = n i P nRT = P i RT . (5.31) We would like to work with a dimensionless quantity, which c i is not, so we introduce the ratio c i c 0 . Now we can express the partial pressure ratio as P i P 0 = RTc i P 0 (5.32) = c i c 0 c 0 RT P 0 . (5.33) 5–17
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Then, at equilibrium we can write K P = i " P eq i P 0 # ν i (5.34) = i " c eq i c 0 c 0 RT P 0 # ν i (5.35) = i " c eq i c 0 # ν i ! c 0 RT P 0 i ν i (5.36) = K C c 0 RT P 0 i ν i . (5.37) REMINDER: Remember that K P is a dimensionless number. So are K X and K C . NOTE: In general, K P , K X and K C are all different for a given reaction.
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