hey all welcome to home school and we are with class 11 chemistry series we are with the first chapter basic concepts of chemistry and this is the last session on a chapter we are with the last topic of the chapter that is reactions in solutions so our today's topic is reactions in solutions See guys, whichever the reaction we conduct in a chemical laboratory, we do it in the form of solution. Imagine when I mix two solids, does the reaction takes place? No. Those solids I must dissolve in some liquid. I should make a solution first.
Then in the solution form, when I add with one another, definitely you can expect a reaction taking place between them. Right. so that means whatever the solid chemical compounds we have if we have to perform a reaction with them first we need to convert them into solutions right say for example the moment i say i have taken nacl solution imagine this is your nacl solution do you have a complete idea about this solution See, can you be able to describe completely about NaCl solution? See, just it is not enough to say that it is NaCl solution.
You must also understand how much amount of NaCl solid dissolved in how much amount of water. Right? So, here how much NaCl you took?
And you dissolve it in how much amount of water? That is the most important information one must get to know about a solution. Okay, once you know this information about a solution, you can actually predict how much amount of product you are going to get when you perform a reaction of this solution with another solution.
Okay, so it's very important to understand everything about a particular solution. You will make a solution whenever some solid dissolved in a liquid. Okay. But you must also have an idea about how much amount of that solid dissolved in a particular solution.
Okay. Particular liquid. Now let us understand very basic things about solution. Okay. So the moment you say solution.
The moment you say solution, it is made up of two components. Okay, now this is a solution. What are the two components it has? One is NaCl.
This is our solid and this NaCl was dissolved in water. So these are the two components of NaCl solution. Okay, and here which is there in a smaller amount? NaCl would be there in a smaller amount.
Right? Then NaCl can be called as solute. And the one which is there in a larger amount is called as solvent. Okay?
So, when you take a solution, it will have two components. One is solute. The other one is solvent. Okay? So, what do you mean by a solute?
The component, the component present in smaller amount. present in small amount is called solute. And what is the solvent?
The component present in large amount. is called solvent. Okay.
So, here the one say for example NaCl solution you know you added a pinch of NaCl in large amount of water. Then which is the component present in a smaller amount? NaCl. So, it is called as a solute.
And which is the component present in a larger amount? Water. So, water is called as a solvent. Water is called as a solvent.
Okay. Say this is how we uh call about the solution i mean this is how we describe two components of a solution okay we call one component as solute the other component as solvent clear okay so now the amount of solute present in a particular solvent is expressed with the help of many terms. It's like if you want to know how much amount of NaCl present in how much amount of water.
So that is what we call concentration. Okay, identifying the amount of solute present in a particular given amount of solvent is what we call concentration. And this concentration can be expressed with the help of many terms.
Okay, so what I meant to tell you is amount of solute. Solute. That is one component. Amount of one component. Present.
Present. In. A given.
Amount. Of. Solvent. Solvent.
Is expressed. Is expressed. With the help of.
With the help of. Following terms. following terms.
Okay. So if you want to know how much amount of one component present in a given amount of another component is always expressed with the help of following terms. So what are those terms? The first one we call it as mass by mass percentage. okay, mass by mass percentage or just we say mass percent, mass percent.
So, this is one concentration term which can tell you how much amount of solute is present in how much amount of solvent, okay. And the second one is mole fraction. This is a very important term, mole fraction, right. Third one, Molarity, molarity, very very important and the next concentration term is molality.
So these are the four concentration terms we are going to study, clear? So these are collectively called as concentration terms. I can also call them as concentration terms. Why can I call as concentration terms? It is because with the help of these terms, we can say whether a solution is concentrated or not.
Okay. Or in other words, I can say how much amount of solute present in how much amount of solvent. So that is mainly expressed with the help of these terms.
Okay. You can identify The concentration of any solution with the help of these terms. And that is the reason we are calling these terms as concentration terms. Now let us discuss what do you mean by mass percentage, mole fraction, molarity and molality individually. See guys, first one I will go for mass by mass percentage.
M in the sense mass, mass by mass percentage. So what do you mean by this mass by mass percentage? it is nothing but mass of mass of solute solute present in present in 100 grams of solution 100 grams of solution is called as mass by mass percent okay say for example whenever i say about five percent n a c l Mass by mass percentage.
Okay. Say what is the meaning of this sentence? Meaning is very very important to understand.
