Question 49

[McatCrusher]

I guessed this question right but i can not underestand why [H+]=[OH-]. Could you please explain how i should get to this answer?

[Dr. Ferdinand]

There are 3 things you need to know about the equivalence point for the MCAT (CHM 6.9 in The Gold Standard):

1) Definition: the equivalence point is defined as the point at which equal quantities of opposite solutions (reactants) exist to cancel each other out. For example 0.8 mol HCl and 0.8 mol NaOH.

2) An indicator is chosen so that its pKa is close to the pH of the equivalence point.

3) The equivalence point on a titration curve is the point of inflection (the point at which the graph's curve appears to change direction).

Of course, this particular problem is solved with knowledge of the definition.

[emory71632]

Via the ionization constant of water K(w)=[H+][OH-]=1x10^-14, it is clear that for [H+] and [OH-] to be equal, [H+]=[OH-]=1x10^-7. This condition necessitates a neutral solution, and a pH of 7.

Therefore, it seems that there is no correct answer listed to this question. Indeed, in a titration between equivalent amounts of a strong acid and a strong base, [H+]=[OH-] (at least approximately). However, this is not at all the case when titrations are performed involving weak acids and/or bases. This is immediately evident from the fact that the equivalence points of such titrations generally do not occur at a pH of 7 due to a difference in relative strengths of the weak acids and bases.

For example, when titrating acetic acid (a weak acid) with NaOH (a strong base), the equivalence point is above pH7 because equimolar concentrations of the two substances in solution create an alkaline solution due to the fact that the base is stronger than the acid (i.e. the base dissociates more heavily than the acid, creating an excess of OH- ions in solution).

[admin]

Interesting discussion but I believe that the answer given is the best answer.

Let's first be clear on the definition of "Equivalence point": it is often defined as the point during a titration when there are equal moles of acid and base.

references:

http://everything2.com/index.pl?node_id=806249
http://chemistry.about.com/od/acidsbases/a/aa082304a.htm

Now let's deal with the second related issue which is making you uncomfortable about the above: if the number of equivalents of acid and base are equal (= equivalent = equivalence point) then how could the equivalence point ever truly be above or below neutrality (ie. pH = 7)?

The reason: side reactions, further hydrolysis. Equivalence point of the titration refers to equal acid and base equivalents in the initial part of the reaction: the titration. However, in the end, if a side reaction occurs creating even less than 1 / 10 million (an incredibly small number) of moles per liter of OH or H then the pH will be other than 7.

Example:

http://antoine.frostburg.edu/chem/senese/101/acidbase/faq/equivalence-point-HF-NaOH.shtml

Please note: the calculation of an equivalence point as shown in the reference above is for your interest only and is unlikely to be on the real MCAT. They may go with the definition, as in this question, or show a titration curve (s) to see if you understand where the equivalence point should be depending on if it is a strong/weak acid/base.

Second Example: weak acid/strong base, for example: HOAc (acetic acid) and NaOH. Again, at the equivalence point of the titration: [H] = [OH], but now what happens?

Well, this is what we have in solution: H and OH (which are equal) plus lots of water plus sodium (a spectator ion) and finally the acetate anion: OAc-. Here is the issue: acetic acid is a weak acid meaning that it prefers to hang on to protons rather than give them up. So the acetate anion mops up the free protons recreating acetic acid and thus leaving a net OH- meaning a pH over 7. None of this changes the definition of the equivalence point of the titration.

[emory71632]

The equivalence point is where there are equal molar concentrations of acid and base: agreed. However, if the base is stronger than the acid, then it will be more heavily dissociated, and there will be an excess of OH- ions in solution. Thus, by logic, [H+] will not equal [OH-]. In fact, they can only be equal when [H+] and [OH-] are both 1x10^-7, as can be seen by the negative logarithmic restatement of the ionization constant of water, which reads pH + pOH =14. We can see that pH and pOH must both be 7 to be equal, with 7 being the negative log of 10^-7, the concentration of each ion.



In reference to your argument:

Quote:
"So the acetate anion mops up the free protons recreating acetic acid and thus leaving a net OH- meaning a pH over 7. None of this changes the definition of the equivalence point of the titration."


You're right, it doesn't change the definition of the equivalence point, but as you can see, if pH is above 7, then by pH + pOH = 14, pOH must be below 7, and since pH and pOH are merely the negative logarithms of [H+] and [OH-] respectively, this requires that the two are in fact unequal.

[admin]

I am certain that you will do extremely well on MCAT PS.

On this particular question, A/B/D are clearly wrong. C pertains to the definition of equivalence point though side reactions or very small differences in ionization (especially in comparison to the other answer choices) will indeed create imbalances. It's not a perfect answer but it is the best answer. It is normal to have 1 or 2 such questions on the real MCAT (they may or may not choose to count it; they admit to putting test questions on the real exam). Our only objective is to get you ready for the real thing.

[bravozullu4764]

emory71632
was totally right. The equivalence point is the point at which all of the moles of the original acid (HA) are eatup up by the titrant. The [H+] may or may not equal [OH-] at the equivalence point, it just depends on the HA in question.

Admin: please revise this, and please admit that this is a bad question. There would never be any such thing like this on the real MCAT. There may be tricky questions on the MCAT, but there would never be something as erronious as this.

[msamadia]

In simple terms I was looking at this question...

a titration is just a base and acid reacting with each other. Equivalence (equal amnt) and see acid as H+ and base as OH-.

The answer is straightforward in my opinion. Still think it should be kept and not revised.

[tjk447963]

I have a question not related to the above discussion. I thought that pH = pka in a titration half way to the equivalence point. Therefore, I am a little confused as to why the passage says that the pka of the indicator should be near the pH of the solution at the equivalence point (rather than half equivalence point)?

Can someone explain this?

[emilie.maz5603]

Correct at one-half the equivalence point, the amount of base is exactly one-half the initial amount of acid (strong or weak acids). Moreover, the base converts exactly half of an acid say HNO2 into its conjugate base form (NO2-), resulting in equal amounts of an acid and its conjugate and therefore as per the Henderson-Hasselbalch equation, pH = pKa + log [base]/[acid], and therefore the pH = pKa.

The pKa of the indicator should be near the pH at the equivalence point because it is after the equivalence point that the pH drastically changes say for a strong acid strong base titration, the pH at the equivalence point is usually of a pH = 7.00. However, the pH changes after the equivalence point and in a titration we are using the indicator to see a color change and so we are not using the analyte itself or say the acid itself that is being titrated.

So essentially, the pKa of the indicator (not the acid or base) has to be close to the equivalence point of the acid-base titration as that is where the actual concentrations of H+ and OH- changes in the acid base solution mixture so then the indicator will change color dependant on the equivalence point of the acid-base titration. So, the pKa OF THE INDICATOR should be near the pH of the SOLUTION AT THE SOLUTIONS EQUIVALENCE POINT. In fact the most effective indicators are within +/- 2 pH points of their pKa.