 Today, we will learn numericals to calculate molecular weight of a given polymer from a topic polymers. This is the learning outcome for today's session. At the end of this session, students will be able to define polymer, degree of polymerization and by applying the knowledge of degree of polymerization, how to calculate molecular weight of a given polymer by making use of two methods such as degree of polymerization and molecular weight by number average molecular weight method. This is the content we are going to learn in this particular session. First we will learn the definition of polymer, degree of polymerization and then we will see how to calculate degree of polymerization and how to calculate molecular weight of polymer. So the first question is that what are polymers? Polymer is a material which consists of several time repetition of the same molecule. Polymers are organic, high molecular weight materials. Polymers are mainly used to prepare different types of plastic. Polymers are of both types that is natural and synthetic. Therefore, the material used to obtain polymer is known as monomer. Some of the examples of the polymeric material are polystyrene, polyvinyl chloride, bacrylate resin, nylon, etc. So what are polymers? Polymers are the high molecular weight material which shows several time repetition of the same molecule. So the monomer is a single molecule which on repetition forms polymer and these are known as polymers which are used to prepare plastic. Now what do you mean by degree of polymerization? If we want to calculate the molecular weight of a non-polymeric molecule it is very easy to calculate. But it is very difficult to calculate molecular weight of a polymer and therefore the degree of polymerization concept we have to learn before going to calculate molecular weight of a polymer. So it is degree of polymerization that is DP. Degree of polymerization indicates the average number of monomer that is repeatedly present in a molecule of polymer. So it is average number which is repeatedly present in a molecule of the polymer. Degree of polymerization can be controlled during the reaction itself by adjusting concentration of monomer, catalyst, temperature etc. Generally polymer with low degree of polymerization exists in the form of liquid state and with moderate degree of polymerization the polymer exists in viscous state whereas the polymer with more degree of polymerization exists in solid state. Therefore degree of polymerization should be more for better durability and quality which is denoted by the small n. So degree of polymerization indicates what is the average number of monomer that is repeatedly present in a molecule of the polymer and which can be controlled during the preparation itself whereas it is expected that in a good polymer the degree of polymerization should be higher for the better durability and quality. Now what is molecular weight of polymer? Generally molecular weight of a molecule is calculated by doing the sum of atomic weights of all the atoms present in that molecule. So it is known as a routine method to calculate molecular weight of any molecule. So what we are doing in case of calculating the molecular weight of any molecule just we are doing the sum of atomic weights of the atoms present in that molecule. It is a routine method but that routine method is not applicable for polymer to calculate molecular weight. So molecular weight of a polymer cannot be calculated by this routine method because in a given polymer the repetition of a monomer is not defined because it depends upon various external conditions that is the concentration of monomer, temperature, catalyst, duration of the reaction etc. Therefore in the same example of a preparation we may get the different polymers with a different molecular weight. Therefore molecular weight of a polymer can be calculated by applying the concept of degree of polymerization and number average molecular weight method. Now we will apply the knowledge of degree of polymerization and number average molecular weight here. So this is the first numerical, ethylene on polymerization forms polyethylene with degree of polymerization 450 calculate its molecular weight. So what is the example given ethylene it is a monomer on polymerization forms polyethylene and particularly for this example the degree of polymerization is given that is 450 it means that in this particular example the average number of monomer that is repeatedly present is 450 calculate its molecular weight. So what is the formula for this one? So we know that degree of polymerization is indicated by small n. So n is equal to m upon m0 where n is degree of polymerization, m molecular weight of polymer, m0 that is molecular weight of monomer. So we can easily calculate the molecular weight of monomer by routine method and for given example it is 28 it is given here. But we have been asked to calculate molecular weight so the modified equation becomes m is equal to degree of polymerization multiplied by the molecular weight of monomer. So for this given example the value of the degree of polymerization is 450 so it is multiplied by the 28 that is a molecular weight of the monomer that is ethylene and the answer is 12600. So this is the molecular weight of ethylene to polyethylene. Now here I would like to ask you one question. Styrene that is one of the monomer on polymerization forms polystyrene with a molecular weight of 18000, its degree of polymerization is dash dash dash. Option A 173.07, option B 273.07, option C 373.07 and option D all of these. Think for a moment and the correct option is that option A 173.07. So how the answer we got this 173.07 because we know the standard formula that is n is equal to m upon m o. So we have been asked to calculate n, m is given what is the m value they have given that is 18000 and what is the value of m 0 that is 104. So 18000 divided by 104 the answer is 173.07. So the correct option is option A 173.07. Now this is one more numerical, this is one more numerical that is vinyl chloride on polymerization forms polyvinyl chloride with a molecular weight of 17500 gram. Calculate its degree of polymerization. So we know the formula n is equal to m upon m o where n is degree of polymerization, m is molecular weight of polymer and m o is molecular weight of monomer. So for a given example the weight of the monomer that is vinyl chloride is 65. So by putting the value we are getting the answer for degree of polymerization for this particular example that is 269.23. So these two numericals we have made a practice on how to calculate degree of polymerization if a molecular weight of a polymer is given or how to calculate molecular weight of a polymer if the degree of polymerization is given. Now this is the second type of the numerical. So what is the numerical? A polymer is obtained which consists of 100 molecules with molecular weight of 1000, 200 molecules with molecular weight of 2000, 300 molecules with molecular weight of 3000. Calculate molecular weight of polymer by number average method. So this is an example where after polymerization we got 3 varieties of molecules of the polymer that is 100 molecules with 1000 weight, 200 molecules with 2000 as a molecular weight and 300 molecules with 3000 as a molecular weight. So the formula is that m bar n is equal to summation of ni mi upon summation of ni. So it is ni n1 plus n2 plus n3 plus that is number of molecules mi is m1 plus m2 plus m3 plus again continued and that is nothing but the molecular weight of the first type of the molecule, molecular weight of the second type of the molecule and so on. So by putting the value what answer we got here that is m bar n is equal to 2333.33. So it is one of the method how to calculate molecular weight of a polymer if the different varieties of molecules we have with their corresponding molecular weight that is m bar n. So one more numerical we will do here as a practice. A polymer is obtained which consists of 150 molecules with molecular weight of 1500, 250 molecules with molecular weight of 2500, 350 molecules with molecular weight of 3500 calculate molecular weight of polymer by number average method. So we know the formula m bar n is equal to summation of ni mi upon summation of ni. So by putting the value what answer we get here that is 2766.66 because we have three types of the molecule 150 with the molecular weight 1500, 250 with the molecular weight 2500, 350 molecules with the molecular weight of 3500. So by putting the value we get the answer 2766.66. So all this I have prepared by referring a textbook of engineering chemistry written by Jain and Jain. Thank you.