So what do you mean by 5% mass by mass percent of NaCl? It means that it means it means say I am talking about meaning of this. It means 5 grams of NaCl present in present in 100 grams of solution that is the meaning okay 5 grams of NaCl present in 100 grams of solution okay say in 100 grams how much amount of solute is there that one can be expressed with the help of the concentration term mass by mass percentage Okay, see in 100 grams of solution if you take, in 100, in 100 grams of solution, you know actually you have 5 gram NaCl, 5 gram NaCl solid and remaining 95 grams water you have.
Okay, so in 100 grams of solution, how much of solute you have? 5 grams. And how much of solvent?
You will use a particular liquid to dissolve the 10 acl. So how much of liquid you took? It is 95 grams.
Okay, so it's in-depth meaning is very very important to understand. Clear? And you know mass percentage, see m by m percent can always calculated with the formula mass of solute, mass of solute divided by mass of solution into 100. Okay, so this is a formula that is used to calculate m by m percentage.
For example, I will have a problem here. Okay, so I am showing you a problem here. See, a solution is made, a solution is made by dissolving, by dissolving the solution. 2 grams of sugar in 18 grams of water. 18 grams of water.
And I'll ask you to calculate. Calculate. Mass of sugar. Calculate the mass of sugar. If this is the question, read carefully.
A solution is made by dissolving 2 gms of sugar in 18 gms of water. Calculate mass of sugar. So use this formula.
M by M percent of sugar is equal to mass of a solute which is a solute here. See the one which is there in a smaller amount is called solute. Say 2 gram is very small right.
So this is your solute. This is your solute and you know the one which is there in a larger amount is always called as a solvent. This is solvent. Okay. So what is our formula?
Mass of solute divided by mass of solution into 100. Mass of solute is how much? 2 grams. Mass of solution is how much? This is solvent.
Solution means what? Solution is equal to solute plus solvent. Solute plus solvent.
Isn't it? So, lieu to mass is 2 gram, solvent to mass is 18 gram. So, altogether 20 gram will be the mass of solution.
Isn't it? So, 2 gram divided by 20 gram into 100 you have to do. Right? So, 2 ones are, 2 tens are. So, you will have your answer 10 percent.
Okay. So what is the mass percent of sugar in that 100 grams of solution? It is 10 percent. It is 10 percent.
So this is how you can calculate mass percent, mass percent of any component present in a solution. Mass percent of any component present in a solution. Okay.
So this is all about mass percent. But understanding the meaning is very very important. okay where is it used it is usually used in the field of medicine if you see behind the syrup bottles or tablets you know in the ingredient column they would be using this say if you take a paracetamol if you take a paracetamol syrup syrup which we use it for small kids you know you read the ingredients behind it it will be written like this five percent mass by mass like this It means that 5% mass by mass paracetamol they will write. Paracetamol.
Right. It's a fever syrup. Isn't it? Fever syrup has paracetamol as the ingredient.
How much it is there? 5% M by M they have mentioned. So what is the meaning of this 5% M by M paracetamol? It means that 5 grams of paracetamol ingredient.
Paracetamol is present in 100 grams of solution. 100 grams of solution. Paracetamol is a solid.
So they took 5 grams of paracetamol and they dissolved in 95 grams of solvent. Altogether the solution has become 100 grams. right so this is the exact meaning say using this particular thing you can able to find out how much amount of ingredient is present in 100 grams of solution right so that is the importance of mass by mass percent so this is used in the field of medicine.
Okay. See when you look at the tablets or when you look at the syrup, mass by mass percent or another term you have volume by volume percent. Okay. This is also a very common concentration term. You considered mass similarly when you consider volume.
So, what is volume by volume percent? It is the volume of a solute present in 100 ml of a solution. Okay, so these are very frequently used to concentration terms in making tablets or syrups. Okay, so looking at this, you can understand how much amount of ingredient is present in 100 gram or 100 ml of a solution, right? So this is all about mass percent.
Now we will go for another concentration term that is mole fraction. See mole fraction is nothing but mole fraction. It is the ratio of number of moles of one component to the total moles of all components present in solution. present in solution is called mole fraction.
