Chemistry 12 Tutorial 10 Ksp Calculations



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Chemistry 12 Tutorial 10 Ksp Calculations Welcome back to the world of calculations. In Tutorial 10 you will be shown: 1. What is meant by Ksp. 2. How to write a "Ksp expression" from a net ionic equation. 3. How to calculate the solubility of an ionic substance in moles/l or in grams/l, given the value of Ksp. 4. How to calculate the value of Ksp, given the solubility of an ionic substance. ********************************************************* What is Ksp? Ksp is really nothing new. It's simply the equilibrium constant (K eq ) for an ionic substance dissolving in water. For example, for the substance, CaCO 3(s), when it dissolves in water, forms the ions Ca 2+ and CO 3 2-. The equilibrium net-ionic equation for this is: CaCO 3(s) Ca 2+ (aq) + CO 3 2- (aq). The equilibrium constant (K eq ) expression for this reaction is: K eq = [Ca 2+ ] [CO 3 2-] (Remember that the [CaCO 3 ] is not included in the expression because it is a solid.) Remember that the solubility was defined as the equilibrium concentration of a substance in water. But when ionic compounds dissolve in water, you always get at least 2 ions formed. (In this case the Ca 2+ and the CO 3 2-.) Multiplying the concentrations of the two ions (multiplication gives a "product"), as you can see, gives the K eq expression: K eq = [Ca 2+ ] [CO 3 2-] K eq can be thought of as the "product of the solubility s of the two ions". So for ionic compounds dissolving in water, the K eq is given a special name: It is called "solubility product constant", or Ksp. Tutorial 10 - Ksp Calculations Page 1

Writing the Ksp expression from the Net-Ionic Equation. There's really nothing new to this. Just remember to leave out the solid. (Include the aqueous ions only) and to change coefficients in the balanced equation to exponents in the Ksp expression. Here are a couple of examples: The net-ionic equation for lead (II) chloride dissolving is: PbCl 2(s) Pb 2+ (aq) + 2Cl - (aq) The Ksp expression for this is: Ksp = [Pb 2+ ] [Cl - ] 2 (Notice that the "2" in front of the Cl - in the equation becomes an exponent in the Ksp expression. It does NOT go in front of the Cl - in the Ksp expression!) The net-ionic equation for silver sulphate dissolving is: Ag 2 SO 4(s) 2Ag + (aq) + SO 4 2- (aq) The Ksp expression would be: Ksp = [Ag + ] 2 [SO 4 2- ] I don't think you should have any more trouble with these as long as you follow the simple rules: 1. leave out the solid. (Include the aqueous ions only) 2. change coefficients in the balanced equation to exponents in the Ksp expression. ********************************************************** Calculating Solubility given Ksp. The first type of calculation we will look at is how to calculate the solubility of a substance in moles per litre (M), given the value of Ksp. NOTE: We only consider the Ksp and the solubility of substances which have "Low Solubility" on the Solubility Table. These are also called "Slightly Soluble Salts" For these calculations, we can define molar solubility as the moles of the substance which will dissolve in one litre of solution to form a saturated solution. On the next page, you will be shown how to calculate the molar solubility of AgCl from the Ksp. Tutorial 10 - Ksp Calculations Page 2

First we obtain a sheet entitled Solubility Product Constants at 25 ºC This has Ksp s for many of the Low Solubility Compounds listed. Always have this table with you on a test! So, we find that the Ksp for AgCl = 1.8 x 10-10 The net-ionic equation for the substance, AgCl dissolving in water is: -s AgCl (s) Ag + (aq) + Cl - (aq) The number of moles of AgCl which dissolve in one litre can be defined as "s". (This is the molar solubility.) Notice, that this is written as "-s" above AgCl in the equation. This is because when you dissolve AgCl in water, the amount of solid will go down by "s" because that much dissolves. The -s is the same thing as [C] or change in concentration in an ICE table. Now by mole ratios, you can see, that in this case [Ag + ] will increase by "s" as the AgCl dissolves. Also, the [Cl - ] will also increase by "s". (The coefficients of Ag + and Cl - are both "1".) 1/1 -s ------> +s AgCl (s) Ag + (aq) + Cl - (aq) 1/1 and -s -------------------> +s AgCl (s) Ag + (aq) + Cl - (aq) so we have: The Ksp expression for this process is: -s +s +s AgCl (s) Ag + (aq) + Cl - (aq) where "s" is the moles/l of AgCl which dissolve. Ksp = [Ag + ] [Cl - ] What we do now is "plug in" the values of [Ag + ] and [Cl - ] in terms of "s". These are the expressions written on top of the net-ionic equation: [Ag + ] = s and [Cl - ] = s (we don't need to write the "+" signs) Tutorial 10 - Ksp Calculations Page 3

