How to tell if Acid is Protonated in Solution

[justadream]

TBR Ochem II page 71 #89

"How does propanoic acid exist after it has been added to water given it has a pKa of 5.0"?

Okay so if I just ignore all my TBR training, then the correct answer (Less than 1% deprotonated) is easy since pKa of 5.0 means Ka of 10^-5 which means barely any of the acid is deprotonated.



However, I just did the TBR titrations chapter where it was beaten into my head that you should compare the pKa of the substance with the pH of the solution to determine whether the substance is protonated.

Here, since pH = 7.0 which is GREATER than the pKa of propanoic acid, I thought that the propanoic acid should be mostly DEPROTONATED in water.

Can someone reconcile this?

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[Teleologist]

Convert pKa to a Ka value and solve.

Before anyone gets the bright idea of using the HH equation - what are you gonna plug in for pH in the HH equation?

 

[justadream]

@Teleologist


I'm not using the HH equation (at least not trying to).

Are you saying the TBR answer (less than 1% deprotonated) is incorrect?

I agree with the TBR answer if you do the calculation involving Ka.

But if I don't use the formula (and do it based on comparing the pKa and the pH of the solution), I get the opposite answer - it should be mostly deprotonated (since pH of 7 is greater than pKa, the substance should be mostly deprotonated).

 

[Teleologist]

@Teleologist


I'm not using the HH equation (at least not trying to).

Are you saying the TBR answer (less than 1% deprotonated) is incorrect?

I agree with the TBR answer if you do the calculation involving Ka.

HH comment wasn't directed toward you; more of a note to self and others who might come along and try to use the HH equation. I actually tried doing the HH equation first and completely failed beacause you can't use it on this problem. Hence the note to self. And others.

And oops, I mean the TBR answer is correct. When I first typed up my answer I had used the HH equation and came to the wrong conclusion. Will edit my earlier post.

But if I don't use the formula (and do it based on comparing the pKa and the pH of the solution), I get the opposite answer - it should be mostly deprotonated (since pH of 7 is greater than pKa, the substance should be mostly deprotonated).

The pH of what is 7?

 

[justadream]

@Teleologist

pH of water is 7.


My logic regarding the pH and pKa comparisons is similar to the logic used for amino acids.

At neutral solution (pH = 7), the COOH group is deprotonated (since its pKa of 2-3ish is < 7) while the amine group is protonated (since its pKa of 9-10ish is >7).


Here, pH of water is 7 and pKa of the acid is 5. Since 5 < 7, the acid should be deprotonated (similar to COOH in water)?

 

[Teleologist]

@Teleologist

pH of water is 7.

I agree.

Here, pH of water is 7 and pKa of the acid is 5. Since 5 < 7, the acid should be deprotonated (similar to COOH in water)?

Will the pH of the water remain the same when you add acid?

 

[justadream]

@Teleologist

No...but let's assume you have much more water than acid.

Do you understand what I am getting at with the amino acid example?

 

[Teleologist]

@Teleologist

No...but let's assume you have much more water than acid.

Do you understand what I am getting at with the amino acid example?

Don't assume stuff randomly in chemistry. Defend assertions. Don't assume conditions. You're also misapplying the amino acid example to this problem.

 

[justadream]

@Teleologist

Care to educate me?

I'd greatly appreciate it.

 

[Teleologist]

@Teleologist

Care to educate me?

I'd greatly appreciate it.

Yeah, try this:

However, I just did the TBR titrations chapter where it was beaten into my head that you should compare the pKa of the substance with the pH of the solution to determine whether the substance is protonated.

Here, since pH = 7.0 which is GREATER than the pKa of propanoic acid, I thought that the propanoic acid should be mostly DEPROTONATED in water.

I increased the font of the part I want you to pay attention to. This is a true statement. The second time I increased the font, I'm emphasizing an assumption that you're making.

I'll ask again, what's the pH of the solution?

 

[justadream]

@Teleologist

So you're saying that the pH of the solution is not 7, but less than 7 since you added in the acid.

Okay, so let's be generous and say the pH of the solution falls all the way to 6.5 (or even 6) from adding the acid into the solution.

The pKa is still less than the pH of the solution.

Are you saying that once you add the acid in to the solution, the pH of solution = pKa of acid?

 

[Teleologist]

@Teleologist

So you're saying that the pH of the solution is not 7, but less than 7 since you added in the acid.

Okay, so let's be generous and say the pH of the solution falls all the way to 6.5 (or even 6) from adding the acid into the solution.

The pKa is still less than the pH of the solution.

Are you saying that once you add the acid in to the solution, the pH of solution = pKa of acid?

Wait, why are we speculating on the pH of the solution when we don't need it to solve the problem? Write out the Ka and let it talk to you.

Ka =([H3O+][CB-])/[A], where CB- = conjugate base and A = acid.
10^-pKa = Ka = ([H3O+][CB-])/[A]
5.0 = Ka = ([H3O+][CB-])/[A]

5.0 = x^2/(1-x)
x = 1.0*10^-2.5 or ~1/1000
This implies that less than 1% has dissociated; less than 1% of the acid has turned into the conjugate base.

 

[justadream]

@Teleologist

Right , I get the math answer you provided.

But can you explain how this is different from the example with amino acids (in which you compare pH of the solution to the pKa of the acid)?

I'm trying to understand the difference between the two situations.

lol I was speculating on the pH of the solution since that's what you asked me.

