Calculating the partial pressure of pure Zinc over a solution? over

AI Thread Summary
To calculate the partial pressure of pure zinc over a solution of 60 mol% copper and 40 mol% zinc at 1200 K, the activity coefficient of zinc is used, derived from the equation RT ln γZn = -38,300 x2Cu. The vapor pressure of pure zinc at this temperature is 1.17 atm. The mole fraction of zinc (xZn) is 0.4, and the Gibbs-Duhem relationship is applied to relate activity coefficients. There is confusion regarding the units of the activity coefficient, as it is typically unitless rather than in joules. The discussion focuses on the correct application of these equations to find the desired partial pressure.
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Homework Statement



The activity coefficient of zinc in liquid brass is given (in joules) by the following equation for
temperatures 1000-1500 K:
RT ln γZn = -38,300 x2Cu

where xCu is the mole fraction of copper. Calculate the partial pressure of pure zinc PZn over a
solution of 60 mol% copper and 40 mol % zinc at 1200 K. The vapor pressure of pure zinc is
1.17 atm at 1200 K.

Homework Equations



For dilute solutions: xs: mole fraction of solvent, xu: mole fraction of solute,
The vapour pressure of the solvent= Ps= P(pure)xs=P(pure)(1-xu) where is P(pure)=vapour pressure of the pure solvent.


Gibbs-Duhem Relationship=
lnaB
lnaA= - ∫ xB/ xa * d(lnaB)
-∞

The Attempt at a Solution



d (lnγA)= - XB/XA * d(lnγB) applying Gibbs-Duhem rel. in the form of this eqnn:
dxcu= -dXzn
lnγCu= - 38.300/ RT * X^2Zn

How can i get the partial pressure of pure zinc PZn?

Thanks! :)
 
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