Two molarity and normality questions from TBR

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This is TBR gen chem I p.330 #54:

How many mL of 0.4M H2SO4(aq) would require the same amount of base to reach full neutralization as would 25mL 0.6M H3PO4?

A. 25.00mL 0.4M H2SO4
B. 37.50mL 0.4M H2SO4
C. 50.00mL 0.4M H2SO4
D. 56.25mL 0.4M H2SO4

So I kind of understand the calculations, although if someone could go over that explaining the concepts I would appreciate it. My main question is on the explanation given for the answer: "Sulfuric acid has only 2 acidic protons, whereas phosphoric acid has three acidic protons to neutralize. Thus, phosphoric acid requires only two-thirds the amount of base that is required for sulfuric acid."

Why does it require only two-thirds? I figured since phosphoric acid has more protons to neutralize, it would need more base?

This is TBR gen chem I p.330 #56:

What is the phosphate cocnentration in Flask 2 after 40 mL of 0.30N NaOH has been added?

A. 0.050M PO4
B. 0.100M PO4
C. 0.450M PO4
D. 0.900M PO4

How would you calculate this? It seems like to me that the back of the book just randomly switches from normality to molarity. If someone could explain the calculations and concepts, I'd appreciate it!

 

[MedPR]

This is TBR gen chem I p.330 #54:

How many mL of 0.4M H2SO4(aq) would require the same amount of base to reach full neutralization as would 25mL 0.6M H3PO4?

A. 25.00mL 0.4M H2SO4
B. 37.50mL 0.4M H2SO4
C. 50.00mL 0.4M H2SO4
D. 56.25mL 0.4M H2SO4

So I kind of understand the calculations, although if someone could go over that explaining the concepts I would appreciate it. My main question is on the explanation given for the answer: "Sulfuric acid has only 2 acidic protons, whereas phosphoric acid has three acidic protons to neutralize. Thus, phosphoric acid requires only two-thirds the amount of base that is required for sulfuric acid."

Why does it require only two-thirds? I figured since phosphoric acid has more protons to neutralize, it would need more base?

This is TBR gen chem I p.330 #56:

What is the phosphate cocnentration in Flask 2 after 40 mL of 0.30N NaOH has been added?

A. 0.050M PO4
B. 0.100M PO4
C. 0.450M PO4
D. 0.900M PO4

How would you calculate this? It seems like to me that the back of the book just randomly switches from normality to molarity. If someone could explain the calculations and concepts, I'd appreciate it!

For the first question. 0.6*1.5*25=0.4*1*x where x=volume required. Normality doesn't affect concentration.

 

[Lunasly]

Sorry for bumping an old thread, but I have the same question as the OP:

What is the phosphate cocnentration in Flask 2 after 40 mL of 0.30N NaOH has been added? (Flask 2 contains 40 mL of 0.3 N H3PO4).

A. 0.050M PO4
B. 0.100M PO4
C. 0.450M PO4
D. 0.900M PO4

I understand how to do the calculation after reading the answer. More specifically, I treated the question as a dilution problem, where nM1V1 = nM2V2. I solved for M2 and set V2 as final volume (80 mL or 0.08 L in this case). I got the correct concentration. Usually when doing these types of problems however, we don't set V2 as the final volume of the solution.

Thanks for the help!

 

[gettheleadout]

Sorry for bumping an old thread, but I have the same question as the OP:

What is the phosphate cocnentration in Flask 2 after 40 mL of 0.30N NaOH has been added? (Flask 2 contains 40 mL of 0.3 N H3PO4).

A. 0.050M PO4
B. 0.100M PO4
C. 0.450M PO4
D. 0.900M PO4

I understand how to do the calculation after reading the answer. More specifically, I treated the question as a dilution problem, where nM1V1 = nM2V2. I solved for M2 and set V2 as final volume (80 mL or 0.08 L in this case). I got the correct concentration. Usually when doing these types of problems however, we don't set V2 as the final volume of the solution.

Thanks for the help!

M1V1 = M2V2 is the dilution equation, so when applied to dilutions the final volume of solution should always be V2. However, in this case two aqueous solutions are being combined; it is not a dilution. It does not seem appropriate to me to amend the equation as you have to form: nM1V1 = nM2V2. Are the "n" variables supposed to be n1 and n2? The concentrations of species in Flask 2 and the solution being added are both 0.3 N but that concentration describes different species. In any case, here's how I would solve the problem:

Knowing that normality is defined as N = M x (n_eq / n) where the factor (n_eq / n) represents a ratio of moles equivalents to moles species in question, we can look at our two solutions' solutes and convert easily to molarity: NaOH is monobasic (only one OH– ion per unit NaOH) and so the factor (n_eq / n) is equal to 1, and M = N. We are adding 40 mL of 0.3 M NaOH. Phosphoric acid (H3PO4) is obviously triprotic, and this means that the factor (n_eq / n) is equal to 3 and thus M = N / 3 = 0.1 M. Flask 2 then already contains 40 mL of 0.1 M H3PO4. Combining the two solutions should yield 80 mL of solution.

The above should all be done mentally and very quickly. Next we should observe that we have equal volumes of the two solutions being combined, and look for a relationship between their concentrations. We see that the NaOH is three times as concentrated as the H3PO4, but that the ratio of NaOH to H3PO4 necessary for neutralization of this triprotic acid is 3:1. Given this information, we are performing a neutralization of the H3PO4, and at the same time cutting the concentration in half by doubling the volume. Thus, instead of converting 0.1 M H3PO4 to 0.1 M PO4^3–, we end up with 0.05 M PO4^3–.

Thus, the best answer is A.

