 Myself, Dr. Sanjay Sarsamkar, working as an assistant professor in the Department of Humanities and Sciences, Walchand Institute of Technology, Sulapur. With this session, we are going to solve some numericals based on hardness of water. So, at the end of this session, student will be able to calculate the temporary, permanent and total hardness of water. So, content of this lecture that is introduction and formula to be used for calculation of hardness of water. So, water which does not produce lather with soap solution readily, but forms a white curdy precipitate is called as hard water. Hard water when treated with soap does not produce lather, but on the other hand forms a white precipitate. This precipitate is formed due to the formation of insoluble soaps of calcium and magnesium. Types of hardness? First, temporary or carbonate hardness, which is caused by the presence of dissolved bicarbonates of calcium, magnesium and other heavy metals and the carbonates of iron. Temporary hardness is mostly destroyed by boiling of water. Permanent hardness or non-carbonate hardness, it is due to the presence of chloride, sulphates of calcium, magnesium, iron, etc. in water. Unlike temporary hardness, permanent hardness is not destroyed by boiling. So, we have to calculate total hardness of water. For this, the hardness produced by each and every compound, which is producing hardness in water, we have to calculate. For this formula to be used is hardness produced due to salt is equal to weight of hardness producing substance into molecular weight of calcium carbonate, which is always 100 and molecular weight of hardness producing substance. First numerical, a sample of water on analysis was found to contain the following impurities in milligrams per liter. Calculate temporary permanent and total hardness of water. Calcium bicarbonate 10 milligrams per liter, magnesium bicarbonate 8.5, calcium sulphate 10.5 and magnesium sulphate 14 milligrams per liter, their molecular weight, these are also given. So, we have to use the same formula that is hardness produced due to each and every salt is equal to weight of hardness producing substance into molecular weight of calcium carbonate and divided by molecular weight of hardness producing substance. So, by putting the values of this weight of hardness producing substance and molecular weight as well as the molecular weight of calcium carbonate, which is always 100, we can calculate the hardness produced. So, in this case of calcium bicarbonate, so 10 into 100 upon 162, the answer is 6.17 milligrams per liter. Similarly, for magnesium bicarbonate by putting the values that is 8.5 into 100 upon 146, the answer is 5.8 milligrams per liter. Well, as the calcium and magnesium bicarbonate produces temporary hardness, hence temporary hardness is some of the hardness produced by calcium bicarbonate and magnesium bicarbonate, so the answer for this is 11.99 milligrams per liter. Now, we can calculate permanent hardness. Hardness produced due to calcium sulphate by putting the values of the same, it is 10.5 into 100 upon 136. The final answer for this is 7.72 milligrams per liter. Magnesium sulphate, its hardness is 14 into 100 upon 120. By calculation, we are getting the hardness that is 11.66 milligrams per liter. As calcium and magnesium sulphates are producing permanent hardness, so permanent hardness is equal to hardness produced by calcium sulphate plus magnesium sulphate, so by putting the answers over here, we are getting the final answer that is 19.38 milligrams per liter. So, the total hardness in this case is temporary plus permanent hardness, it is 11.19 plus 19.38, it gives 30.57 milligrams per liter. Second, a sample of water on analysis was found to contains the following impurities in milligrams per liter. Calculate temporary permanent and total hardness of water in milligrams per liter. Impurities, calcium bicarbonate amount 119, magnesium bicarbonate 81, calcium chloride 33, magnesium sulphate 25 milligrams per liter. So, by putting the values of given contents that is amount as well as their molecular weight, we can calculate the hardness. So, hardness produced due to calcium bicarbonate is 119 into 100 upon 162, answer is 73.45 milligrams per liter. Similarly, for magnesium bicarbonate, the answer is 55.47 milligram per liter by putting all these values in equation. So, temporary hardness produced due to calcium and magnesium bicarbonate is 73.45 plus 55.47 milligram per liter, it is 128.92 milligrams per liter. In this particular case of calcium chloride, again by putting the values amount and molecular weight, we can calculate the hardness produced due to calcium chloride, it is 29.72 milligrams per liter. Hardness produced due to magnesium sulphate that is 25 into 100 upon 120, the answer for this is 20.83 milligrams per liter. So, permanent hardness in this particular case is permanent hardness produced due to calcium chloride plus magnesium sulphate, it is 29.72 plus 20.83 milligrams per liter. So, the permanent hardness is 50.55 milligrams per liter. Overall, the total hardness is 179.47 milligrams per liter. Well, at this juncture pause the video and answer this question. Water or analysis was found to contain following impurities in milligrams per liter. Calcium sulphate 42 milligrams per liter, calcium chloride 51 milligrams per liter with their respective molecular weights. The temporary and permanent hardness of water respectively is A 0 and 63.58 milligram per liter, B 63.58 and 0 milligram per liter, C 0 and 58.63 milligram per liter and D 58.63 and 0 milligrams per liter. Well, the answer is A 0 and 63.58 milligrams per liter. Next numerical, a sample of water analysis was found to contain the following impurities in milligrams per liter. Calculate temporary permanent and total hardness of water in milligrams per liter. Calcium bicarbonate 173, magnesium bicarbonate 129, calcium sulphate 68, magnesium chloride 37 milligrams per liter. So, by following the same procedure, we can calculate hardness produced due to each of these compound present. So, hardness produced due to calcium bicarbonate is 173 into 100 upon 162, it is 106.79 milligrams per liter. Hardness produced due to magnesium bicarbonate is 129 and 100 divided by 146. So, the answer is 88.35 milligrams per liter. So, the temporary hardness is 106.79 plus 88.35 milligrams per liter, it is equal to 195.14 milligrams per liter. Then, hardness produced due to calcium sulphate is equal to 68 into 100 upon 136, that gives us 50 milligrams per liter. Whereas, in case of magnesium chloride, it is 37 into 100 upon 95, it gives 38.94 milligrams per liter. So, permanent hardness in this case is 50 plus 38.94 milligrams per liter, it is equal to 88.94 milligrams per liter. So, total hardness in this particular case is, we can calculate, we are getting the final answer, that is 284.08 milligrams per liter. Well, for this, I have used a reference, that is a textbook of engineering chemistry by Jane and Jane. Thank you.