Mass Percent, Volume Percent and ppm

Transcript

0:00Introduction

Hello everyone! Here's one small puzzle before we start. There is a famous solution called normal saline, the salt water used in hospital drips. Its label says: zero point nine percent sodium chloride. Now tell me, zero point nine percent of what? Of the mass? Of the volume? Of the water? Honestly, most students have never even asked this question, right? By the end of this video, you will read that label like a chemist, and even find the molarity hidden inside it. And look, in JEE, every concentration problem starts with exactly this: knowing what goes on top, and what goes below. So, let's begin.

0:43Mass percent: the part over the whole

So, let's start with the simplest one. We dissolve a solute, call it B, in a solvent like water, and we get a solution, okay? Now, percent always means a part, divided by the whole, times a hundred. Here the part is the solute. But what is the whole? Yes, the whole solution! So, mass percent, written w slash w percent, equals m sub B, divided by m of the solution, times a hundred. The little B under the m just means the solute, so m sub B is the mass of the solute. Clear? And what is the mass of the solution? Simple: the mass of the solute, plus the mass of the solvent. Everything in the beaker, together. Look, this is the first JEE trap of today. Below the line, we always put the whole solution, never just the solvent. Many students divide by the mass of water alone, and lose an easy mark. Don't do that, got it?

1:42Volume percent and mass by volume percent

Alright, now what if we measure volumes instead of masses? Same idea. Volume percent, v slash v percent, equals V sub B, the volume of the solute, divided by the volume of the solution, times a hundred. And again, below the line goes the whole solution, okay? Now a strange one. What if we put a mass on top, and a volume below? Can we even do that? Absolutely, we can! This is mass by volume percent, w slash v percent. The mass of the solute in grams, divided by the volume of the solution in millilitres, times a hundred. But careful, the units are fixed here. Grams on top, millilitres below. Not kilograms, not litres, right? So what does it really mean? Take the volume of the solution as one hundred millilitres, and the percent is simply the grams of solute. So w slash v percent is the grams of solute in one hundred millilitres of solution. Clear? Hold on to this line; it will crack our saline puzzle.

2:45Parts per million (ppm)

Now, sometimes the solute is present in a really tiny amount. Then the mass percent comes out as a very small decimal, with lots of zeros after the point. Not nice, right? So what can we do? We multiply by a much bigger number. Parts per million, p p m, equals the mass of the solute, divided by the mass of the solution, times ten to the power six. Ten to the power six is one million, hence the name, okay? Look carefully: it is exactly mass percent, just times a million instead of times a hundred. So what does one p p m mean? One gram of solute in ten to the power six grams, that is one million grams, of solution. Really tiny, isn't it? So p p m turns such tiny amounts into easy numbers. Quick question. You may have heard that one p p m is one milligram per litre. Is that always true, for every solution? No, not always! For dilute solutions in water, one p p m is approximately one milligram per litre: the m g L to the power minus one on screen. See the wavy equals sign? It means approximately equal, not exactly. So use this shortcut only when both conditions hold: dilute, and in water. With me?

4:03Topper's trick: read the letters

Now let me share a trick that toppers use, so you never mix these up. In these labels, small w means mass, and small v means volume, okay? The first letter tells you how the solute is measured. And where does the solute always go? Yes, on top! The second letter tells you how the whole solution is measured. It goes below. So w slash v: the mass of the solute on top, the volume of the solution below. And v slash v? Volume on top, volume below. Read the letters, and the formula writes itself. That's it!

4:39Example 1: mass percent of NaCl in water

Right, time for the first example. Five grams of sodium chloride, NACL, is dissolved in forty five grams of water. Find the mass percent of sodium chloride. Pause the video, and try it first. Done? Okay, let's check. Five grams of salt, forty five grams of water. So, five over forty five, times a hundred, right? No, no, careful! That is the trap we just saw. Forty five grams is only the water. The whole solution is the salt plus the water. Five plus forty five: fifty grams. So, the mass percent is five over fifty, times a hundred. Ten percent. Exactly ten, not eleven point one, which is what the trap gives. Got it?

5:29Example 2: molarity of 0.9% w/v normal saline

Now a slightly harder one, JEE level, and it is our puzzle from the start. Normal saline is zero point nine percent, w slash v, sodium chloride. Find its molarity. Molarity means the moles of solute in one litre of solution; we will study it properly in a later video. Hint: first find the grams in one litre. Pause the video, and try it. Done? Okay, let's check. First, read the label with our trick. W slash v means the mass of the solute on top, and the volume of the solution below. So zero point nine percent means zero point nine grams of sodium chloride in one hundred millilitres of solution. Puzzle solved: the percent on that label is mass by volume! Now, many students rush here. Zero point nine grams, divided by the molar mass, and done, right? No, no! That gives the moles in one hundred millilitres, not in one litre. That answer comes out ten times too small. So, first go to one litre. One litre is one thousand millilitres, that is ten times one hundred. So multiply by ten: nine grams in one thousand millilitres. That is nine grams per litre, the g L to the power minus one on screen. Makes sense? Now, the molar mass of sodium chloride is fifty eight point five grams per mole, okay? So the moles in one litre are nine divided by fifty eight point five. Zero point one five four. So the molarity of normal saline is zero point one five four M, where the capital M on screen means moles per litre. See? From a hospital label, straight to a JEE answer. As simple as that!

7:17Quick revision: percent, w and v letters, ppm

So, quick revision. One: percent is always the solute, over the whole solution, times a hundred. Never the solvent alone. Two: read the letters, w for mass and v for volume. The first goes on top, the second goes below. Three: p p m is the same idea, times a million, and for dilute solutions in water, one p p m is about one milligram per litre. And remember our saline: zero point nine grams in one hundred millilitres. Now go and try the practice problems on this page. You will find them easy, I promise. All the best!