A generic salt, AB, has a molar mass of 293 g/mol and a solubility of 2.20 g/L at 25 °C. What is the Ksp of this salt at 25 °C?
To find the Ksp (solubility product constant) of the salt AB at 25 °C, we first need to determine the concentration of AB in the saturated solution.
We know that the solubility of AB is given as 2.20 g/L at 25 °C. We can convert this solubility from grams per liter to moles per liter (Molar concentration) using the molar mass of AB.
First, we calculate the molar concentration (in mol/L) of AB:
Molar concentration (in mol/L) = (mass of AB / molar mass of AB) / volume (in L)
Mass of AB = 2.20 g
Molar mass of AB = 293 g/mol
Volume = 1 L (since the solubility is given in grams per liter)
Molar concentration = (2.20 g / 293 g/mol) / 1 L
Molar concentration = 0.00751 mol/L
Now, the concentration of AB in the saturated solution is 0.00751 mol/L.
Since AB is a generic salt, we can assume that it dissociates completely in water into its constituent ions. Let's say it dissociates into A+ and B-. Therefore, the concentration of A+ and B- in the saturated solution is also 0.00751 mol/L.
The solubility product constant (Ksp) expression for the dissociation reaction can be written as follows:
Ksp = [A+][B-]
Substituting the concentrations we found earlier, we get:
Ksp = (0.00751 mol/L)(0.00751 mol/L)
Ksp = 5.633 × 10^-5 mol^2/L^2
Therefore, the Ksp of the salt AB at 25 °C is 5.633 × 10^-5 mol^2/L^2.