The Common-Ion Effect and the Effect of pH

Transcript

0:00Introduction

Hello everyone! Okay, one small puzzle before we start. Silver chloride hardly dissolves in water, right? Now I first dissolve some common salt, sodium chloride, in the water. Will more silver chloride dissolve now, or less? Or the same? Keep your answer in mind. By Example one, we will have the exact number, and it is a big surprise. And why does acid help some salts dissolve, but not others? Both ideas come up often in JEE, so let's begin.

0:33A common ion lowers the solubility

So, silver chloride in its saturated solution. Solid A g C l, the s in brackets, on the left. On the right, silver ions, A g plus, and chloride ions, C l minus; the sign up top is the charge, and a q means dissolved in water. The two half arrows mean equilibrium. Okay? Now the solubility product, K s p, with a small s p below. It equals A g plus times C l minus; square brackets mean concentration, in moles per litre. And K s p is fixed at a given temperature. Right? Now I add sodium chloride, N a C l. Extra chloride pours in, but K s p cannot change. So what must happen to the silver ions? They must fall, exactly! Chloride goes up, so silver must come down. That is Le Chatelier's principle: the extra chloride pushes the equilibrium back to the left. With me? This is the common ion effect. Chloride is common to both salts, okay? An ion already present lowers the solubility. Clear?

1:39How much does the solubility fall?

Now, how much does it fall? Take a salt A B in a solution that already has c molar of B minus; capital M means molar. If s is the molar solubility, then A plus is s, and B minus is c plus s. Okay? So s times, c plus s, equals K s p. But s is much smaller than c, the double less than sign, so c plus s is about c. The double arrow means, so this gives: s is approximately K s p over c; the wavy equals sign means approximately. Check at the end that s really is tiny. Got it? Now a salt A B two; the small two is an atom count. Say the common ion is A two plus, at c molar; s is tiny, so A two plus stays about c. Then B minus comes only from the salt: two s. So c times, two s whole squared, gives four s squared c, equals K s p. Right? And if the common ion is B minus, at c molar? Then A two plus is just s, B minus stays about c, and s equals K s p over c squared. With me? Now compare the two. Which common ion cuts the solubility more: A two plus, or B minus? B minus, yes! It is squared in K s p, so its c gets squared too. The ion that is squared has the larger effect. Clear?

3:00The effect of pH: hydroxides

Now the second half, the effect of p H, starting with a metal hydroxide: MOH two, with the O H in brackets taken twice. It gives one M two plus ion and two O H minus ions. Okay? From K s p, M two plus equals K s p over O H minus, squared. Now, if I lower the p H, what happens to the metal ion concentration? It goes up, exactly! Lower p H means fewer O H minus ions, and O H minus is squared in the bottom. So, at lower p H, more hydroxide dissolves. Got it?

3:36Salts of weak acids dissolve more in acid

Now take a salt M A, where H A is a weak acid. It gives M plus and A minus. In acid, H plus grabs the A minus to make H A, the weak acid, which hardly ionises; the two half arrows again mean equilibrium. So A minus keeps getting removed, and more salt dissolves. Okay? In one line: s squared equals K s p, times, one plus H plus over K a. K a, small a for acid, is the dissociation constant of H A, the weak acid. More H plus, a bigger bracket, a bigger s. Right? And when H plus is much greater than K a, the double greater than sign, the one hardly matters. Then s is about the square root of K s p times H plus, over K a. But only then; otherwise use the full formula. With me?

4:29Trap: which salt dissolves more in dilute HCl?

Now a trap. Calcium fluoride, C a F two, dissolves more in dilute hydrochloric acid than in water. So silver chloride will too, right? No, no, careful! F minus comes from H F, a weak acid, so H plus removes it as H F, and more calcium fluoride dissolves. Okay? But C l minus comes from H C l, a strong acid, so H plus does not remove it. For salts of strong acids, like silver chloride, p H hardly matters. Right? Worse, the acid brings its own chloride: a common ion! So silver chloride is even less soluble in dilute H C l than in water. Both halves of today's lesson, in one question. Clear?

5:15Example 1: solubility of AgCl in 0.10 M NaCl

Okay, Example one. Find the solubility of silver chloride, K s p one point eight times ten to the minus ten, in zero point one zero molar sodium chloride. Pause the video, and try it first. Done? Okay, let's check. Sodium chloride gives zero point one zero molar chloride. Silver chloride adds only s, which is tiny, so chloride is about zero point one zero. Right? So s equals K s p over c: one point eight times ten to the minus ten, over zero point one zero. That is one point eight times ten to the minus nine molar. Tiny next to zero point one zero, so our approximation holds. Very good! Now compare with pure water: s is the square root of K s p, about one point three times ten to the minus five molar. So in sodium chloride, the solubility is about seven thousand times less. Puzzle solved: the common chloride ion did it! Got it?

6:14Example 2: solubility of salt MA in a pH 3 buffer

Now a harder one. Salt M A has K s p one point zero times ten to the minus ten, and H A has K a one point zero times ten to the minus five. Find the solubility of M A in a buffer of p H three. Pause and try. Hint: the buffer fixes H plus. Done? M A is like silver chloride, so s is the square root of K s p: one point zero times ten to the minus five molar, right? No, no, careful! That is the answer in pure water. Here the buffer holds H plus at ten to the minus three molar. Over K a, ten to the minus five, that gives one hundred. Okay? Dissolved salt ends up as A minus or H A, so s is A minus plus H A, both together. And H A is one hundred times A minus. So s is one hundred and one times A minus. With me? Now K s p equals M plus times A minus. M plus is s, and A minus is s over one hundred and one; the dot means times. So s squared is one point zero one times ten to the minus eight. Right? Take the square root: s is one point zero times ten to the minus four molar. That is ten times the solubility in water. Clear?

7:31Quick revision: common ion, hydroxides, weak acid salts

So, quick revision. First, a common ion lowers the solubility: s is about K s p over c for an A B salt, and the squared ion matters most. Second, at lower p H, hydroxides dissolve more. Third, salts of weak acids dissolve more in acid, while salts of strong acids hardly change. Now go and try the practice problems on this page. You can do them, I promise. All the best!