 

[Teleologist]

@Teleologist

Right , I get the math answer you provided.

But can you explain how this is different from the example with amino acids (in which you compare pH of the solution to the pKa of the acid)?

I'm trying to understand the difference between the two situations.

lol I was speculating on the pH of the solution since that's what you asked me.

pH is something you don't need to know. Just know it ain't 7 after adding acid. Now, because it's not 7 doesn't mean to guess 6.5 or whatever ... There are a lot of numbers lower than 7. That's the point. For the amino acid problem you KNOW the pH of the amino acid solution. Here you don't know the exact pH, but if you solve Ka with the assumption you have a 1 molar solution of the acid you find that dissociation extent is low.

 

[justadream]

@Teleologist

So you're saying just because we don't know the pH means we completely ignore it?

I'm sure I could take a pH meter and go measure it.

But okay then let's look at a hypothetical scenario in which:

We KNOW for sure that the pH is 6.5

Does the answer change?

 

[Teleologist]

@Teleologist

I'm sure I could take a pH meter and go measure it.

Are you planning on doing that on the MCAT?

Also, you weren't given initial molarity.

 

[justadream]

Are you planning on doing that on the MCAT?

Also, you weren't given initial molarity.

No, I don't plan on doing it on the MCAT (although if given the pH meter, I would go do it lol)

But if the pH were given, you are saying that it then depends on initial molarity?

 

[Teleologist]

No, I don't plan on doing it on the MCAT (although if given the pH meter, I would go do it lol)

But if the pH were given, you are saying that it then depends on initial molarity?

Yes, pH depends on initial molarity.

 

[rabidricky]

@Teleologist

But can you explain how this is different from the example with amino acids (in which you compare pH of the solution to the pKa of the acid)?

Sorry to bump an ancient thread, but I came across this in a search and figured I'd give my 2c, for posterity's sake :V

I think you are just under-estimating the complication of amino acids.

Propionic acid is only acidic when in protonated form; it donates this proton and becomes ionic with a negative charge.

These protons will be swimming around in solution (but as H3O+) and will affect the pH you read from a meter, which is probably one source of confusion.

What was probably meant was in order to have complete dissociation of an ACID the pH of the solution must be LOWER than the pKa. Once at equilibrium, the pH is a measure of the concentration these swimmers on a (negative) logarithmic scale once you subtract [OH-] from its conjugate base. Therefore, if the pH < pKa it has completely dissociated, if it's the only acid in solution.

Amino acids are not quite as simple. They have a carboxylic acid group that makes them acidic, and an amine group that makes them basic. To complicate matters even worse, it is what is known as a zwitterion, which means it has a resonance structure that is both acidic and basic. The reason for this is the de-protonated amine group can donate its proton to the carboxilic acid (though it is a limiting factor since the de-protonated amine is much more basic than the protonated form is acidic). Since the pKb and pKa of these can change depending on the type of amino acid, the net pH of the solution can change depending on the types and concentration of amino acids in solution, and can end up being basic as well as acidic.

(Not too important, but if you really want to nit-pick, you need to add a slight amount since water that is not in an inert atmosphere is slightly acidic due to dissolved CO2 and its reaction with water to form carbonic acid [pKa = 6.3]. This is in equilibrium with another reaction where it forms sodium bicarbonate [pKb = 7.7, pKa = 10.3]).

 

[BerkReviewTeach]

@Teleologist

pH of water is 7.


My logic regarding the pH and pKa comparisons is similar to the logic used for amino acids.

At neutral solution (pH = 7), the COOH group is deprotonated (since its pKa of 2-3ish is < 7) while the amine group is protonated (since its pKa of 9-10ish is >7).


Here, pH of water is 7 and pKa of the acid is 5. Since 5 < 7, the acid should be deprotonated (similar to COOH in water)?

Because this got resurrected, I want to make a point that should help.

Once propanoic acid was added to water, the solution was no longer pure water and thus the pH dropped (and is no longer 7). That was the source of the confusion, using the pH of pure water rather than the pH of the propanoic acid solution.

The easiest way to solve the question is to use Ka = 10exp-5 and estimate, as what shown in the answers. However, you can do it by comparing pH with pKa if you wish, as long as you solve for the pH.

If you recall from the Acid-Base section, the pH of a weak acid solution can be quickly found by averaging the pKa and the pH it would have if it fully dissociated. In this case, you're averaging 0 and 5, for a pH = 2.5

With a pH (2.5) that much lower than the pKa (5.0), the species will exist predominantly in its protonated form. This method works for solving this question, but it really is a case of overthinking. Take the simplest route whenever possible.

 

[BerkReviewTeach]

I want to address a few things for the sake of clarity.

I think you are just under-estimating the complication of amino acids.

Just to be clear, propanoic acid is a standard carboxylic acid and not an amino acid.

What was probably meant was in order to have complete dissociation of an ACID the pH of the solution must be LOWER than the pKa. Once at equilibrium, the pH is a measure of the concentration these swimmers on a (negative) logarithmic scale once you subtract [OH-] from its conjugate base. Therefore, if the pH < pKa it has completely dissociated, if it's the only acid in solution.

You actually have this backwards. When the pH is lower than the pKa, then the environment feels acidic for the compound, under which conditions it will be protonated. Consider the HH equation. If pH < pKa, then the log [A-]/[HA] must be a negative number, which occurs if [HA] > [A-], indicating that the dissociated form (A-) is in low concentration and the protonated form (HA) is in high concentration.