Is this stoichiometric question answerable? (unknown variable)
This question kind of borders on the fields of both semantics and math, as well as chemistry, but I still believe this is the right place to ask.
On a test I took, a question was posed as such:
Via titration we are adding a solution of 25 ml, with 0.5 M NaOH, to 25 ml of HCl. What will the concentration of the acid be?
Now, this question seemed a bit strange to be, and it was definitely new. I'm used to calculating concentrations after dilution and other stoichiometric calculations, but this question seemed like a misworded version of those other questions I've grown familiar to.
So, I asked my teacher if she could clarify. First I asked whether the 25 ml of HCl was pure HCl, or a water solution with HCl in it. She said it was pure HCl. Then I asked if she was looking for the concentration of the acid before ANY reaction between the NaOH and the HCl had occured. To this, she also said yes.
The options were:
0.25 M
0.5 M
0.75 M
1 M
I answered 1 M, my reasoning being that 25 ml of HCl is the same volume as 25 ml of water with NaOH. Obviously, this reasoning is quite flawed, but I didn't have anything better. The answer was wrong. 870
However, when my teacher told me what was meant by the question afterwards, her explanation did not align with the question, nor her previous clarifications. She said that this was a simple case of:
$$C_1 \times V_1 = C_2 \times V_2$$
Where $C_2$ was the unknown, since the concentration of HCl was not specified. I don't see how this makes sense. All the question is saying, is that there is a 25 ml container, with HCl in it. It doesn't even say that this 25 ml consists of a water solution with HCl in it, but a more knowledgeable chemist would've known that HCl cannot exist outside of a water solution (that's what my teacher said at least).
Then the the question says that 25 ml of water, with a concentration of 0.5 M of NaOH is added. And from those two values, I'm supposed to find the concentration of HCl. That basically means:
$0.025$ l of H$_2$O$ \times 0.5$ M NaOH(aq) $= 0.025$ l of water $\times x$ M HCl (aq)
Which would then make the answer 0.5 M. Maybe she wanted me two add the two volumes, which would make sense:
$0.025$ l of H$_2$O$ \times 0.5$ M NaOH(aq) $= 0.05$ l of water $\times x$ M HCl (aq)
Which would then make the answer 0.025, which wasn't even an option.
But even if it was, it still wouldn't make sense to me. Just because you have a solution with a given volume and an unknown concentration, adding another solution with a known volume AND concentration won't just magically let you know what the unknown concentration in the original solution is, now in this new solution. Or am I wrong? 870