...However, there is a nuance to this scenario that is overlooked by the question. If there were another answer choice less than 0.05 M PO4^3–, say choice (E) was 0.025 M PO4^3–, this would in fact be the best choice. Can you figure out why?

 

[Lunasly]

M1V1 = M2V2 is the dilution equation, so when applied to dilutions the final volume of solution should always be V2. However, in this case two aqueous solutions are being combined; it is not a dilution. It does not seem appropriate to me to amend the equation as you have to form: nM1V1 = nM2V2. Are the "n" variables supposed to be n1 and n2? The concentrations of species in Flask 2 and the solution being added are both 0.3 N but that concentration describes different species. In any case, here's how I would solve the problem:

Knowing that normality is defined as N = M x (n_eq / n) where the factor (n_eq / n) represents a ratio of moles equivalents to moles species in question, we can look at our two solutions' solutes and convert easily to molarity: NaOH is monobasic (only one OH– ion per unit NaOH) and so the factor (n_eq / n) is equal to 1, and M = N. We are adding 40 mL of 0.3 M NaOH. Phosphoric acid (H3PO4) is obviously triprotic, and this means that the factor (n_eq / n) is equal to 3 and thus M = N / 3 = 0.1 M. Flask 2 then already contains 40 mL of 0.1 M H3PO4. Combining the two solutions should yield 80 mL of solution.

The above should all be done mentally and very quickly. Next we should observe that we have equal volumes of the two solutions being combined, and look for a relationship between their concentrations. We see that the NaOH is three times as concentrated as the H3PO4, but that the ratio of NaOH to H3PO4 necessary for neutralization of this triprotic acid is 3:1. Given this information, we are performing a neutralization of the H3PO4, and at the same time cutting the concentration in half by doubling the volume. Thus, instead of converting 0.1 M H3PO4 to 0.1 M PO4^3–, we end up with 0.05 M PO4^3–.

Thus, the best answer is A.

...However, there is a nuance to this scenario that is overlooked by the question. If there were another answer choice less than 0.05 M PO4^3–, say choice (E) was 0.025 M PO4^3–, this would in fact be the best choice. Can you figure out why?

Thanks for the reply, gettheleadout. That is the same thought process I had, but I can't remember the last time I did a question where a neutralization reaction took place and I had to add the volumes. I guess it just threw me off. For instance, if I want to find the concentration of base required to neutralize an acid and I am given V1, M2, and V2 (solving for M1), would V2 be the combination of of the two solutions provided in the question?

I also gave your question at the end some thought and I haven't been able to come up with anything concrete. Do you have any hints? 😛 I am assuming that it has something to do with the instability of PO4^3- in solution that may perhaps affect the equilibrium?

 

[gettheleadout]

Thanks for the reply, gettheleadout. That is the same thought process I had, but I can't remember the last time I did a question where a neutralization reaction took place and I had to add the volumes. I guess it just threw me off.

What if I asked you to give me the coordinates of the equivalence point on a titration plot? 😉

For instance, if I want to find the concentration of base required to neutralize an acid and I am given V1, M2, and V2 (solving for M1), would V2 be the combination of of the two solutions provided in the question?

Yep!

I also gave your question at the end some thought and I haven't been able to come up with anything concrete. Do you have any hints? 😛 I am assuming that it has something to do with the instability of PO4^3- in solution that may perhaps affect the equilibrium?

Going back to the titration reference, how can the neutralization of H3PO4 here be related to a titration and what's happening therein?

 

[Lunasly]

What if I asked you to give me the coordinates of the equivalence point on a titration plot? 😉

Yep!


Going back to the titration reference, how can the neutralization of H3PO4 here be related to a titration and what's happening therein?

Its seems as if many questions regarding neutralization ask how many ml of titrant is required to neutralize an acid or base so we don't consider the final volume. However, I suppose in the case where they are asking for the moles or molarity of a given species then we have to consider the final volume of the solution?

With regard to your last response. Its to my understanding that we are dealing with a polyprotic acid. Once we add titrant base, we eventually neutralize the polyprotic acid acid to its equivalence point whereby only its conjugate base is present. This continues on until we have neutralized each acidic species to its conjugate base form, leaving us with PO4^-3. I clearly have a basic understanding of this, haha. I hope I am not misunderstanding a fundamental point you're making.

 

[gettheleadout]

Its seems as if many questions regarding neutralization ask how many ml of titrant is required to neutralize an acid or base so we don't consider the final volume. However, I suppose in the case where they are asking for the moles or molarity of a given species then we have to consider the final volume of the solution?

Yes, you would.

With regard to your last response. Its to my understanding that we are dealing with a polyprotic acid. Once we add titrant base, we eventually neutralize the polyprotic acid acid to its equivalence point whereby only its conjugate base is present. This continues on until we have neutralized each acidic species to its conjugate base form, leaving us with PO4^-3. I clearly have a basic understanding of this, haha. I hope I am not misunderstanding a fundamental point you're making.

Haha no, you've got it. Titration of any acid to its equivalence point is by definition a neutralization, and as you've pointed out, when we neutralize H3PO4 we end up with only PO4^3– in solution. However, as we know, the pH at equivalence is only 7 for titration of strong acids or bases, so we won't have a neutral pH at that point. Why? Because the remaining species (phosphate ion) is reactive as a base! Some portion of the PO4^3– yielded by the neutralization reaction will react with water to form HPO4^2–, and some of that will react with water to form H2PO4–, and so on in a complex equilibrium.

The relevance to the question I initially posed you is that the actual concentration of free phosphate ([PO4^3–]) in solution after the mixing of the two solutions will be some value less than the 0.05M we calculate by simply looking at the stoichiometry of the neutralization.

 

[Lunasly]

Ah, yes that makes sense. Thank you 🙂