Solving for pH: when to use pH equation vs. Ksp

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orangeblue

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12) What would be the pH of a 1.0 M solution of the unknown salt hydroxide given that the metal is monovalent?

11
8.0
7.5
13.0
INCORRECT:
Your Answer: D I did pOH = -log [1] =0 so picked 13. This is wrong b.c 1 M is the molarity, I need to get the mL or L to know the [OH-] concentration correct?

Correct Answer: A



Using Kb = ([X+][OH-])/[XOH]; X is most probably a Group I metal since no decomposition occurred (P3, L3-4), implying that the anion (OH-) and cation (X+) are of comparable size (P2, L1-4).
Assuming that [X+] = [OH-] approximately

Kb = [OH-]2/[XOH], where XOH approximates 1.0 M at equilibrium, thus:

1.0 x 10-6 = [OH-]2/1

[OH-]2 = 1.0 x 10-6

[OH-] = 1.0 x 10-3 mol dm-3

pOH = -log[OH-] = -log(1.0 x 10-3) = -(-3) = 3

Using pH + pOH = 14, we get:

pH = 14 - pOH = 14 - 3 = 11

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Kb = [OH-]2/[XOH], where XOH approximates 1.0 M at equilibrium, thus:

That's the step that looks really fishy to me. If it's NaOH or KOH then a 1M solution is not going to have a 1M concentration of the undissociated molecule.

That approximation is used for things like, say, acetic acid that have a Ka on the range of 10^-5
 
That's the step that looks really fishy to me. If it's NaOH or KOH then a 1M solution is not going to have a 1M concentration of the undissociated molecule.

That approximation is used for things like, say, acetic acid that have a Ka on the range of 10^-5
so how are you supposed to solve this because i also picked 13
 
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If it is a strong base, then you should do:

pOH = -log(1) = 0
pH + pOH = 14
pH = 0 + 14
pH = 14

So even using this method, you would not get pH =13.

Although perhaps some salt hydroxides aren't strong bases? I'm not sure.
 
If it is a strong base, then you should do:

pOH = -log(1) = 0
pH + pOH = 14
pH = 0 + 14
pH = 14

So even using this method, you would not get pH =13.

Although perhaps some salt hydroxides aren't strong bases? I'm not sure.

Some salt hydroxides are insoluble. Consider the bivalent magnesium hydroxide. Limited solubility. As a matter of fact, a saturated solution of Mg(OH)2 exhibits a pH of ~10. But then the original question is talking about monovalent metal hydroxides.
 
Some salt hydroxides are insoluble. Consider the bivalent magnesium hydroxide. Limited solubility. As a matter of fact, a saturated solution of Mg(OH)2 exhibits a pH of ~10. But then the original question is talking about monovalent metal hydroxides.
can you please explain how you would solve this problem? I do not understand the explanation given
 
can you please explain how you would solve this problem? I do not understand the explanation given
Very odd question since most monovalent hydroxides are very strong and dissociate 100% (group 1 hydroxides). I was curious so did some searching to see if it the Ksp of AgOH (which has a +1 oxidation state) fell in line with that answer choice. On Wikipedia (regarding transition metal hydroxides): "Hydroxides of metals in the +1 oxidation state are also poorly defined or unstable. For example, silver hydroxide Ag(OH) decomposes spontaneously to the oxide (Ag2O). Copper(I) and gold(I) hydroxides are also unstable, although stable adducts of CuOH and AuOH are known." This is a very unusual question.
 
Using Kb = ([X+][OH-])/[XOH]; X is most probably a Group I metal since no decomposition occurred (P3, L3-4), implying that the anion (OH-) and cation (X+) are of comparable size (P2, L1-4).
Assuming that [X+] = [OH-] approximately

Kb = [OH-]2/[XOH], where XOH approximates 1.0 M at equilibrium, thus:

1.0 x 10-6 = [OH-]2/1

OP, how did the book get Kb for the unknown metal hydroxide to = 1.0*10^-6? Was there a passage related to this question?
 
On Wikipedia (regarding transition metal hydroxides): "Hydroxides of metals in the +1 oxidation state are also poorly defined or unstable. For example, silver hydroxide Ag(OH) decomposes spontaneously to the oxide (Ag2O). Copper(I) and gold(I) hydroxides are also unstable, although stable adducts of CuOH and AuOH are known." This is a very unusual question.

Beyond the scope of the MCAT, unfortunately, but I'm still curious as to why AgOH might be unstable while AgO is exceedingly stable.
 
OP, how did the book get Kb for the unknown metal hydroxide to = 1.0*10^-6? Was there a passage related to this question?
lol it's some alien hydroxide apparently
gs.JPG
 
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