It is the ratio of number of moles of one component to the total moles of all components present in a solution. It means, it means, say for example, you have a solution, you have a solution, okay, containing a molecule. containing two components okay you have a solution containing two components like one is solute the other one is solvent okay two components component one and component two okay there are two components component one and component two solution means two components would be there solute and solvent right say if i have to know about the mole fraction of component one say mole fraction is indicated with the letter x okay fine okay let us call component one as solvent and component two as solute Right. Say if I have to calculate mole fraction of solvent then what is the formula I can use? It is the number of moles of solvent present in a solution divided by total moles.
How do you get total moles? It is the number of moles of solvent plus number of moles of solute. Isn't it?
So this is how I can calculate mole fraction of a solvent. Similarly, if I have to calculate mole fraction of solute, then what is the formula I can write? It is the number of moles of solute divided by number of moles of solute plus number of moles of solvent.
Right? So, these are the formulas I can use for calculating mole fraction of solute as well as mole fraction of solvent. Okay?
So, it is nothing but the ratio of number of moles of a component to the total moles present in a solution. How many total moles would be there? It is the moles of solute plus moles of solvent.
If you have a solution with two components, right? Okay. So, now let us understand this concept with the help of one numerical. Let's see one numerical, okay?
Say for example, let me have a question like this. a solution say for example you have 20 percent uh sugar solution 20 percent sugar solution is provided is provided okay so what is what is the mole fraction the mole fraction of Sugar. Okay.
You see here, it's very, very important to understand the question. See, what is the solution given for you? 20% sugar solution. 20% sugar solution means what?
20% sugar solution. Meaning I'm telling you. Okay.
20% sugar solution has 20 grams of sugar in it. Okay, dissolved in 80 grams of water, isn't it? So that is the meaning of 20% sugar solution, 20% M by M sugar solution. That means you have solute as sugar, how much?
20 grams and you have solvent as water. It is dissolved in water, right? How much water?
80 grams. Okay, so here you need to calculate mole fraction of sugar. so what is the formula to calculate mole fraction of sugar okay so this is what say i can instead of solute if i take if i have to calculate mole fraction of sugar sugar is nothing but glucose okay so here sugar is nothing but what glucose its formula is c6 h12 o6 okay say mole fraction of sugar or glucose if i have to calculate say what is the formula The formula is number of moles of glucose divided by number of moles of glucose plus number of moles of water.
Yes or no? So it is the number of moles of glucose to the total number of moles present in a solution. Total number of moles is number of moles of glucose plus number of moles of water. Okay. So this is the formula you have to apply.
This is the formula you have to apply. Okay. So now, do you have enough information to calculate?
Do you have number of moles of glucose directly given? No. Do you have number of moles of water directly given?
No. You have to calculate number of moles. Isn't it? So how do you calculate number of moles of glucose?
glucose. It is the formula you have, right? So, what is the formula to calculate number of moles? Formula is mass divided by molar mass. Mass divided by molar mass, right?
So, this is the formula you have to use to calculate number of moles. Mass divided by molar mass. So, now you calculate here mass of sugar is how much?
20 grams, right? Divided by molar mass of sugar is how much molar mass is 180 right so that is 12 into 6 plus 12 plus atomic mass of oxygen is 16 into 6 you have to do okay so you will get around 180 so 20 divided by 180 if you do how much do you get 0 0 cancel 1's are 9's are right so you will have 0.1 So now you can calculate number of moles of water. Number of moles of water.
Right. So same formula mass divided by molar mass. So what is the mass that we came to know here?
0.444. Right. So number of moles of glucose is 0.1.
Number of moles of water is 0.4. So, now substitute here. Mole fraction of glucose, they asked you.
Mole fraction of glucose is equal to number of moles of glucose divided by number of moles of glucose plus number of moles of water. Isn't it? So, now substitute.
How much do you get? Number of moles of glucose is 0.1 divided by 0.1 plus 0.4. Isn't it?
So, it is nothing but 0.1. divided by 0.5. So, almost how much do you get? 1 by 5. So, you would get around 0.2 something, right? So, 0.2.
So, mole fraction of glucose, mole fraction of glucose is 0.2, isn't it? Fine. So now if they have asked you to calculate mole fraction of water also.
Okay. Say mole fraction of water. Mole fraction of glucose is over 0.2 you got. If they had asked mole fraction of water what will you do?
You will calculate using this formula. Number of moles of water divided by number of moles of water plus number of moles of glucose. Right. So, number of moles of water is how much? 0.4 divided by number of moles of water 0.4, 0.1, isn't it?
