pH of Strong Acids, Strong Bases and their Mixtures

Transcript

0:00Introduction

Hello everyone! Okay, one small puzzle before we start. I take hydrochloric acid, and I dilute it a lot, down to ten to the minus eight molar. Put it in the formula: minus log of ten to the minus eight is eight. So, p H eight? But that is basic! An acid, giving a basic solution? Something is wrong here, right? Today we find the real answer. On the way, we learn the p H of strong acids, strong bases, and their mixtures. Questions on these come up often in JEE, so let's begin.

0:36Strong acids: count the protons

So, first, a quick recall from the last lesson. p H equals minus log of the H plus concentration, with log to the base ten. The square brackets mean concentration in moles per litre, and the small plus sign up top is a positive charge. Okay? Now, H C l, hydrochloric acid, is a strong acid: it ionises completely in water. So take c molar H C l. The capital M on screen means molar, moles per litre. Each molecule gives one H plus, so the H plus concentration is just c. Simple, right? Now, sulphuric acid, H two S O four. The small two and four are subscripts: two hydrogen atoms, four oxygen atoms. If I take c molar sulphuric acid, what is the H plus concentration? Two c, yes, exactly! Each molecule has two protons to give, so H plus is two times c. Writing just c here is a very common slip, so be careful. With me? But the second proton has its own constant, K a two. The subscript a two means the acid constant for the second proton, okay? Unless the question gives you K a two, JEE assumes both protons are fully released. So, two c. Clear?

1:52Strong bases: find pOH first

Now, bases. N a O H, sodium hydroxide, is a strong base. So c molar sodium hydroxide gives an O H minus concentration equal to c. The small minus sign up top is a negative charge. Okay? Next, barium hydroxide. On screen it is B a, then O H in brackets, with a subscript two outside. So, from c molar barium hydroxide, what is the O H minus concentration? Two c, correct! The two outside the brackets means two O H groups in each formula, so O H minus is two times c. Same for calcium hydroxide, C a, O H in brackets, two. Got it? Now, a trap. You have the O H minus concentration. So you take minus log of it, and that is the p H, right? No, no, careful! Minus log of the O H minus concentration gives p O H, not p H, okay? Then, to get p H, subtract p O H from fourteen. But this fourteen holds at two hundred ninety eight kelvin, that is twenty five degrees Celsius, where K w, the ionic product of water, is ten to the minus fourteen. At other temperatures, K w changes. Right?

3:04Mixing a strong acid with a strong base

Now the most common type of question: mixtures. First, count everything in millimoles. Millimoles equals molarity times the volume in millilitres; m L on screen means millilitres, and the cross is times. Okay? When they mix, H plus and O H minus react to make water. The arrow means react to give. So they cancel each other, one for one. With me? So, after mixing, which amount decides the p H? Yes, exactly! Only the excess, whatever is left over. Subtract the smaller from the bigger, then divide by the total volume; the line with two dots is the division sign. And total means both solutions added together, not just one of them. Clear? And if O H minus is left over, find p O H first, then subtract it from fourteen to get the p H, got it?

3:55Very dilute acids: water joins in

Now the last idea, and the key to our puzzle. Water itself gives a little H plus. But when c is about ten to the minus six molar or less, the acid's H plus is so small that water's own H plus starts to matter. The less than sign with a wavy line below means less than, or about equal to. Okay? So, let the total H plus concentration be x. The acid gave c of it, so water gave x minus c. And water gives H plus and O H minus in equal amounts. So the O H minus concentration is also x minus c. Right? Now, you know K w, the ionic product of water. So what equation do we get? Correct! H plus times O H minus equals K w. So, x times, x minus c, in brackets, equals K w. Solve this for x, and you have the H plus. Clear? And see the big result. However much you dilute an acid, its p H only comes closer to seven; it never goes above seven. An acid stays an acid. With me?

4:59Example 1: pH of an H2SO4 and NaOH mixture

Now, Example one. Twenty five millilitres of zero point one molar sulphuric acid is mixed with twenty five millilitres of zero point one molar sodium hydroxide. Find the p H of the mixture. You are given log five equals zero point seven zero. Pause the video, and try it first. Done? Okay, let's check. Same molarity, same volume. So they cancel exactly, and the p H is seven, right? No, no, careful! Sulphuric acid gives two protons. So H plus is two times zero point one, that is zero point two molar. Times twenty five millilitres: five point zero millimoles; m mol on screen means millimoles. Okay? O H minus: twenty five times zero point one, which is two point five millimoles. Right? So H plus is left over: five minus two point five, that is two point five millimoles. Total volume: twenty five plus twenty five, fifty millilitres. Two point five over fifty: zero point zero five molar. Got it? Now, p H is minus log of zero point zero five. Write it as five times ten to the minus two, so p H equals two minus log five. Two minus zero point seven zero: one point three zero. That's it!

6:22Example 2: pH of 10^-8 M HCl, and why it is not 8

Now, back to our opening puzzle, and this is the harder one. Find the p H of ten to the minus eight molar H C l. Pause the video and try it. Hint: think about the water. Done? Okay, let's check. Minus log of ten to the minus eight gives eight, a basic p H from an acid. Not possible! Here c is ten to the minus eight, far below ten to the minus six, so water's own H plus matters. Okay? So, use our equation. x times, x minus ten to the minus eight, equals K w, which is ten to the minus fourteen. Right? Open the bracket: x squared, minus ten to the minus eight times x, minus ten to the minus fourteen, equals zero. The small two on x means squared, so this is a quadratic. Clear? Solve it with the quadratic formula, and keep the positive root. x comes out as one point zero five times ten to the minus seven molar. Just a little more than ten to the minus seven. With me? So, p H equals six point nine eight. Just below seven, still acidic, exactly as an acid should be. Puzzle solved!

7:38Quick revision: strong acids, bases, mixtures, dilute acid

So, quick revision. Count the H plus or O H minus each formula gives: sulphuric acid and barium hydroxide give two c. For mixtures, subtract the millimoles, and divide the excess by the total volume. And for a very dilute acid, x times, x minus c, equals K w, and the p H stays below seven. Now go and try the practice problems on this page. You are ready for them now. All the best!