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 the activities of Zn2+ and Pb2+ in a solution in equilibrium with sphalerite and galena, we need to use the equilibrium constant expression.
The equilibrium constant expression for the reaction is as follows:
ZnS(sphalerite) + PbS(galena) ⇌ Zn2+ + Pb2+
The equilibrium constant expression (K) is defined as the product of the activities of the products divided by the product of the activities of the reactants, each raised to the power of their respective coefficients in the balanced equation.
Mathematically, it can be expressed as:
K = ([Zn2+] * [Pb2+]) / ([ZnS] * [PbS])
Since the activity of a solid is considered to be constant, we can ignore the activities of ZnS and PbS. Therefore, we can simplify the expression to:
K = [Zn2+] * [Pb2+]
Now, if we let x be the activity of Zn2+ and y be the activity of Pb2+, the equilibrium constant expression becomes:
K = x * y
Since it is a ratio, we can also express the equilibrium constant expression as:
K = [Zn2+]/[Pb2+]
Therefore, the ratio of the activities of Zn2+ and Pb2+ in the solution in equilibrium with sphalerite and galena is equal to the equilibrium constant (K).