Molarity and Molality

Transcript

0:00Introduction

Hello everyone! Now, one small puzzle before we start. Twenty grams of sodium hydroxide is dissolved in five hundred grams of water, and the solution measures five hundred ten millilitres. Ravi works out the concentration and gets one. Priya works with the same solution and gets zero point nine eight. And the teacher gives both of them full marks! So how can one solution have two different concentrations? By the end of this video, you will answer this yourself. And look, molarity and molality sound almost the same, so in JEE, examiners love to test whether you really know the difference. One small mix-up, and the marks are gone. So, let's begin.

0:43Molarity: moles per litre of solution

So, first question. When we say a solution is concentrated or dilute, what are we really measuring? We count the moles of solute, the substance we dissolve, okay? But moles per what? Per litre of water, or per litre of something else? Yes, per litre of the whole solution! That is molarity. Capital M equals n B divided by V of the solution, in litres. Here n B, with the little B, is the number of moles of solute, and V solution is the volume of the complete solution, solute and solvent together, not the solvent alone. Clear? So the unit of molarity is moles per litre. We usually write it with just the capital M you see on screen, and we read it as molar, okay? Now a topper's trick. In the lab, volumes usually come in millilitres. Instead of converting to litres every time, just multiply: millimoles equals M times V in millilitres. Molarity times millilitres gives you millimoles directly. No conversion, no mistake. Really simple.

1:49Molality: moles per kilogram of solvent

Alright, now its twin, molality. The top stays the same: n B, the moles of solute. Only the bottom changes. Small m equals n B divided by the mass of the solvent, in kilograms. See, capital M is molarity, and small m is molality. Don't mix them up! So its unit is moles per kilogram, and we write it with the small m you see on screen. One mole per kilogram is read as one molal, okay? Now tell me. Molarity used the whole solution. So molality also divides by the mass of the whole solution, right? No, no, careful! This is exactly where students lose marks in JEE, okay? Look at the two side by side. Molarity uses the volume of the solution, in litres. But molality uses the mass of the solvent only, in kilograms. Just the solvent, without the solute. Solution with molarity, solvent with molality. Write these two lines in your notebook. Got it?

2:52Which one changes with temperature?

Now for the trap that examiners love the most. Take a solution, and warm it up. Nothing is added, nothing is taken out. Does its molarity change? Does its molality change? Molarity changes! Why? Because the volume of the solution changes with temperature, the capital T on screen, okay? Same moles on top, a different volume at the bottom, so a different molarity. But molality does not change. Molality uses moles and the mass of the solvent, and there is no volume in it at all. The same is true for mole fraction and mass percent: none of them depends on temperature. So if a question asks which of these four depends on temperature, the answer is molarity, and only molarity. Those are guaranteed marks.

3:39Example 1: molarity of an NaOH solution

Okay, example one, an easy start. Four grams of sodium hydroxide is dissolved in water to make two hundred fifty millilitres of solution. Find the molarity. The molar mass of sodium hydroxide is forty. Pause the video, and try it first. Done? Okay, let's check. Step one: always moles first. Four grams divided by forty grams per mole: zero point one mole of sodium hydroxide. Now the volume is two hundred fifty millilitres. So the molarity is zero point one divided by two hundred fifty, right? No, no, careful! You will get a tiny answer, and it is wrong. Molarity needs litres. Two hundred fifty millilitres is zero point two five litre. Okay? Now divide. Zero point one by zero point two five is zero point four. So the molarity is zero point four moles per litre, which we read as zero point four molar. And let's check it with our topper's trick. Zero point four times two hundred fifty millilitres gives one hundred millimoles, and that is zero point one mole. Matches exactly!

4:52Example 2: molarity and molality of one NaOH solution

Perfect. Now a slightly harder one, JEE level, and this is our puzzle from the start. Twenty grams of sodium hydroxide in five hundred grams of water, and the volume of the solution is five hundred ten millilitres. Find the molarity and the molality, and explain why they differ. Pause the video, and try it. Done? Okay, let's check. Moles first, as always. Twenty divided by forty: zero point five mole. Now molarity. The question gives two numbers: five hundred grams, and five hundred ten millilitres. Which one goes at the bottom? Yes, the volume of the solution! Five hundred ten millilitres is zero point five one zero litre. Zero point five divided by zero point five one zero: zero point nine eight molar. And molality? Now we need the mass of the solvent, the water: five hundred grams, which is zero point five kilogram. Zero point five divided by zero point five: one point zero molal. And notice, we used only the five hundred grams of water, not water plus the twenty grams of sodium hydroxide. Solvent only, remember? So why are the two numbers different? Molarity counts per litre of solution, and molality counts per kilogram of water. One litre of this solution holds less than one kilogram of water, because the solute also takes up mass and volume, okay? So the two numbers come out close, but not equal. Now remember Ravi and Priya from the start? Ravi's one was the molality, and Priya's zero point nine eight was the molarity. Both were right. Mystery solved!

6:38Quick revision: molarity, molality and temperature

So, quick revision. Molarity: moles of solute per litre of solution. Molality: moles of solute per kilogram of solvent. And molarity changes with temperature, molality does not. Now go and try the practice problems on this page. You will find them easy, I promise. All the best!