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## AP®︎/College Chemistry

### Course: AP®︎/College Chemistry>Unit 13

Lesson 3: Solubility equilibria

# Worked example: Calculating solubility from Kₛₚ

A compound's molar solubility in water can be calculated from its Kₛₚ value at 25°C. To do so, first prepare an ICE (Initial, Change, and Equilibrium) table showing the equilibrium concentrations of the ions in terms of x, the molar solubility of the compound. Then, plug these expressions into the solubility-product expression for the compound and solve for the value of x. Created by Jay.

## Video transcript

- [Instructor] Let's calculate the molar solubility of calcium fluoride if the Ksp value for calcium fluoride is 3.9 times 10 to the negative 11th at 25 degrees Celsius. The first step is to write the dissolution equation for calcium fluoride. So, solid calcium fluoride will dissolve in solution to form aqueous calcium two plus ions and fluoride anions. And to balance that out, we need to make sure and include a two in front of the fluoride anions. The next step is to set up an ICE table, where I stands for initial concentration, C stands for the change in concentration, and E stands for equilibrium concentration. Before any of the solid calcium fluoride dissolves, the initial concentrations of calcium two plus ions and fluoride anions in solution is zero. So we can go ahead and put a zero in here for the initial concentration of the ions in solution. Some of the calcium fluoride will dissolve, and we don't know how much. So I like to represent that by writing -X on the ICE table, where X is the concentration of calcium fluoride that dissolves. Looking at the mole ratios, it's a one-to-one mole ratio between calcium fluoride and calcium two plus ions. So if we're losing X for the concentration of calcium fluoride, we must be gaining X for the concentration of calcium two plus ions. And since it's a one-to-two mole ratio for calcium two plus ions to fluoride anions, if we're gaining +X for calcium two plus, we must gain plus +2X for fluoride anions. So the equilibrium concentration of calcium two plus ions is zero plus X, or just X, and the equilibrium concentration of fluoride anions will be zero plus 2X, or just 2X. The next step is to write the Ksp expression from the balanced equation. So Ksp is equal to the concentration of calcium two plus ions, and since there's a coefficient of one in the balanced equation, that's the concentration of calcium two plus ions raised to the first power, times the concentration of fluoride anions, and since there is a coefficient of two in the balanced equation, it's the concentration of fluoride anions raised to the second power. Pure solids are not included in equilibrium constant expression. So we're going to leave calcium fluoride out of the Ksp expression. The concentration of ions in our Ksp expression are equilibrium concentrations. Therefore we can plug in X for the equilibrium concentration of calcium two plus and 2X for the equilibrium concentration of fluoride anions. We can also plug in the Ksp value for calcium fluoride. So that would give us 3.9 times 10 to the negative 11th is equal to X times 2X squared. Next we need to solve for X. So, 3.9 times 10 to the negative 11th is equal to X times 2X squared. Well, 2X squared is equal to 4X squared times X is equal to 4X cubed. So to solve for X, we need to divide both sides by four and then take the cube root of both sides. So we'd take the cube root of the left side and the cube root of X cubed. That gives us X is equal to 2.1 times 10 to the negative fourth. And looking at our ICE table, X represents the equilibrium concentration of calcium two plus ions. So 2.1 times 10 to the negative fourth molar is the equilibrium concentration of calcium two plus ions. For the fluoride anions, the equilibrium concentration is 2X. So two times 2.1 times 10 to the negative fourth is 4.2, let me go ahead and write that down here, 4.2 times 10 to the negative fourth molar for the equilibrium concentration of fluoride anions. Our goal was to calculate the molar solubility of calcium fluoride. And molar solubility refers to the concentration of our salt that dissolved to form a saturated solution at equilibrium. So if X refers to the concentration of calcium two plus ions at equilibrium, looking at our mole ratios, that's also the concentration of calcium fluoride that dissolved. Therefore, 2.1 times 10 to the negative fourth molar is also the molar solubility of calcium fluoride. Technically at a constant temperature of 25 degrees, the concentration of a solid doesn't change. And so you'll see most textbooks not to put in -X on the ICE table. I like to just put it in though to remind me that X in this case does refer to the molar solubility.