At 50oC, the solubility of silver chloride, AgCl, is 5.2 x 10-4 g/100 mL. Calculate the Ksp at this temperature.
To calculate the Ksp (solubility product constant) at a specific temperature, you need to know the molar solubility of the compound. The molar solubility is the number of moles of the compound that will dissolve to form a saturated solution.
In this case, you are given the solubility of silver chloride, AgCl, in grams per 100 mL of solvent. To convert this value to molar solubility, you need to convert the grams to moles.
1. Start by calculating the moles of silver chloride dissolved:
- Convert the given solubility from grams/100 mL to grams/mL:
Solubility = 5.2 x 10^-4 g / 100 mL = 5.2 x 10^-6 g/mL
- Since 1 mL is equal to 0.001 L, we can convert grams/mL to grams/L:
Solubility = 5.2 x 10^-6 g/mL x 1000 mL/L = 5.2 x 10^-3 g/L
- Calculate the moles of silver chloride dissolved using its molar mass (107.87 g/mol):
Moles = 5.2 x 10^-3 g/L / 107.87 g/mol = 4.82 x 10^-5 mol/L
2. Based on the chemical equation for the dissolution of AgCl in water:
AgCl (s) ⇌ Ag+ (aq) + Cl- (aq)
The molar solubility of AgCl is equal to the molar concentrations of Ag+ and Cl- ions in a saturated solution.
Therefore, the molar solubility of AgCl is also the molar concentration of Ag+ and Cl- ions, which are equal.
Therefore, the molarity of Ag+ (Molar solubility of AgCl) and Cl- is:
[Ag+] = [Cl-] = 4.82 x 10^-5 mol/L
3. Finally, to calculate the Ksp at this temperature, you need to use the expression for Ksp, which is the product of the molar concentrations (raised to the power of their stoichiometric coefficients) of the ions in the balanced equation:
Ksp = [Ag+] x [Cl-] = (4.82 x 10^-5)^2 = 2.32 x 10^-9
Therefore, the calculated Ksp of AgCl at 50oC is 2.32 x 10^-9.
Convert 5.2 x 10^-4 g/100 mL to moles/L.
Then Ksp = (Ag^+)(Cl^-)