chemistry solubility question

Question

100 ml of a 1.0x10^-4M BaCl2 solution is mixed with 100ml of a 1.0 x10^-5M PbSO4 solution. which of the statements below is true?

The correct answer is. A PPT will form and the identity of the PPT is BaSO4.

Can someone please explain why?

Answer 1

First you need to see whether both reactants are soluble themselves:

Using standard solubility rules PbSO4 is insoluble in water. BaCl2 is fully soluble,

Find its solubility using its Ksp = 1.3 x 10-8 for PbSO4 (per internet)

PbSO4 >>>> Pb+2 + SO4-2

<<<<

0 0

+x +x

x x

Ksp = {Pb+2}{SO4}

Ksp = 1,3 x 10-8 = x2

Take the square root of x2 and 1.3 x 10-8 = a solubility of 1.14 x 10-4 M which is greater than the given amount of 1x10-5 M so PbSO4 is soluble at this concentration and can be used in the calculations below.

When 100 ml of each BaCl2 and PbSO4 are added, their concentrations are being diluted.

To correct for the dilution of each:

1) BaCl2 0.1 L x 1 X10-4M = 1 x 10-5 mol/,2 L = 5 X10-5 M (new concentration)

2) PbSO4 ),1 L x 1 x 10-5 M = 1 X 10-6mol/.2L = 5 x 10-6 M (new concentration)

Using these two new concentrations you have:

BaCl2 + PbSO4 >>> BaSO4 + PbCl2 both products are relatively insoluble, so at this point using the above concentrations we need to find Q (reaction quotient} for each and compare it to their Ksp values to see which will precipitate,

The reaction quotient. Q is the concentration as an initial concentration before equilibrium is reached.

1) Q for PbCl2

<<<<<

PbCl2>>>>> Pb+2 + 2Cl-1 Q = (Pb+2)(Cl-1)2 = (5 x 10-6)(5 x 10-5)2 = 1.25 x 10-14

Comparing Q to Ksp

Ksp PbCl2 (per internet) = 1.6 X 10-5

Q PbCl2 = 1.25 x 10-14

Q is much smaller than the Ksp so it will NOT precipitate.

2) Q for BaSO4

<<<<<

BaSO4>>>>> Ba+2 + SO4-2 Q = (Ba)(SO4) = (5 x 10-5)(5 x 10-6) = 2.5 x 10-10

Comparing Q to Ksp

Ksp BaSO4 (per internet) = 1.1 x 10-10

Q BaSO4 = 2.5 x 10-10

Q is slightly larger than its Ksp so it WILL precipitate

Using the reaction quotient, Q.

if Q > than the Ksp the substance will precipitate

if Q< than the Ksp the substance will not precipitate

if Q = the Ksp the substance is at equilibrium