Classical Thermodynamics of Non-Electrolyte Solutions by H. C. Van Ness (Auth.)

By H. C. Van Ness (Auth.)

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2-73) for the general case where άμι is the total differential of μι as a result of changes in temperature as well as in pressure and composition. If we imagine that constituent i is changed from its actual state in solution to a pure ideal gas at the same temperature and pressure, the above equation integrates for this change to give Gid - μχ = R Tlnfid - R Tlnf. It should be noted that for a pure material μι becomes Gi9 and in this case, Gjd. We have already shown that for an ideal gas the fugacity equals the pressure.

However, it cannot be easily used with Eq. (3-3) for the devel­ opment of an expression for A H'. We return instead to Eq. (2-77) : d i„ / = J_ d P + £^dr. If temperature and volume are taken as independent variables, then changes at constant volume must come about solely as a result of temperature changes. Under these conditions the above equation can be written : AHr RT2 * /gin A =JV_(dP\ RT\dTJv (- dT lv Since PV=ZRT or "(&ι-"(£),+*ζ (dP\ _ /_5Z\ {jTÎv~\ëT)v RT + Z Y* Our first equation now becomes TTT = VWlv - VÔTÎV ~ T' (3 38) " From Eq.

P* If we apply this equation to an ideal gas, Z f is unity and ln y4 = ln 7^· THERMODYNAMIC PROPERTIES OF FLUIDS 29 But /,* = P*, where the asterisk denotes values at a pressure approaching zero. Hence for an ideal gas/i = P. For a solution we proceed in the same fashion and write by way of defi­ nition : d G = R T d I n / (const T) (2-56) and L 11 lim-^ = ^ = l . ;Ό Ρ P* (2-57) Again it is easily shown that for an ideal gas f = P. For a constituent of a solution we proceed in an analogous manner, and write by definition: d Gi = R T d In ft (const T), (2-58) where ft is called the fugacity of component / in solution.

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