What volumes of solutions A and B were mixed together to form the final solution in the following case?
Two solutions (A and B) are mixed together, solution A contains 0.200 M CaCl2 and solution B contains 0.300 M NaCl. The final volume of the combined solution is 90.0 mL, the total concentration of Cl- is 0.330 M.
Solution A is a solution of CaCl2 and solution B that is made by dissolving NaCl in water are mixed together to create a solution. The volume of the solution created is 90 mL. Let the volume of solution A used be X mL, the volume of solution B used is 90 - X mL.
As solution A has 0.2 M of CaCl2, and each atom of CaCl2 gives 2 ions of Cl-, the concentration of Cl- ions is 0.4 M. The number of moles of Cl- ions in X mL of the solution is 0.4*X/1000
Solution B is made of NaCl and has a molarity of 0.3 As each atom of NaCl gives one ion of Cl-, the molarity of Cl- ions is 0.3 In 90 - X mL of solution B there are 0.3(90 - X)/1000 moles.
In the mixture of solutions the molarity of Cl- ions is (0.4*X/1000 + 0.3(90 - X)/1000)/(90/1000) = 0.33
=> .4X + 27 - .3X = .9*33
=> .1*X = 2.7
=> X = 27
The volume of solution A used is 27 mL and the volume of solution B used is 63 mL