Indicate the concentration of each ion present in the solution formed by mixing (a) 42.0 mL of 0.170 M NaOH and 37.6 mL of 0.400 M NaOH. Assume that the volumes are additive.
Hey guys, so here we have to calculate the concentration of each ion given to us in the following mixture. So what we have here is, we have 42 mLs of 0.170 molar NaOH, and we also have 37.6mLs of 0.400 molar NaOH. Now remember the word of when it's between numbers it means multiply, and remember that molarity equals moles over litres. And realise that when you multiply both sides by litre, you will see that moles equals litres times molarity. So we're going to have to change these mLs into litres.
So we have 42 mLs, remember for every one milli- it's ten to the negative of 3, remember that molarity really means that number in moles divided by one litre. So litres can swap now we have moles. Now we need to figure out what the new concentration will be, because what we have here originally was 42 mLs, but those 42 mLs mixed with these 37.6 mLs. So we add those two numbers together to get our new concentration, our new volume, which is 79.6 mLs, and when we change that to litres, that gives me, 0.0796 litres. So I'm going to have a new concentration for NaOH, which is 0.08698 molar.
Now we're going to do the same thing with this. We're going to change this into litres, so remember again one milli- is ten to the negative 3 litres, again remember, molarity really means that number in moles divided by one litre. So here we're going to get 0.01504 moles of NaOH. Again, we're dividing it by the new total volume, which is 0.0796 litres. That gives me a molarity of 0.188945 molar of NaOH. Now realise that both of these are NaOH. So let's just add up their totals together. Since they're the same concentration we can add them. Together comes out as 0.278643 molar of NaOH. So now that we have the new total concentration we can figure out what the concentration of each ion is. Remember, molarity really means that number in moles over one litre. And we're going to say for every one mole for the entire compound, we have one mole of Na+ ion, because there's exactly one Na in the formula. So that gives me 0.278643 molar of Na+. And again we have the same concentration again and we have to figure out now the concentration of your hydroxide ion. So for every one mole of NaOH we have one more of Na+ so this comes out the same exact number. Here we're not worrying too much about sig figs, I'm just showing you the process that would take to find the answer.
So a lot of work had to be done, we had to find what the new moles would be, divided by the new total volume. Once we found the concentration of the compound, we could then figure out the concentration of each ion within that compound.