Ion concentration in acid and base

Question

Hello here is a question that is a bit confusing I hope you can help me solve it and understand it:

Determine the hydronium and hydroxide ion concentrations in a solution that is $10^{-4} M \ce{Ca(OH)2} \text{ AND } 10^{-4} M \ce{HCl}$

Note: the "and" is actually capitalised in my book..

So what I understood from this question is that they are both in one solution. Now I thought of two ways to solve it: A) the concentrations are equal and they are both strong which means they we're neutralise each other completely and end up being a neutral solution and both $\ce{H3O+}$ and $\ce{OH-}$ will be $10^{-7}$.

B) the calcium base has 2 $\ce{OH-}$ while HCl has 1 H+ so the base concentration is double that of the acid which means that the solution is going to be basic but I don't know how can I solve this to find the actual concentrations.

Which way is right and when does an acid and base really react to become neutral?

Answer 1

Your second (B) way of thinking is correct.

In the solution there are twice as many OH- ions as H+ ions.

All the H+ from HCL will react with half the OH- from calcium hydroxide.

Half the OH- will remain ($10^{-4} OH-).

Then use $K_w$ to determine the final concentration of H+.