Hardness of Water

Transcript

0:00Introduction

Hello everyone! Okay, one small puzzle before we start. Here is a water sample. Its only hardness salt is magnesium sulfate, sixty milligrams in every litre. No calcium salt at all, okay? And yet, the lab report says: hardness, fifty PPM, as calcium carbonate. Calcium carbonate? Where did that come from? And why fifty, when we put in sixty? Strange, right? By the end of this video, you will solve this in three short lines. And look, hardness questions in JEE quietly test your moles and your equivalents together. So, let's begin.

0:39What makes water hard, and how we measure it

So, first question. When we say water is hard, what is actually inside it? Which ions are responsible? Yes, calcium and magnesium! Salts of calcium ions and magnesium ions make water hard, okay? On screen, the little two plus on each one is its charge. Remember that two; it will matter very soon. But look, here is the problem. One sample has calcium chloride, another has magnesium sulfate, a third has both. Different salts, different molar masses. So how do you compare them fairly? We need one common unit; the double arrow on screen means so. Just like you convert every currency into rupees before comparing prices, right? And chemists chose calcium carbonate as that common unit. Whatever calcium or magnesium salt is present, we ask: how much calcium carbonate is it equivalent to? So, hardness is the mass of calcium carbonate, in milligrams, equivalent to those salts, in one litre of water. Notice the word equivalent. Not equal in grams; equivalent. Keep that word in mind. Clear? Now, why do we call it PPM, parts per million? One litre of water is about ten to the power six milligrams; the wavy equals sign on screen means about, okay? So milligrams per litre is roughly milligrams per million milligrams, and that is parts per million. Really neat.

2:09Why 50? The equivalent mass of CaCO3

Alright, now where does that number fifty come from? Remember from earlier in this chapter: for a salt, the n factor is its total positive charge. So tell me, what is the n factor of calcium carbonate? Two, exactly! One calcium ion, with a charge of two plus. And M, the molar mass of calcium carbonate, is one hundred, okay? So E, the equivalent mass of calcium carbonate, is one hundred divided by two, that is fifty. Fifty milligrams in every milliequivalent. Got it? And this gives us the key result of today. One milliequivalent of hardness in a litre of water means fifty milligrams of calcium carbonate per litre. So, fifty PPM, okay? Write this down. Now, the topper's way to use it. Calcium and magnesium ions both carry a charge of two, right? So one millimole of either one is two milliequivalents. Two times fifty is one hundred. So: millimoles per litre times one hundred, or milliequivalents per litre times fifty. Same answer, two roads.

3:18The three-step method, and two traps

Okay, here is the full method, in three steps. Step one: take the milligrams of the salt in one litre, and divide by M, its molar mass. The arrow means that gives you millimoles, okay? Step two: each calcium ion or magnesium ion is equivalent to one calcium carbonate, because they all carry the same charge of two. The three lines on screen mean equivalent to. So millimoles of these ions equal millimoles of calcium carbonate. Step three: millimoles of calcium carbonate per litre, times one hundred, gives milligrams per litre. And that is your hardness in PPM, directly. That's it, three steps. Now, the first trap. One litre of water has one hundred and eleven milligrams of calcium chloride. So the hardness is one hundred and eleven PPM, right? No, no, careful! Hardness is never the mass of the salt itself. It is the mass of calcium carbonate it is equivalent to. Calcium chloride has a molar mass of one hundred and eleven, so one hundred and eleven milligrams of it is one millimole. One millimole of calcium carbonate is one hundred milligrams. So the hardness is one hundred, not one hundred and eleven. Got it? And the second trap: mixing up the two numbers. Fifty goes with milliequivalents, and one hundred goes with millimoles, okay? Multiply millimoles by fifty, and you get exactly half the right answer. And that half value is a very tempting wrong option in the exam.

4:54Example 1: hardness from 60 mg of MgSO4 per litre

So, remember our puzzle from the start? Let's solve it now. One litre of water contains sixty milligrams of magnesium sulfate, molar mass one hundred and twenty. Find its hardness. Pause the video, and try it first. Done? Okay, let's check. Step one: sixty divided by one hundred and twenty is zero point five millimoles of magnesium sulfate. So, zero point five millimoles of magnesium ions. Now, some students multiply zero point five by fifty and write twenty five PPM, okay? Is that correct? No! That is trap number two. Zero point five is in millimoles, not milliequivalents. Each magnesium ion is equivalent to one calcium carbonate, so we have zero point five millimoles of calcium carbonate. Times its molar mass, one hundred: fifty milligrams, in one litre. So the hardness is fifty PPM, okay? Quick check with equivalents: zero point five millimoles with charge two is one milliequivalent, and one times fifty is fifty. Perfect match. And there you go, puzzle solved! No calcium carbonate was ever in that water. It is only the unit we report hardness in. That is why sixty milligrams of magnesium sulfate shows up as fifty, not sixty.

6:18Example 2: washing soda to soften 1000 L of hard water

Now a slightly harder one, JEE level. What mass of washing soda, taken as anhydrous sodium carbonate, is needed to soften one thousand litres of water of hardness one hundred PPM? Pause and try. Hint: first find the total calcium carbonate in the whole tank. Done? Okay, let's check. One hundred PPM means one hundred milligrams of calcium carbonate in every litre, okay? And we have one thousand litres. So one hundred times one thousand: one hundred thousand milligrams, which is one hundred grams. And one hundred grams of calcium carbonate is exactly one mole. Nice round number, right? Now, how does washing soda remove this hardness? Its carbonate ion pairs with the calcium ion: calcium ion plus carbonate ion gives calcium carbonate. One to one, okay? So one mole of hardness needs one mole of carbonate. So, one hundred grams of washing soda, right? Careful! That is the trap here. We match moles, not grams. We need one mole of sodium carbonate. And the molar mass of sodium carbonate? Two times twenty three, plus twelve, plus forty eight: one hundred and six. So one mole of it is one hundred and six grams. So, one hundred and six grams of washing soda softens the whole thousand litre tank. Want to check with equivalents? One hundred grams of calcium carbonate, divided by fifty, is two equivalents. Sodium carbonate also has an n factor of two, so its equivalent mass is one hundred and six by two, fifty three. And two times fifty three is one hundred and six again. Exactly the same. See how fast that was?

8:07Quick revision: ppm as CaCO3, 100 per mmol, 50 per meq

So, quick revision. Hardness is the milligrams of calcium carbonate equivalent, per litre, and that is PPM, okay? One millimole of calcium or magnesium ions per litre is one hundred PPM, and one milliequivalent is fifty. And for softening, match the moles: one carbonate for one calcium. Now go and try the practice problems on this page. You will find them easy, I promise. All the best!