A solution is prepared by mixing 50.7 mL of 0.28 M Pb(NO3)2 with 70.8 mL of 1.0 M KCl. Calculate the concentrations of Pb2+ and Cl - at equilibrium. Ksp for PbCl2(s) is 1.6 10-5.
To calculate the concentrations of Pb2+ and Cl- at equilibrium, we first need to determine if a precipitate forms when Pb(NO3)2 and KCl are combined.
The Ksp, or solubility product constant, is a measure of the solubility of a compound. If the product of the concentrations of the ions in a solution exceeds the Ksp value, a precipitate will form.
The balanced equation for the reaction between Pb(NO3)2 and KCl is:
Pb(NO3)2 + 2KCl → PbCl2 + 2KNO3
From this equation, we can see that one mole of Pb(NO3)2 reacts with two moles of KCl to produce one mole of PbCl2. Therefore, the number of moles of Pb(NO3)2 can be calculated using the volume (in liters) and molarity:
moles of Pb(NO3)2 = volume of Pb(NO3)2 (in liters) × molarity of Pb(NO3)2
moles of Pb(NO3)2 = 50.7 mL × (1 L / 1000 mL) × 0.28 M
Similarly, we can calculate the moles of KCl using the given volume and molarity:
moles of KCl = volume of KCl (in liters) × molarity of KCl
moles of KCl = 70.8 mL × (1 L / 1000 mL) × 1.0 M
Since the stoichiometry of the reaction is 1:2 (Pb(NO3)2:KCl), we need to divide the moles of Pb(NO3)2 by 1 and the moles of KCl by 2 to find the limiting reactant.
Next, we calculate the maximum amount of product that can form, which will be determined by the limiting reactant. In this case, the limiting reactant will produce the smaller amount of product.
To calculate the amount of PbCl2 that can form, we multiply the moles of the limiting reactant (either Pb(NO3)2 or KCl) by the stoichiometric coefficient of PbCl2:
moles of PbCl2 = limiting reactant (moles) × (1 mole PbCl2 / 1 mole Pb(NO3)2 or 2 moles KCl)
Now, we need to calculate the volume of the solution in liters by adding the volumes of Pb(NO3)2 and KCl:
total volume of solution = volume of Pb(NO3)2 (in liters) + volume of KCl (in liters)
total volume of solution = 50.7 mL × (1 L / 1000 mL) + 70.8 mL × (1 L / 1000 mL)
Finally, we can calculate the concentrations of Pb2+ and Cl- at equilibrium by dividing the moles of PbCl2 by the total volume of the solution:
concentration of Pb2+ = moles of PbCl2 / total volume of solution
concentration of Cl- = 2 × moles of PbCl2 / total volume of solution
Now, plug in the values you obtained into these equations to find the concentrations of Pb2+ and Cl-.