Hard water often contains dissolved Ca²⁺ and Mg²⁺ ions. One way to soften water is to add phosphates. The phosphate ion forms insoluble precipitates with calcium and magnesium ions, removing them from solution. A solution is 0.050 M in calcium chloride and 0.085 M in magnesium nitrate. What mass of sodium phosphate would you add to 1.5 L of this solution to completely eliminate the hard water ions? Assume complete reaction.

Video transcript

Welcome back everyone. To another video, hard water often contains dissolved calcium and magnesium ions. One way to soften water is to add carbonates. The carbonate ion forms insoluble precipitates with calcium and magnesium ions removing them from the solution. The solution is 0.070 molar in calcium sulfate and 0.093 molar in magnesium chloride. What mass of sodium carbonate which you add to 2 L of the solution to completely eliminate the hard water ions assume a complete reaction. Therefore, answer choices. They're all given in grams. A is 56.2 B 12.1 C 27.8 and D 34.6. First of all, what we're going to do is just write down the reactions taking place or so calcium cion reacts with carbonate to form calcium carbonate. Now, for the second reaction, magnesium cion reacts with carbonate to produce magnesium carbonate. Those are 1 to 1 reactions. Notice that they are already balanced. What we want to do is just calculate the moles of each substance or basically each cion starting with calcium cion. Now, what do we have? Well, we have the molarity of calcium sulfate, which contains an equivalent molarity of calcium CS because calcium sulfate is cso four. So one mole of it contains one mole of calcium, two plus cion. And we can say that if we take the molarity of 0.070 molar and multiply by the volume of 2.0 L, this is how we get our most. So we can say that if we do the math here we get 0.1 of four moles. And now the number of moles of magnesium CS similarly, we have magnesium chloride, which is MGCL two, once again, 1 to 1 ratio, meaning the number of moles of magnesium chloride would be equal to the number of moles of magnesium cion. We take 0.093 molar multiplied by 2 L. And that would give us the number of moles of magnesium Canion. In this case, we get a zero point 186 moles. Let's not round it off two significant figures yet. What we simply want to understand is that the number of moles of carbonate in the first reaction would be equal to the number of moles of calcium CS. And same thing for the second reaction, meaning the total number of moles of carbonate would be equal to the sum of the moles that we have just found. So we're going to take 0.14 moles plus 0.186 mode. Now, if we actually want to turn this into mass, we know that this number of moles should be multiplied by the molar mass of sodium carbonate, which is 105.99 g per mole. Therefore, the final answer would be 34.6 g, right? So that would be the mass of carbonate or it would be more accurate to say that this will be the mass of sodium carbonate because this is our substance. So we're going to replace carbonate with sodium carbonate. And now we can clearly see that the correct answer choice is option D 34.6 g. That's our final answer. And thank you for watching.