The Solubility Product

Transcript

0:00Introduction

Hello everyone! Okay, one small puzzle before we start. Two silver salts that hardly dissolve in water: silver chloride, and silver chromate. Each has a number called K s p, the solubility product. Silver chloride: one point eight times ten to the minus ten. Silver chromate: one point one times ten to the minus twelve, more than a hundred times smaller! So, which salt dissolves more? Many students would say silver chloride, since its K s p is bigger. Are they right? Hold that thought; by the end of this video you will know for sure. K s p questions come up often in JEE, so let's begin.

0:44What is the solubility product?

So, what is K s p? Take a sparingly soluble salt, one that dissolves only a tiny bit. Shake it with water until no more dissolves. Now the solution is saturated, with some solid still in contact with it. Okay? So we have an equilibrium. On the left, the solid salt, A x B y; s in brackets means solid, and the small x and y count the ions. The half arrows mean equilibrium. On the right, x ions of A with charge y plus, and y ions of B with charge x minus; a q means aqueous, in water. With me? Now think. When we write the equilibrium constant for this, which of these go into it? Only the ions, yes! K s p, capital K with small s p, equals the concentration of A y plus to the power x, times the concentration of B x minus to the power y. Square brackets mean concentration in moles per litre. And K s p is fixed at a given temperature. Clear?

1:46From Ksp to molar solubility s

Now, K s p links straight to solubility. Let small s be the molar solubility: moles of salt dissolved per litre of saturated solution; the minus one up top means per. Okay? So, if s moles of A x B y dissolve in a litre, how many moles of A y plus do we get? x times s, exactly! Each formula unit releases x ions of A, so A y plus is x s. Likewise, B x minus is y s. Right? Put these into K s p: x s to the power x, times y s to the power y. Collecting the s terms: x to the x, times y to the y, times s to the x plus y. One formula for every such salt. Got it?

2:33The standard cases

Alright, the standard cases. First, type A B, like silver chloride, A g C l, or barium sulphate, B a S O four. Each ion is at s, so K s p is s times s; the cross means times. That is s squared! Next, silver chromate, A g two C r O four. It gives two A g plus ions and one chromate ion, C r O four two minus; the two minus up top is its charge. So silver is two s, and chromate is s. Okay? Now K s p. Silver times chromate: two s times s, that is two s squared, right? No, no, careful! This is the classic trap. The silver concentration is raised to the power two, its coefficient. So two s, the whole squared, times s: four s cubed. Lead iodide, P b I two, and calcium fluoride, C a F two, work the same way. Clear? Next, type A B three, like ferric hydroxide or chromium hydroxide; the brackets hold the O H group. One metal ion at s, three hydroxide ions at three s. So K s p is s, times the cube of three s: twenty seven s to the power four. With me? Your turn now. Calcium phosphate: C a three, P O four in brackets, two. So it is type A three B two. What is its K s p in terms of s? Three calcium ions at three s, two phosphate ions at two s. So three s, the whole cubed, times two s, the whole squared. Twenty seven times four: one hundred and eight s to the power five. It is a solved example on this page.

4:13Comparing solubilities

Right? Now, which of two salts dissolves more? If both are the same formula type, say both type A B, K s p is s squared for both. So larger K s p means larger s; the double arrow means, so. Okay? But for different types, the powers of s differ: s squared for one, four s cubed for another. Then a smaller K s p need not mean a smaller s. So compare s, not K s p. Example two will show you. Got it? One last tool. To get the solubility in grams per litre, multiply s times the molar mass of the salt. That's it! Clear?

4:51Example 1: Ksp of AgCl from its solubility

Okay, Example one, nice and easy. The solubility of silver chloride in water at two hundred and ninety eight kelvin is one point three times ten to the minus five moles per litre; the capital K is for kelvin. Find K s p. Pause the video, and try it first. Done? Okay, let's check. Solid silver chloride gives one A g plus and one C l minus, so each ion is at s, the given solubility. Right? So K s p is s squared. Quick, what is one point three times ten to the minus five, squared? One point six nine times ten to the minus ten, very good! One point three squared is one point six nine, and ten to the minus five, squared, is ten to the minus ten. With me? Rounded, about one point seven times ten to the minus ten; the wavy equals sign means approximately. And it holds at two hundred and ninety eight kelvin, since K s p changes with temperature. Okay?

5:51Example 2: AgCl or Ag2CrO4, which is more soluble?

Now Example two: our puzzle. K s p of silver chloride is one point eight times ten to the minus ten; of silver chromate, one point one times ten to the minus twelve. Which is more soluble in water? Pause and try it. Hint: find s for each salt. Done? Silver chromate has the much smaller K s p, so silver chloride is more soluble, right? Oh no, careful! That is the trap again. Different formula types, so compare s. Silver chloride is type A B: s squared equals one point eight times ten to the minus ten. Square root: s is one point three times ten to the minus five molar; capital M means molar. Okay? Silver chromate is the four s cubed type: four s cubed equals one point one times ten to the minus twelve. Divide by four: s cubed is two point seven five times ten to the minus thirteen. Right? Now take the cube root; the one third up top means cube root. So s comes out to six point five times ten to the minus five molar. With me? Now compare. Six point five versus one point three, both times ten to the minus five. How many times bigger is the first? Five times, exactly! Silver chromate is about five times more soluble, though its K s p is smaller. Puzzle solved! Different formula types: compare s, never K s p. Clear?

7:19Quick revision: s^2, 4s^3, 27s^4, 108s^5 and comparing s

So, quick revision. For a saturated solution at a fixed temperature, K s p equals x to the x, times y to the y, times s to the x plus y: s squared, four s cubed, twenty seven s to the four, one hundred and eight s to the five. Raise each concentration to its coefficient: two s, the whole squared, not just two s. And for different formula types, compare s, not K s p. Now try the practice problems on this page. You can do this. All the best!