[cherryblossom]

Alright, I am absolutely horrible at chemistry, so please be gentle. I'm having problems with a word problem, and I think that what I need to do is find the proper chemical equation (the issue I'm having problems with) and solve mathematically from there.

The problem:

Hard water contains calcium, magnesium and iron (II) which interfere with the action of soap and leave an insoluble coating on the insides of popes and containers when heated. Water softeners replace these ions with sodium. If 1.0 x 10^3 L of hard water contains 0.010 M of calcium and 0.005 M of magnesium, how many moles of sodium are needed to replace these ions?

I feel dumb, because this is very basic chemistry, and I know I'm missing out on a basic assumption about the reaction, but I can't figure out what it is. My best guess would be the combination reaction of magnesium hydroxide plus sodium = sodium hydroxide plus magneisum? But that just seems horribly off the mark.

Anyway, any help or hints or suggestions about this problem would really make my day. Thank you!

[Schrödinger]

Ok, let me help you get through it step by step.

Step 1 : What are the valencies of Ca, Mg and Na ions? (i.e., what charge will each species bear when in ionic form?)

[cherryblossom]

Mg and Ca will be 2+ whereas Na will have a single positive charge.

[Schrödinger]

Yes correct. So, let us say we have to replace one Mg²⁺ ion. In order to maintain electrical neutrality, we will need 2 Na⁺ ions. Similarly so for Ca²⁺. That brings us to step 2 :
What is molarity? (rather, how do you calculate moles, given volume of solution and molarity?)

[cherryblossom]

We calculate moles via the ratio of the charges, so for every 1 mol of Ca+ and every 1 mol of Mg+ we need 2 mols of Na+.

I may be jumping the gun here, but is it really as simple as doubling the mols of Mg and Ca, adding and then you have the number of moles of sodium needed? Because I thought of that, and then thought it was far too simple and I must be skipping some vital clue about the reaction happening in water.

Although it would really plump up my ego if you told me my initial idea was correct.

[cherryblossom]

Wait! Those tricky litres! I have to multiply the moles by litres first, don't I?

[Schrödinger]

Considering the data given in the question, it really is as simple as doubling the moles of Ca and Mg and adding them (get moles of Ca and Mg using the formula for molarity). Your initial idea was correct
The 0.010 M and 0005 M refer to molarity. Not number of moles. So you do have to multiply molarity and litres to get number of moles.

[cherryblossom]

Oh my god! I am a chemistry genius and I didn't even know it! Thank you very much for your careful guidance!

[discodermolide]

Alright, I am absolutely horrible at chemistry, so please be gentle. I'm having problems with a word problem, and I think that what I need to do is find the proper chemical equation (the issue I'm having problems with) and solve mathematically from there.

The problem:

Hard water contains calcium, magnesium and iron (II) which interfere with the action of soap and leave an insoluble coating on the insides of popes and containers when heated. Water softeners replace these ions with sodium. If 1.0 x 10^3 L of hard water contains 0.010 M of calcium and 0.005 M of magnesium, how many moles of sodium are needed to replace these ions?

I feel dumb, because this is very basic chemistry, and I know I'm missing out on a basic assumption about the reaction, but I can't figure out what it is. My best guess would be the combination reaction of magnesium hydroxide plus sodium = sodium hydroxide plus magneisum? But that just seems horribly off the mark.

Anyway, any help or hints or suggestions about this problem would really make my day. Thank you!

You are not asked for the reaction only for the number of moles so the answer is really quite easy.
By the way I didn't know that "popes" were affected by hard water

[cherryblossom]

Absolutely! Kind of like the Wicked Witch of the West, except popes don't decompose if there aren't some minerals in that reaction.