The Ionic Product of Water and the pH Scale

Transcript

0:00Introduction

Hello everyone! Okay, one small puzzle before we start. Take pure water, nothing added, and boil it. At a hundred degrees Celsius, its p H is about six point one. And p H below seven means acidic, right? So is boiling water acidic? Same water, just hotter! Today, we find out. In JEE, p H questions come up often, and they start from today's idea: K w and the p H scale. So, let's begin.

0:32Water ionises, just a little

So, even pure water ionises, just slightly. Two H two O, giving H three O plus and O H minus. The small numbers are subscripts, the little plus and minus are the charges, and the two half arrows mean the reaction is reversible. With me? For short, we write H three O plus simply as H plus. Multiply the two concentrations, and you get K w, the ionic product of water: capital K, small w for water. The square brackets mean concentration, in moles per litre. K w is one point zero times ten to the minus fourteen, at two hundred and ninety eight kelvin, that is twenty five degrees Celsius. This value holds only at that fixed temperature. Okay? In pure water, every ionisation gives one H plus and one O H minus, so the two are equal. Their product is ten to the minus fourteen. So what is each one? Ten to the minus seven, yes, exactly! The capital M means molar, that is, moles per litre. So in pure water, both are ten to the minus seven molar. Right? Now, water itself is about fifty five point five molar. So the degree of ionisation, ten to the minus seven over fifty five point five, is only one point eight times ten to the minus nine: fewer than two molecules in every billion! Clear?

1:55The pH scale

Powers of ten are messy, so we use the p H scale. p H equals minus log of the H plus concentration, with the log to base ten. Here is the scale on screen, running from zero to fourteen. Got it? Quick question. Pure water at two hundred and ninety eight kelvin has H plus at ten to the minus seven molar. What is its p H? Seven, correct! Look, pure water sits right at seven on the scale. In the same way, p O H equals minus log of the O H minus concentration. Okay? Take minus log of the K w equation: p K w equals p H plus p O H, which is fourteen at two hundred and ninety eight kelvin. So the small p just means minus log. Right? Now the words. Acidic means more H plus than O H minus; this sign is greater than. With me? Neutral means the two are equal, and basic means less H plus than O H minus; this sign is less than. On the scale, the reddish left end is acidic, like gastric juice and lemon juice. The dark blue right end is basic, like milk of magnesia and ammonia solution. Rain water sits a little below seven, and blood a little above it. The wavy equals sign on the labels means approximately. Clear?

3:17One pH unit is ten times

Now, a trap. One solution has p H three, another has p H six. Three is half of six, so the p H three solution has twice as much H plus, right? No, no, careful! p H is a log scale. One p H unit is a tenfold change in the H plus concentration. Got it? So three units apart means ten to the power six minus three, which is one thousand. One thousand times more H plus at p H three, not two times! Okay?

3:48Temperature changes Kw

Now, what if we heat the water? Breaking water into ions takes in heat, so the ionisation is endothermic. Remember the last chapter: for an endothermic reaction, what happens to the equilibrium constant on heating? It goes up, yes, exactly! So K w increases with T, the temperature. Right? At three hundred and seventy three kelvin, that is a hundred degrees Celsius, K w is about five point five times ten to the minus thirteen. Bigger, just as we expected. With me? So there is more H plus, and the p H of pure water drops to about six point one. Our boiling water from the start! So, p H below seven: is boiling water acidic? No! It is still neutral. Pure water gives one H plus for every O H minus, so the two are still equal, and that is what neutral means. Puzzle solved! Clear? So here is the JEE trap. p H seven means neutral only at two hundred and ninety eight kelvin. At other temperatures, neutral water has a different p H value. Got it?

4:58Example 1: pH and OH- when H+ is 3.0 x 10^-4 M

Now, example one. The H plus concentration of a solution is three point zero times ten to the minus four molar. Find its p H, and its O H minus concentration, at two hundred and ninety eight kelvin. Pause the video, and try it first. Done? Okay, let's check. First, a topper's habit: estimate. Ten to the minus four molar gives p H four, and we have three times more H plus. So is our p H more than four, or less than four? Less than four, exactly! More H plus means a lower p H value. Now, minus log of three point zero times ten to the minus four is four minus log three. Right? Log three is zero point four seven seven, so the p H is three point five two. Below four, as predicted. Okay? Now O H minus: at two hundred and ninety eight kelvin, it is K w over the H plus concentration. Ten to the minus fourteen over three point zero times ten to the minus four: three point three times ten to the minus eleven molar. Tiny, as it should be for an acidic solution. Clear?

6:10Example 2: is pH 6.5 acidic, neutral or basic at 373 K

Now a harder one, back to boiling water. At three hundred and seventy three kelvin, K w is five point five times ten to the minus thirteen. We have a solution at this temperature with p H six point five. Is it acidic, neutral, or basic? Pause and try it. Hint: find the neutral p H first. Alright. p H six point five is below seven, so the solution is acidic, right? No, no, wait! That is the trap. Seven is neutral only at two hundred and ninety eight kelvin. Neutral means H plus equals O H minus, so p H equals p O H, and each is one half of p K w. With me? Now, p K w is minus log of five point five times ten to the minus thirteen, which is twelve point two six. Right? So the neutral p H here is half of twelve point two six: six point one three. The same six point one we saw for boiling pure water. Okay? Now compare. Ours is six point five; neutral is six point one three. Higher p H means less H plus. So which side is our solution on? Basic, yes, perfect! Six point five is greater than six point one three, so the solution is slightly basic, even though its p H is below seven. Clear?

7:32Quick revision: Kw, pH + pOH = 14 and neutral pH

So, quick revision. K w is ten to the minus fourteen at two hundred and ninety eight kelvin, and it increases with temperature. p H is minus log of the H plus concentration, p H plus p O H is fourteen there, and one p H unit is a tenfold change. And neutral means H plus equals O H minus: that is p H seven only at two hundred and ninety eight kelvin. Now go and try the practice problems on this page. You will find them easy, I promise. All the best!