What is the ratio of the activities of Zn 2+ and Pb 2+ in a solution that is in equilibrium with respect to sphalerite and galena?disregard hydrolysis effect
To determine the ratio of activities of Zn2+ and Pb2+ in a solution in equilibrium with sphalerite and galena, we need to consider the equilibrium constants for the dissolution reactions of these minerals.
The equilibrium reactions governing the dissolution of sphalerite (ZnS) and galena (PbS) are as follows:
For sphalerite:
ZnS(s) ⇌ Zn2+(aq) + S2-(aq)
For galena:
PbS(s) ⇌ Pb2+(aq) + S2-(aq)
Now, let's denote the equilibrium constants for these reactions as K1 and K2, respectively.
To find the ratio of activities, we need to use the Nernst equation, which relates the equilibrium constant and the activities of the reacting species:
K = (activity of products) / (activity of reactants)
The activities can be approximated by the concentrations in dilute solutions. Therefore, we can rewrite the equation as:
K = ([Zn2+] / [S2-]) for sphalerite
K = ([Pb2+] / [S2-]) for galena
Taking the ratio of the two equilibrium constants, we get:
K1 / K2 = ([Zn2+] / [S2-]) / ([Pb2+] / [S2-])
Since [S2-] appears on both sides of the equation, it cancels out, giving us:
K1 / K2 = [Zn2+] / [Pb2+]
Hence, the ratio of the activities of Zn2+ and Pb2+ in equilibrium with sphalerite and galena is equal to the ratio of the equilibrium constants (K1 / K2).
To obtain the exact value of this ratio, you'll need to know the numerical values of the equilibrium constants for these reactions. These values can be found in chemical databases or experimental literature for specific temperature conditions.