 Myself, Dr. Nitin Gramopadhyay, from Department of Basic Sciences and Humanities, Walton Institute of Technology, Solapur, today we are going to learn a topic polymer and from that particular topic we are going to learn a problem solving section. Therefore, we are going to learn how to calculate the molecular weight of a given sample of polymer. This is the learning outcome of the today's session. At the end of this session, students are able to describe the terms such as polymer, degree of polymerization, molecular weight and the second objective outcome of the today's session is calculate molecular weight of a polymer by using concept of molecular weight. So, we will start with the today's content. First, we will see the definition such as polymer, degree of polymerization, molecular weight that is number average molecular weight and then we will learn how to calculate the molecular weight of a given polymer. What do you mean by polymer? Polymer is the term indicates many molecules are joined together. These are the macro molecules with high molecular weight. Polymers are used to prepare different varieties of plastics that can be used in domestic, agriculture, industry, transportation, construction, medicine, etcetera. So, polymers are nothing but a macro molecules which are formed by linking together a several molecules. Polymer is obtained from a single molecule which is known as monomer. Polymer may exist in the form of solid, liquid or semi-solid. Polymers with specific properties are converted into plastic by using different molding methods. Now, what do you mean by degree of polymerization? Degree of polymerization into bracket dp is the average number of monomer that is repeatedly present in a molecule of polymer. What is degree of polymerization? It indicates the average number of monomer that is repeatedly present in a molecule. For example, we are using the 100 molecules of ethylene and we are getting from ethylene to polyethylene as a polymer. But, out of 100, how many have joined together to form a polyethylene that number is called as the degree of polymerization. For example, we will assume that in 95 molecules have joined together. So, in a given example, 95 is a degree of polymerization for a given polyethylene example. Now, degree of polymerization of a polymer is directly proportional to its molecular weight. Therefore, more degree of polymerization, higher is the molecular weight of a polymer and vice versa. If the dp is low, then the molecular weight is also lower one. Degree of polymerization is the concept that decides the molecular weight of a polymer. Polymer with low degree of polymerization exists in liquid state. With moderate degree of polymerization, it exists in semi-solid state and with high degree of polymerization, it exists in solid state. Degree of polymerization of a polymer can be controlled by adjusting concentration of monomer, reaction temperature, catalyst, duration of reaction, etc. So, degree of polymerization can be controlled. We have to decide how many time the molecule should get repeatedly present in a molecule of the polymer and that can be adjusted by adjusting the monomer concentration, by adjusting the reaction temperature, by selecting a proper catalyst or by adjusting the duration of the chemical reaction, because everywhere the high degree of polymerization is not expected. Then we can prepare the polymer with low dp, polymer with moderate dp or polymer with the high dp. Now, number average molecular weight method. Just now we have learned that what are polymers. Polymers are the organic and macromolecules. These are obtained by repeated of the monomer present in a molecule. Therefore, always these are high in molecular weight and we know that how to calculate the molecular weight of any material which is not polymer, because it is a routine method. How we are calculating? The routine method is that we are doing the sum of atomic weights of the atoms present in a molecule. For example, if we take the example as magnesium sulphate as a molecule, mg its weight is 24, sulphur its weight is 32 and oxygen is 16 multiplied by 4 that becomes 64 and the total sum of such atomic weight is that 120. So, the molecular weight of magnesium sulphate is 120. It is easy to calculate, but if you take the example such as ethylene to polyethylene, we cannot calculate the molecular weight of polyethylene by simple method of making the sum of atomic weights of the atoms present in a molecule. Because if you take the example of ethylene, what is its structure? CH2 double bond CH2. The same molecule is coming into polyethylene, CH2 single bond CH2, simple but the question is that how many time the structure has repeated and therefore by routine method we cannot calculate its molecular weight. Therefore, the reason for this is that the repetition of a monomer in a molecule of polymer is not constant, but it gets changed with respect to the reaction condition. Molecular weight of any polymer can be calculated by using the concept of degree of polymerization, weight average method, viscosity average method and number average method. These are the sum of the possible method where we are using to calculate the molecular weight of a given polymer. Number average molecular weight method of determination of polymer is the total mass of all the molecules in a polymer sample divided by the total number of molecules present in that. What is its formula? M bar N is equal to summation of Ni, Mi divided by summation of Ni, where M bar N indicates the number average molecular weight of a polymer and what is Ni? That is number of molecules of corresponding mass Mi. So, Ni is nothing but N1, N2, N3, N4, etc. N1 is the first type of the molecule, N2 is the second type of molecule, N3 is the third type of molecule, M1 is a molecular weight of the first type of the molecule, M2 is a molecular weight of second type of the molecule, M3 is a molecular weight of third type of the molecule. That is in short it is expressed as M bar N is equal to summation of Ni Mi divided by summation of Ni. Now, here I would like to ask you one question polymer with high degree of polymerization exists in the form of think for a moment we will come with answer and the correct answer is that the solid when the degree of polymerization is more it exists as solid when it is low it exists as liquid and when it is moderate it exists as semi solid. Now, we will apply the knowledge to learn the problem solving it is a problem one. A polymer is obtained which consists of 100 molecules with 1000 as molecular weight, 150 molecules with 100 and 1500 as molecular weight and 200 molecules with 2000 as molecular weight. Calculate molecular weight of a given polymer by using number average molecular weight method. Now, what is the given data if you look to the numerical statement it consists of three types of the molecule. Therefore, I will write N1 its number is 100, N2 that is the second type its number is 150, N3 its number is 200. Now, what is the weight of the first type of the molecule that is M1 1000, what is the weight of the second type of the molecule that is M2 that is 1500, what is the molecular weight of the third type of the molecule that is M3 that is 2000. Now, we know the formula M bar N is equal to summation of Ni Mi divided by summation of Ni where Ni is equal to number of molecules of mass Mi. So, if you see here the first is 100 multiplied by its molecular weight 1000 plus the second is number 150 its molecular weight is 1500 plus the third number is 200 its molecular weight is 2000 and divided by only summation of Ni. So, here we will do the sum of 100 plus 150 plus 200. So, by solving this step we will come to the answer that is 1611.11 is the molecular weight that is average molecular weight for a given example. Just now we have learnt it is very difficult to calculate the molecular weight of a given polymer by a routine method, but one of the method is the number average and by knowing the number average method for the given example we got the answer for a given example of polymer the average weight molecular weight of that particular polymer is 1611.11. We will see one more it is a second, but in the same way here in this example what it consists polymer 110 molecules with 1700 as molecular weight 185 molecules with 1800 as molecular weight and 230 molecules with 2500 as molecular weight calculate molecular weight of a given polymer. Again in the same way what is the first number N110 its molecular weight is 1700 what is the second molecule number that is N285 its molecular weight is 1800 now what is the third type of the molecule N3 number that is 230 and its molecular weight is 2500. So, by putting all these values in a particular formula that is M bar N is equal to summation of Ni Mi divided by summation of Mi. So, in this example also what is N110 what is its molecular weight 1700 plus because summation of Ni Mi it is a first molecule now what is second N2 its number is 185 its molecular weight is 1800 it is N2 now what about N3 its number is 230 and its molecular weight is 2500 divided by summation of only number that is Ni. So, N1 plus N2 plus N3 that is 110 plus 185 plus 230. So, by solving this step we come to the answer that is 2085.71 therefore, molecular weight of a given polymer is 2085.71.