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

In summary, the conversation discusses the calculation of the partial pressure of pure zinc in a solution of 60 mol% copper and 40 mol% zinc at a temperature of 1200 K. The equation for the activity coefficient of zinc is given, along with the Gibbs-Duhem relationship and the equation for calculating the vapor pressure of the solvent. The solution also considers the mole fractions of the solvent and solute, and the vapor pressure of pure zinc at 1200 K.
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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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  • #2
Activity coefficient in Joules? Shouldn't it be unitless?
 

1. How do you calculate the partial pressure of pure Zinc over a solution?

To calculate the partial pressure of pure Zinc over a solution, you will need to know the total pressure of the system, the mole fraction of Zinc in the solution, and the vapor pressure of Zinc. The partial pressure can then be calculated using the formula: PZn = Ptotal * XZn * P°Zn, where PZn is the partial pressure of Zinc, Ptotal is the total pressure, XZn is the mole fraction of Zinc, and P°Zn is the vapor pressure of Zinc at a given temperature.

2. What is the significance of calculating the partial pressure of pure Zinc over a solution?

The partial pressure of pure Zinc over a solution is important in understanding the behavior of Zinc in a gaseous state. It can also provide insight into the thermodynamic properties of the system, such as the equilibrium constant and the activity coefficient of Zinc in the solution.

3. How does the partial pressure of pure Zinc over a solution affect its solubility?

The partial pressure of pure Zinc over a solution can affect its solubility by influencing the equilibrium between the gaseous and dissolved states of Zinc. As the partial pressure increases, more Zinc molecules will enter the solution, increasing its solubility. Conversely, a decrease in partial pressure will lead to a decrease in solubility.

4. What factors can affect the partial pressure of pure Zinc over a solution?

The partial pressure of pure Zinc over a solution can be affected by temperature, pressure, and the concentration of Zinc in the solution. The vapor pressure of Zinc will also vary with changes in temperature, which in turn will affect the partial pressure.

5. How can the partial pressure of pure Zinc over a solution be experimentally determined?

The partial pressure of pure Zinc over a solution can be experimentally determined by using a gas collection system and measuring the pressure of the collected gas. This pressure can then be used to calculate the partial pressure using the ideal gas law. Alternatively, the partial pressure can also be measured using a gas chromatography technique.

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