Since: Ksp = [Ag + ] [Cl - ] Ksp = (s) (s) or Ksp = s 2 Now we can solve for s. Remember we found from the Ksp table that the value for Ksp = 1.8 x 10-10 So s 2 = 1.8 x 10-10 or s 1.8 x 10-10 = = 1.34164 x 10-5 M Since "s" was defined as the molar solubility of AgCl: -s +s +s AgCl (s) Ag + (aq) + Cl - (aq) where "s" is the moles/l of AgCl which dissolve. We can say, the molar solubility of AgCl is 1.34164 x 10-5 moles/l or 1.3 x 10-5 M (2 sig. digs.) (The Ksp given on the table has 2 SD s) NOTE: It looks awful tempting at this point to just say that the solubility is the square root of the Ksp. It is in this case, but not in all cases. Make sure when you do these problems that you always write: 1. The net-ionic equilibrium equation (with the "s"s on top according to the coefficients), 2. The Ksp expression, and 3. The concentrations plugged into the Ksp expression to solve for "s". DON'T TAKE SHORT CUTS! They could lead to trouble in the next type of problem! ************************************************************ The next problem, you should try on your own, keeping the last three points in mind. Don't worry too much if you get it wrong the first time. Just make sure you understand the solution given on page 1 of Tutorial 10 - Solutions. 1. Calculate the solubility of SrF 2 in moles/litre in water. Answer Check your answer on page 1 of Tutorial 10 Solutions Tutorial 10 - Ksp Calculations Page 4

Now, let's say you're given the Ksp table and asked to find the solubility of a substance in grams/l. What you would do is determine the solubility in moles/l (or M) first, then convert to grams/l using the following: moles MM grams grams x = Litre 1 mole Litre Where "MM" stands for the Molar Mass. Try this example: 2. Calculate the solubility of Ag 2 CO 3 in grams/litre. Check your answer on page 2 of Tutorial 10 - Solutions Answer ********************************************************** Tutorial 10 - Ksp Calculations Page 5

Calculating Ksp, Given Solubility The first example we will do is to calculate the Ksp of a substance given it's molar solubility. In this type of problem we don't use "s"s. The molar solubility is known, so we find the concentration of each ion using mole ratios (record them on top of the equation). Next we write out the expression for Ksp, then "plug in" the concentrations to obtain the value for Ksp. Let's do an example: The solubility of Ag 2 CrO 4 in water is 1.31 x 10-4 moles/l. Calculate the value of Ksp. The first thing we do is write out the net-ionic equation for a saturated solution of Ag 2 CrO 4 : Ag 2 CrO 4 (s) 2Ag + (aq) + CrO 4 2- (aq) The solubility given is 1.31 x 10-4 moles/l, so we write that right on top of the Ag 2 CrO 4(s) (I usually write it as a negative (-) because it is going down (the solid is dissolving)) -1.31 x 10-4 moles/l Ag 2 CrO 4 (s) 2Ag + (aq) + CrO 4 2- (aq) Using mole ratios, the [Ag + ] will go up by (2 x 1.31 x 10-4 moles/l) = 2.62 x 10-4 moles/l. x 2/1-1.31 x 10-4 moles/l -----------> + 2.62 x 10-4 moles/l Ag 2 CrO 4 (s) 2Ag + (aq) + CrO 2-4 (aq) [CrO 4 2- ] will go up by 1.31 x 10-4 moles/l: x 1/1-1.31 x 10-4 moles/l ------------------------------------------> + 1.31 x 10-4 M. Ag 2 CrO 4 (s) 2Ag + (aq) + CrO 4 2- (aq) So once the solution is saturated (reaches equilibrium): [Ag + ] = 2.62 x 10-4 moles/l [CrO 4 2- ] = 1.31 x 10-4 moles/l Tutorial 10 - Ksp Calculations Page 6

The Ksp expression is: Ksp = [Ag + ] 2 [CrO 4 2-] [Ag + ] = 2.62 x 10-4 moles/l [CrO 4 2-] = 1.31 x 10-4 moles/l Plugging in the concentrations directly we get: Ksp = (2.62 x 10-4 ) 2 (1.31 x 10-4) Ksp = 8.99 x 10-12 Our answer has 3 SD s because that was the lowest # of SD s given in the data. We did not use a Ksp table. ********************************************************************** Now, here s a question for you to try: 3. At a certain temperature, the solubility of SrCO 3 is 7.5 x 10-5 M. Calculate the Ksp for SrCO 3. Check your answer on Page 4 of Tutorial 10 - Solutions Answer *********************************************************** The next type of problem involves calculating the value of Ksp given the solubility in grams per Litre. For this, you simply change grams/l to moles/l using the following: grams 1 mole moles x = Litre MM grams Litre where "MM" stands for the Molar Mass. Then write out the Net-Ionic equation for the equilibrium, and the Ksp expression. Tutorial 10 - Ksp Calculations Page 7

