The Mass of PbF2 From Solubility Product Constant

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The amount of Lead (II) Fluoride is dissolved in 250 ml of water until the solution is exactly saturated. What is the mass of PbF2, if the solubility product constant of PbF2 is 2.7x10⁻⁸.

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00:00The amount of lead-2-fluoride is dissolved in 250 mL of water until the solution is exactly saturated.

00:08The question is, what is the mass of PbF2, if the solubility product constant of PbF2 is 2.7 x 10-8?

00:19OK, the first step is identification.

00:22The volume of water, V is equal to 0.25 liters.

00:27Ksp of PbF2 is equal to 2.7 x 10-8.

00:34The relative molecular mass of lead-2-fluoride, 207.2 plus 2 x 19.

00:43The result is 245.2 g per mole.

00:49The next step is to analyze the ion equilibrium.

00:56In water, a molecule of lead-2-fluoride ionizes into a Pb2 plus ion and 2 F minus ions.

01:04The Ksp value in saturated and supersaturated solutions is exactly the same.

01:10The following illustration is a supersaturated condition because there is already a precipitate in the solution.

01:17Assume that the number of Pb2 plus ions is S mole.

01:22So the number of F minus ions is 2 S mole.

01:27And the volume of the solution is 1 liter.

01:33So the molarity of Pb2 plus ions is S molar.

01:37And the molarity of F minus ions is 2 S molar.

01:42The next step is to write the chemical equilibrium equation.

01:47A molecule of PbF2 will ionize into a lead ion, 2 fluoride ions.

01:54Now, we can calculate the value of S from the Ksp equation.

01:59Ksp is equal to the concentration of Pb2 plus ions, multiplied by the concentration of F minus ions to the power of 2.

02:09Plugging in the values of ion concentration and Ksp.

02:15For S to the power of 3 is equal to 2.7 times 10 to the power of negative 8.

02:23We can write this equation as S to the power of 3.

02:29Using a calculator, S is about 1.89 times 10 to the power of negative 3.

02:37This value of S is also the value of moles of PbF2 dissolved in 1 liter of water in a perfectly saturated solution.

02:49So, the molarity of PbF2 is 1.89 times 10 to the power of negative 3 molar.

02:58The fifth step is to calculate the mass of PbF2.

03:02Using the concept of molarity, big M equals N over V.

03:08Putting both values in.

03:11N equals 4.75 times 10 to the power of negative 4 moles.

03:17This is the mole value of PbF2 in a 250 milliliter solution.

03:23The mass of PbF2 dissolved is N times the relative molecular mass.

03:28Putting both values in.

03:31The result is equal to 0.115857 grams or 115.9 milligrams.

03:41This is the mass of PbF2 dissolved in 250 milliliters of water so that the solution is exactly saturated.

03:51Yup, hopefully useful.

03:53And, don't forget to follow this channel.

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