So, it is 0.4, 0.5. So, you would get around how much? It is 4 divided by 5, that is 0.8, right? So, mole fraction of water is 0.8 and mole fraction of glucose is 0.2. clear everyone fine so this is the entire concept so this is how the question will not have number of moles directly given they will just mention 20 percent of this solution 20 percent of that solution etc and they'll ask you to calculate mole fraction of individual component so first from mass okay from mass you calculate moles then you substitute in a formula and you will get the answer right so this is one important model of question that can be asked on mole fraction clear and one more trick i will tell you here so try to remember sum of the mole fraction of all components present in a solution will be equal to one Okay, say you may have, there are two components in a solution, take it as A plus B, sum of the mole fractions of all components, you may have three components in a solution, you may have five components in a solution, whatever.
So sum of the mole fractions is always equal to 1. okay or say once you know the mole fraction of a if you want to find out mole fraction of b then we can always find out like this xb is equal to 1 minus xa if you do you will get the mole fraction of b see i said no here you consider A as glucose, B as water. I know mole fraction of glucose here 0.2. When I asked you to find out mole fraction of water, you used the formula, you substituted and calculated, right?
Instead of that, you can use this. right? So, xb that is mole fraction of water is equal to 1 minus mole fraction of glucose you can do.
So, that means 1 minus mole fraction of glucose, how much you got? 0.2. So, definitely you will get your answer as 0.8.
Much simple calculation compared to this, right? Once you know the mole fraction of any one component, then you can use this formula to calculate mole fraction of the other component. Okay, when you know mole fraction of one component, you can calculate mole fraction of other component using this formula, right?
So just you have to remember, sum of the mole fractions of all components in a solution is always equal to 1. Okay, so that's all about mole fraction. And mole fraction is unitless, it doesn't have any unit. Remember this point also.
Mole fraction is unitless because number of moles do not have any units. So that's why mole fraction is unitless. So these are some aspects you have to remember about mole fraction. And now let me go for another concentration term, molarity.
See next important concentration term is molarity. Okay, so this is the most important concentration term which we use it in chemical laboratories actually. That is molarity which is indicated with the letter capital M.
So what do you mean by this molarity? It's very simple. It is nothing but number of moles of solute. Solute dissolved in.
1 liter or 1 dm3 of solution is called molarity. So, you have 1 liter solution. In that 1 liter solution, the number of moles of solute can be expressed with the help of molarity. Okay, so now let us try to derive a formula for molarity. So based on the definition we can write molarity is equal to number of moles of solute that means the component which is present in a smaller quantity divided by volume of solution in liter.
Volume of solution in liter. Say in short, number of moles of a solute can be denoted as n divided by volume of a solution can be denoted as v. So, molarity is equal to n by v can be a formula for molarity. Okay, now let me talk about its units. Units is also very very important to understand.
So, what is the unit for moles? It is just moles we say. And units per volume is liter. Okay, moles per liter or moles per dm cube is the unit for molarity. Moles per liter or moles per dm cube.
Clear? Fine. And now we will elaborate this formula in a simple way to calculate the numericals.
Okay, see how I can write the formula. Number of moles of solute. We know the formula for number of moles, right? So number of moles is equal to mass divided by molar mass.
Mass divided by molar mass. So number of moles of solute is equal to mass of solute. Mass of solute divided by molar mass.
Of solute. Isn't it? Into 1 by V we can write. So just I elaborated number of moles into mass of solute divided by molar mass into 1 by V. Right?
And this volume it is given in liters. In case of ml. See volume most of the time it will be given in ml only in the question.
So your molarity is equal to 2 I can write mass of solute into 1000 divided by molecular mass of solute right into volume of solution in ml. Okay. So whenever volume is given in ml in the numerator you should add 1000. This is the conversion factor between volume from liter to ml. Okay. So this is our final formula that we get to use for calculating a numerical.
Now let us try to understand how we can do a numerical based on this particular formula. Look at the question here. Calculate the molarity of NaOH solution. NaOH solution prepared by dissolving 4 grams of NaOH to form 250 ml of solution, right?
So, what is given here? They have given mass of NaOH. So, how much is the mass of NaOH? 4 gram. And they also gave you volume of solution, right?
So how much is the volume of solution? It is 250 ml. Isn't it?
