Concentrations of Pb2+ and Cl2 at equilibrium

[magma_saber]

Homework Statement

A solution is prepared by mixing 50.0 mL of 0.36 M Pb(NO3)2 with 50.0 mL of 1.7 M KCl. Calculate the concentrations of Pb2+ and Cl2 at equilibrium. Ksp for PbCl2(s) is 1.6 x 10-5.

Homework Equations

I think its Ksp = [Pb(NO₃)2][KCl]²

Pb(NO₃)2 = 0.018 mol
KCl = 0.085 mol

Is this right? what do i solve for?

 

[Borek]

Your Ksp is wrong. It should be made of ions concentrations.

Otherwise it is limiting reagent question. Once everything precipitates out, you will be left with the excess of one of the ions involved. Use this concentration to calculate concentration of the other using (correct) Ksp formula.

 

[Blueshift5]

I would like to clarify that the equation for calculating the equilibrium concentration of Pb2+ and Cl2 is not Ksp = [Pb(NO3)2][KCl]2. The correct equation is Ksp = [Pb2+][Cl-]^2, where [Pb2+] and [Cl-] represent the equilibrium concentrations of Pb2+ and Cl-, respectively.

Using the given information, we can calculate the equilibrium concentrations as follows:

First, we need to determine the moles of Pb2+ and Cl- in the solution. Since the volumes are the same for both solutions and the molarities are given, we can use the formula moles = molarity x volume (in liters).

Moles of Pb2+ = 0.36 mol/L x 0.050 L = 0.018 mol
Moles of Cl- = 1.7 mol/L x 0.050 L = 0.085 mol

Next, we need to use the stoichiometry of the reaction to determine the equilibrium concentrations of Pb2+ and Cl-. From the balanced equation, we can see that 1 mole of Pb(NO3)2 produces 1 mole of Pb2+ and 2 moles of Cl-. Therefore, the equilibrium concentrations are:

[Pb2+] = 0.018 mol/L
[Cl-] = 2 x 0.085 mol/L = 0.17 mol/L

Finally, we can plug these values into the equation for Ksp to calculate the equilibrium constant:

Ksp = [Pb2+][Cl-]^2
Ksp = (0.018 mol/L)(0.17 mol/L)^2 = 0.0058

Therefore, the equilibrium concentrations of Pb2+ and Cl- in the solution are 0.018 mol/L and 0.17 mol/L, respectively. It is important to note that these concentrations will only remain constant if the conditions of the solution (temperature, pressure, etc.) do not change. Any changes to these conditions can affect the equilibrium concentrations and ultimately, the value of Ksp.