Determine the concentrations of the ions and plug them into the Ksp expression to solve for Ksp. Here's an example: 6.60 grams of MnF 2 will dissolve in one Litre of solution at 25 C. Calculate the value of Ksp for MnF 2 at 25 C. Step 1- Change solubility in grams/l to moles/l using Molar Mass: The molar mass of MnF 2 = 54.9 + 2(19.0) = 92.9 grams/mole 6.60 grams 1 mole 0.071044 moles x = Litre 92.9 grams Litre So, from step 1, the molar solubility of MnF 2 is 0.071044 moles/litre. Step 2- Write out the Net-Ionic Equation: MnF 2(s) Mn 2+ (aq) + 2F - (aq) Step 3 - Write the molar solubility above the MnF 2(s) and determine the [Mn 2+ ] and [F - ] using mole ratios: x 1/1-0.071044 moles/l ------------> +0.071044 moles/l 1 MnF 2(s) 1 Mn 2+ (aq) + 2F - (aq) x 2/1-0.071044 moles/l --------------------------------------------> + 0.14209 moles/l 1 MnF 2(s) 1 Mn 2+ (aq) + 2F - (aq) It is important that you understand here that [F-] is 0.14209, not the [2F - ]! ([F - ] happens to be 2 times the solubility of MnF 2 just because of the mole ratio in the balanced equation.) So [Mn 2+ ] = 0.071044 M and [F - ] = 0.14209 M Step 4 - Write out the Ksp expression: Ksp = [Mn 2+ ] [F - ] 2 (not [2F - ] 2 ) Tutorial 10 - Ksp Calculations Page 8

Step 5 - "Plug-in" the values for [Mn 2+ ] and [F - ] and solve for the value of Ksp. [Mn 2+ ] = 0.071044 M and Ksp = [Mn 2+ ] x [F - ] 2 = ( 0.071044 ) ( 0.14209 ) 2 Ksp = 1.43 x 10-3 [F - ] = 0.14209 M *********************************************************** In summary, we have covered the following: 1. What is meant by Ksp. 2. How to write a "Ksp expression" from a net ionic equation. 3. How to calculate the solubility of an ionic substance in moles/l or in grams/l, given Ksp. 4. How to calculate the value of Ksp, given the solubility of an ionic substance. Self-Test on Tutorial 10 Check your answers starting on page 5 of Tutorial 10 - Solutions The lowest # of SD s in the data was 3 SD s. As we were working out the problem, we kept more SD s than this. Then, in the very last step, we rounded the answer to 3 SD s. 1. The Ksp is just a for an ionic substance dissolving in water. 2. Give the Net-Ionic Equation and the Ksp expression for each of the following dissolving in water. (The first one is done as an example.) Substance Net-Ionic Equation Ksp Expression Ag 2 SO 4(s) Ag 2 SO 4(s) 2Ag + (aq) + SO 4 2- (aq) Ksp = [Ag + ] 2 [SO 4 2- ] CaCO 3(s) Ca 3 (PO 4 ) 2(s) AgClO 3(s) Tutorial 10 - Ksp Calculations Page 9

3. a) Calculate the molar solubility (solubility in moles/litre) of Fe(OH) 2 in water. b) What is the [OH - ] in a saturated solution of Fe(OH) 2? Answer 4. Calculate the solubility of BaCO 3 in grams per Litre. Answer Answer Tutorial 10 - Ksp Calculations Page 10

5. The solubility of PbI 2 at a certain temperature is 0.70 grams per Litre. a) Calculate the solubility in moles/litre b) Calculate the value of Ksp for PbI 2 at this temperature Answer Answer 6. It is found that 0.043 grams of MgCO 3 is all that can dissolve in 100.0 ml of solution at a certain temperature. From this information, calculate the Ksp for MgCO 3 at this temperature. Answer Tutorial 10 - Ksp Calculations Page 11

7. Two separate experiments were done with combinations of Cu 2+ and IO 3 - ions. Use the information given to fill in the missing value. The Net-Ionic Equation for equilibrium is: Cu(IO 3 ) 2(s) Cu 2+ (aq) + 2IO 3 - (aq) Experiment # [Cu 2+ ] [IO 3 -] 1 0.00327 M 0.00654 M 2 0.00240 M? Check your answers starting on page 5 of Tutorial 10 - Solutions *************************************************************** This is the End of Tutorial 10 Tutorial 10 - Ksp Calculations Page 12

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