250 ml of solution. That means it's a volume of a solution. Mass of NaOH is there, volume of solution is there.
Asking you to calculate molarity of NaOH solution. So what is the formula? Mass of a solute here, which is a solute? NaOH is a solute.
Okay, water is a solvent. So mass of a solute into 1000. So let me substitute everything in a formula. Mass of a solute is how much?
4 into 1000 divided by molecular mass of a solute. Okay. NaOH. What is its molecular mass?
Na, atomic mass 23, oxygen 16 plus 1. Okay. So how much do you get? You will get around 40. Isn't it?
So 40 into what is the volume of a solution 250 okay see when to take this thousand when not to take this thousand is very very important you will take this thousand in the numerator when volume of a solution is given in ml okay if the volume is given in liter directly then you are not supposed to consider this thousand in the numerator you have to be careful with this thousand you Okay. So now we have substituted everything and how much do you get? You will get around 0.4 right moles per dm cube.
So unit of molarity is 0.4 moles per dm cube. Okay. So this is how the questions can be asked on molarity. Mass they will give right volume they will give molar mass they won't give molar mass formula will be given. molar mass you should calculate okay or you know sometimes molarity will be given volume is given they will ask you to calculate mass of a solute okay so here molarity will be given volume is given molar mass formula will be given they'll ask you to calculate mass okay so any one variable they'll ask you to calculate clear so this is one major concept that you have to remember on molarity And now coming to one more formula that is dilution formula.
We have something called dilution formula. okay so what do you mean by this dilution formula for example imagine you have a particular solution initially you have some solution imagine this is some hcl solution this is some hcl solution okay so this is solution this is solution number one okay its molarity is m1 Okay. And if you apply the formula M1 is equal to N1 by V1 I can write.
M1 is the molarity of this solution. N1 is number of moles of HCl present in this solution 1 and volume is volume of this solution 1. Okay. Now what I will do is I will add little amount of water to this.
Okay, so I will add some amount of water to your original solution, right? And now the solution will become, you know, volume will increase. It's not like the original solution, right? This has become the solution to now. Okay, the moment I add water to this solution, the same solution has converted into something else.
Solute is same. Here also HCL, here also HCL. Solute is same.
Just you added some amount of water. The moment you add. the water molarity changes to m2 okay number of moles let it be n2 and volume also changes you added extra water automatically volume changes let it be v2 okay so solution once molarity is m1 is equal to n1 by v1 solution 2's molarity is n2 by v2 okay and you see here molarity of this solution is different molarity of this solution is different because volume is changed But the number of moles will not change.
Say the number of moles of HCL, how many ever present in this state will remain same even after adding water. Number of moles will not change. Everything will change. Molarity will change because volume will change. You added water, no?
Volume changed. As volume changes, molarity changes. So these two factors will change.
But number of moles will not change. That means I can write n1 is equal to n2. I told you know number of moles will not change. So n1 is equal to n2. So here can I write m1 v1 is equal to n1.
Here also m2 v2 is equal to n2. So when I wrote n1 is equal to n2, can I write m1 v1 is equal to m2 v2? So this is what we call dilution formula.
So what is m1 here? It is the molarity of initial solution. What is v1? Volume of initial solution.
What is m2? Molarity of final solution after adding water. What is V2? Volume of final solution after adding water.
So this is what we call dilution formula. Clear? Fine. So this is the concept of molarity.
Now we will go for learning molality. See even molality is also very important concentration term. Molality. That was molarity.
R-I-T-Y. Here it is L-I-T-Y. Okay.
Molality is indicated with the letter small m. clear fine so listen to the definition carefully it is nothing but number of moles of solute of solute present in present in one kg of solvent one kg of solvent okay so this is called molality that was number of moles of solute present in one solution that was molarity. But here number of moles of solute present in 1 kg solvent. This is molality. Okay.
So here it is represented with small m I told you know. So what is the formula you can write? Number of moles of solute divided by mass of solvent, mass of solvent, isn't it? So, can I write number of moles as n divided by mass of solvent as m, okay, mass, mass of solvent, okay, in kg, mass of solvent in kg. So, this is the basic formula for molality.
If I have to elaborate this and write molality is equal to number of moles again you can write it as mass of solute. right? Divided by molar mass of solute, right? Into 1 by mass of solvent. If mass of solvent is given in grams, then in the numerator, you will add 1000, right?
