Problem 62E

If 3.5 L of a 4.8 M SrCl2 solution is diluted to 45 L, what is the molarity of the diluted solution?

Solution: Here, we are going to calculate the molarity of the given solution. Also, we are going to calculate the number of moles of KBr present in 150 mL of a 0.112 M solution and volume in millilitres of a 6.1 M HCl solution needed to obtain 0.150 mol of HCl. Step1: Molarity is defined as the number of moles of the solute(Here Na CrO is th2solu4) in 1 litre of the solution. Mathematically, Number of moles of solute Molarity(M) = -------------------------------------- ------(1) Volume of solution in litres In order to calculate molarity of Na CrO2solu4on, we have to first calculate the number of moles of Na C2 di4olved in the solution. Number of moles can be calculated by the following mathematical formula: Mass of the solute Number of moles(n) = ------------------------ Molar mass of the solute. Step2: a) Now, molar mass of Na CrO = 2 X a4mic mass of Na) + (1 X atomic mass of Cr) + (4 X atomic mass of O) = (2x22.9897) + (1x51.9961) + (4x15.9994) = 45.9794 + 51.9961 + 63.9976 = 161.9731 g Therefore, number of moles of Na CrO = 12.5 / 161.9731 2 4 = 0.077 moles Now, Volume of the solution in litres = 750 mL / 1000 L = 0.750 L Putting these values in equation (1), we get, Molarity = 0.077 mol / 0.750 L = 0.103 M Thus, molarity of the solution is 0.103 M. Step3: b) Let us calculate the number of moles of 150 mL of a 0.112 M solution of KBr. Number of moles of KBr Molarity = ---------------------------------- KBr Volume of solution in litres Therefore, number of moles of KBr = Volume of solution in L X Molarity KBr = (150 / 1000 L) X 0.112 M = 0.150 L X 0.112 M = 0.0168 moles Thus, the number of moles of KBr is 0.0168 mol. Step4: c) Given, molarity of the HCL solution = 6.1 M and Number of moles of HCl = 0.150 mol From equation (1), Number of moles of HCl Molarity = ---------------------------------- HCl Volume of solution in litres Therefore, Volume of the solution in litres = number of moles of HCl / Molarity HCl = 0.150 moles / 6.1 M = 0.0246 L = 0.0246 X 1000 mL = 24.6 mL Thus, the required volume of HCl is 24.6 mL. ------------