[Phoebe]

Hello

I'm working through a multiple choice question where I'm asked:

"If 0.2 M HCl is added to an equal volume of 0.4 M NaOH, what are the new concentrations of OH^- and H₃O⁺?"

My working out is:

C2 = C1 x V1 / V2

HCl C2 = 0.2 x 1/2
           = 0.1

NaOH C2 = 0.4 x 1/2
              = 0.2

So because OH^- and H₃O⁺ neutralise each other somewhat but not completely - the new OH^- concentration is 0.1 M

and because [H₃O⁺] [OH^-] = Kw =10-14

to work out the new H₃0⁺ concentration:

10-14 / 0.1 = 1x 10-13     

(apologies, I'm not sure how to superscript the larger numbers -13 and -14 etc)

So by my working out:
[OH^-] = 0.1
and [H₃O⁺] = 1 x 10-13


However, the options I'm given to choose between are:

a. [H₃O⁺] = 0.2 M, [OH^-]= 0.4 M

b. [H₃O⁺] =0.1 M, [OH^-]= 0.2 M

c. [H₃O⁺] = 2.5 x 10-14 M, [OH^-]= 0.4 M

d. [H₃O⁺] = 1.0 x 10-15 M, [OH^-]= 0.1 M

e. [H₃O⁺] =5.0 x 10-14, [OH^-]= 0.2 M


I think the correct answer is d. but I'm totally thrown by the power -15?

Again - sorry about the lack of superscript for the larger numbers, I hope it's legible.

Does anyone see where I've erred?

Thanks in advance

[mjc123]

The power -15 must be a typo for -13. As you say, [H₃O⁺][OH^-] = 10^-14. a and b are obviously wrong; c, d and e have (or should have) the right product, but are seeing if you have worked out [OH^-] correctly.

BTW, when you are writing a post, look at the buttons and symbols above the text window. Use the "sup" button to write superscript figures.

[Phoebe]

 Thank you for taking a look! I'm reassured you also think it's odd.
 
 I might email the tutor and see if there's been a mistake.

 Thanks for the sub button tip too

[Phoebe]

 Hmm, I emailed my tutor and she double checked and said that there isn't an issue with the correct answer.

 So, the options are:

 a. [H3O+] = 0.2 M, [OH-]= 0.4 M

 b. [H3O+] =0.1 M, [OH-]= 0.2 M

 c. 2.5 x 10^-14 M, [OH-]= 0.4 M

 d. [H3O+] = 1.0 x 10^-15 M, [OH-]= 0.1 M
 
 e. [H3O+] =5.0 x 10^-14, [OH-]= 0.2 M


 Is there any circumstance in which ^-15 could be correct?

[mjc123]

No. Perhaps your tutor thinks e is the correct answer, forgetting about the dilution?
Books can make mistakes. Tutors can make mistakes. Even I make the occasional mistake, believe it or not!

[Phoebe]

 Haha, thank you for your help - it's much appreciated!

 Ah Chemistry, so mysterious.

[Phoebe]

 Update: I've just had it pointed out to me that the correct answer is probably b. -they were probably only
 looking for me to solve for c1v1=c2v2

 It is very like me to overcomplicate things, thank you mjc123 for all your input

 

[Borek]

Well, as you already know, b is completely wrong and can be rejected even without knowing the data given in the question.

[mjc123]

But they are not going to sit there without reacting. Of course, working out the concentrations immediately after mixing (as you did) is an important part of correctly working out the concentrations after reaction. (Theoretically, anyway; practically you won't be able to mix them faster than the reaction occurs.) But if that was what was wanted, it should have been clearly stated.

[Phoebe]

I agree, it's a poorly constructed question. I wasted a lot of time trying to figure out what I'd done wrong.

But if d. isn't a typo, b. is really the only contender left.

It's a disappointing result. I am -however- very grateful for everyone's input.

[AWK]

If this problem

"If 0.2 M HCl is added to an equal volume of 0.4 M NaOH, what are the new concentrations of OH^- and H₃O⁺?"

has valid numbers, then your answer

So by my working out:
[OH^-] = 0.1
and [H₃O⁺] = 1 x 10^-13

is correct.
So there is no possible answer to choose from or one answer missing:
f. None of the above