So, this is our final formula to calculate molality of a solution. Okay? Fine. So what is the unit?
Unit is equal to moles per kg. So this is the unit of molality. Okay? Fine. And the major difference between mola Lity and molarity.
Molarity is what? Number of moles of a solute divided by volume of a solution. Molarity is what? Number of moles of a solute divided by mass of solvent.
Okay. See here, this molarity is there. No, this is temperature dependent.
This is temperature dependent. Clear everybody? It depends on temperature because we all know you must have heard about the Charles law in your basic classes right? See what the Charles law says that volume is always directly proportional to temperature okay.
So as the temperature increases expansion of a volume increases. Expansion of volume takes place. Volume expands. Temperature decreases. Volume decreases.
Okay, so it is, you know, volume is directly proportional to temperature. You see here, volume, our molarity is inversely proportional to volume, no? Molarity is inversely proportional to volume.
So what we can write here is, observe carefully the things I am writing. As temperature increases, what happens to the volume? Volume is directly proportional to temperature. So volume also increases. And what would happen for your molarity?
Molarity will decrease. Okay. So that means as temperature increases, your molarity decreases. So that's why I'm telling you molarity is a temperature dependent. Okay.
Whereas molarity, coming to a molarity, it is temperature. temperature independent it is temperature independent right that means it it do not do not depend on temperature it do not depend on temperature because there is no volume term in the molality right always mass mass mass everywhere mass mass doesn't depend on temperature okay mass remains constant whatever may be the variation in temperature mass remains constant okay Okay, clear. So molality is the best concentration term compared to molarity. Okay, so molarity is always more preferred concentration term compared to molarity.
Okay, I repeat once again molality, molality is more preferred, more preferred compared to molarity. Thank you. Compared to molarity.
Okay. Molarity. Because this molarity is temperature dependent.
Clear. Say for example. I will tell you one practical situation for you.
For example. Today you prepared 5 molar solution of NaOH. For the experiments that you are doing after 10 days. So today you are making arrangements of all solution. After 10 days you are going to use those solutions for your experiment.
So you prepared 5 molar solution. This much concentrated NaOH solution is necessary for your reaction. You prepared today and kept.
But after 10 days, the room temperature has changed. Say today the room temperature was around 28 degree centigrade. But suddenly summer started. After 10 days, your room temperature became 30 degree centigrade.
Will you have the concentration of solution as 5 molar? Or do you find variation in this 5 molar? Definitely. there is a variation in 5 molar.
Your molarity will get decreased. Yes or no? Say your 5 molar solution whatever you prepared 10 days before has now converted into 4 molar solution. Okay, molarity decreased because molarity involves volume, isn't it?
As temperature increases, volume increases, our molarity decreases. So volume is not remaining constant. Molarity is not remaining constant throughout the days.
It will depend on temperature. So whenever you are preparing concentration with the help of molarity, you should prepare freshly then and there before your experiment. You are not supposed to prepare and keep it.
for rest of the days right but molality is not like that today you prepared 5 molal solution today you prepared 5 molal solution after 10 days you come and check the concentration will be 5 molal only there is no change in the concentration okay because this does not depend on temperature whereas our molarity depends on temperature you Got to know? So practically speaking, which is the more preferable concentration term? Molarity is the more preferable concentration term compared to molarity. Clear? So this is all about the concentration terms.
so i gave you the basic introduction and the basic formulas on these concentration terms actually for the competitive examinations you must know many other relationships and many other ways of using these formulas okay so all of them also i will teach you which will come in the coming videos okay or let me finish all the basic aspects of all chapters and then i will start with the competitive aspects right but definitely within few days I will provide the competitive aspects of these concepts also like this is the basic thing first thing is you must know at least this basic about all the concentration terms next you have so many variations in the formula which we will use it for the competitive exams like NEET and JEE right so all of them also will be discussed but as of now as of NCIT textbook concerned our chapter that is basic concepts of chemistry is completed okay so i may come up with the competitive aspects of this or i may start a new chapter it depends on the uh you know demand okay so you can post it in a comment that whether you want uh competitive aspects or the different questions to be solved on this concept or to start with the next chapter depends on your opinion clear so please post it in a comment uh saying what you want in the next whether a new chapter or a few competitive questions on this particular topic fine so with this i will end this session we will meet up in the next video till then keep revising a concept take care and all the best