TBR GChem Buffers Question

[leathersofa]

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I do not understand what Choice C is even saying, and the answer explanation is still confusing. Would someone please explain choice C for me? Thank you!!
I understand why the answer is NOT A, B, or D. But I just do not get what C is even saying, thank you!

41. Even though the NaOH concentration in the third trial is 100 times greater than the NaOH concentration in the first trial, the two graphs follow a similar slope' This is BEST explained by which of the following statements?
Note: The first trial is 25 mL 0.01 M HCI titrated by 0.01 M NaOH
The third trial is 25 mL 1.00 M HCI titrated by 1.00 M NaOH

A. The solution is a buffered solution, so the pH change is minimal.
B. The NaOH is a weak base and does not fully react with the HCl.
C. The pH is a log scale, so as the pH increases up to 7.0, the amount of base necessary to increase the pH becomes less.
D. The pH changes only at the equivalence point.

Explanation: Choice C is the best answer, because the log scale means that as long as the concentrations are 100 times different, then the linear difference is 2.0 on the log scale. This in turn means that the slopes are equal through most of the titration, except near the equivalence point. Perhaps the answer would be better if it mentioned the different concentrations of the titrant bases in each trial. The best answer is not always perfect.

Thank you in advance 🙂

 

[eudovcic]

I'm not sure how to explain it all but I looked at this way: For purposes of simple math, in trial 2 pH=-log[10/25]=0.4. For trial 1 pH=-log[0.1/25]=2.4. Since each pH point corresponds to a 10 fold increase or decrease in acidity, by increasing concentration by 100 you changed pH by exactly 2. From that I figured the graph simply shifted but retained the same slope. If you play around with log functions in a graphing calculator it should show that -log(x) and -log(100x) are identical except for one is shifted 2 units up or down depending on how you compare them.

 

[FeinMS]

I do not understand what Choice C is even saying, and the answer explanation is still confusing. Would someone please explain choice C for me? Thank you!!
I understand why the answer is NOT A, B, or D. But I just do not get what C is even saying, thank you!

41. Even though the NaOH concentration in the third trial is 100 times greater than the NaOH concentration in the first trial, the two graphs follow a similar slope' This is BEST explained by which of the following statements?
Note: The first trial is 25 mL 0.01 M HCI titrated by 0.01 M NaOH
The third trial is 25 mL 1.00 M HCI titrated by 1.00 M NaOH

A. The solution is a buffered solution, so the pH change is minimal.
B. The NaOH is a weak base and does not fully react with the HCl.
C. The pH is a log scale, so as the pH increases up to 7.0, the amount of base necessary to increase the pH becomes less.
D. The pH changes only at the equivalence point.

Explanation: Choice C is the best answer, because the log scale means that as long as the concentrations are 100 times different, then the linear difference is 2.0 on the log scale. This in turn means that the slopes are equal through most of the titration, except near the equivalence point. Perhaps the answer would be better if it mentioned the different concentrations of the titrant bases in each trial. The best answer is not always perfect.

Thank you in advance 🙂

I would use POE. A is definitely not true because you need to titrate weak acid with strong base (or weak base with strong acid) to create a buffer. Strong vs Strong will not result in a buffer. B is definitely a no because NaOH is a strong base that fully react with HCl. Also HCl is a strong acid that fully reacts with even weak bases. D is false because pH does change at every point of titration (even in the buffer region although the change is really small)

It turns out that C actually is true. Say you have a 0.1M HCl, it's pH is 1 (-log(0.1)) If you repeat some simple math, you will see that at pH=2,3,4,5,6, the [H+]=0.01, 0.001, 0.0001, and so on. Each pH change reflects ten fold difference in [H+]. To change the [H+] from 0.1 to 0.01, you need 0.09 equivalence of base. To go from 0.01 to 0.001, you need 0.009 and so on. You can see that the required amount of base decreases as you approach pH7. (This is explained in TBR chapter though)

I don't know why this explains that the slope is similar though. I thought the same ratio of the concentration of acid/base would better explain the similarity in slope..

 

[leathersofa]

okay, i get what you mean by how the amount of base needed decreases as pH increases but i still don't get how that explains slope either.
does anyone understand the connection between this and the slope?