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I am a high school student and I am very confused in salt hydrolysis

My confusion is that: when we talk of hydrolysis of salt of weak base and weak acid, we internally assume the degree of hydrolysis of both cation and anion of the salt is assumed to be same but I think it is a very wrong assumption, why don't we simply do the pH calculation like I have done in this example? what is the problem with this?this image shows my approach,if my approach is also correct then why doesn't it matches with the standard answer?this image shows how do we derive the standard formula what is the mistake in it? I have found some similar questions but no one has given the exact answer to those that's why I am asking it here please, explain it in a simplified way because I am only at high school level.

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    $\begingroup$ The way you write the letter H is very unique as a mirror image of N! It is hard to follow the picture, can you clarify your question by typing? "We internally assume the degree of hydrolysis of both cation and anion of the salt is assumed to be same". No this is not correct nor it is a requirement. $\endgroup$
    – M. Farooq
    Jan 30 at 4:43
  • $\begingroup$ No, it is a assumption,,, this is even my problem that if we are assuming the hydrolysis of both to be same then concentration of OH- as well H+ will be same due to hydrolysis and then we consider the dissociation of the formed acid and base,, to find the concentration of H+ and OH- ,but then why we dont'' subtract their concentrations here to find net concentration of H+ or Oh-?,,,In this image I have mentioned the results if we don't assume it,,,which is very different from the result which we drive by using the direct formula,,,,please try to understand the image $\endgroup$ Jan 30 at 5:15
  • $\begingroup$ How does your textbook solve this or a similar problem like this? $\endgroup$
    – M. Farooq
    Jan 30 at 5:47
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    $\begingroup$ Please practice writing H properly. People will have trouble reading your hand writing in general. It looks like a Russian letter. en.wikipedia.org/wiki/I_(Cyrillic) $\endgroup$
    – M. Farooq
    Jan 30 at 7:28
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    $\begingroup$ Using photos/screenshots of ( even handwritten) text instead of typed text itself is strongly discouraged. It is impossible to index/search for it, or reuse it in answers referring to it. In a case of handwritten text, it puts extra burden on responders to properly decipher it. That all may lead to the question being ignored or even closed. Consider copy/paste or retyping and using eventually MathJax for expressions and formulas. $\endgroup$
    – Poutnik
    Jan 30 at 7:50
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The general approach to solve acido-basic equilibrium problems is:

  • respecting charge balance and charge conservation
  • respecting mass conservation
  • respecting dissociation equilibrium constants for acids, bases and water itself.

Generally, it leads to a set of nonlinear equations for a set of independent variables. The application of a substitution method usually results to a polynomial equation for $\ce{[H+]}$ of the second up to the forth order. The latter is hard to solve analytically.

Fortunately, in many scenarios, there can be made justified simplifications, like

  • neglecting water autodissociation
  • neglecting concentration of one substance form wrt the other one or their sum.

That largely simplifies an equation to be solved.

E.g. to calculate $\mathrm{pH}$ of solution of acetic acid, ammonia, or sodium carbonate, we can consider none of $\ce{H+}$, resp. $\ce{OH-}$ are created by the water autoionization and just negligible part of the compound underwent the acido-basic reaction.

E.g. for sodium acetate hydrolysis

$$K_\mathrm{b}=\frac{\ce{[HA][OH-]}}{\ce{[A-]}}\approx \frac{{\ce{[OH-]}}^2}{\ce{[A-]}}\approx \frac{{\ce{[OH-]}}^2}{c_0} $$

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  • $\begingroup$ but,,,I want to know what is the problem with my solution of above problem,,why it is incorrect,,,or if isn't incorrect, why don't we simply do it like this and not go for the formula? $\endgroup$ Jan 30 at 8:51
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    $\begingroup$ I kind of refuse to read your manuscript, sorry. $\endgroup$
    – Poutnik
    Jan 30 at 9:16
  • $\begingroup$ @ArunBhardwaj, Can you type the solution in Word? It is hard to follow that picture. Convert that Word typed solution in pdf and then you can use Mathpix Snip to convert your equations into LaTeX which be pasted here. mathpix.com $\endgroup$
    – M. Farooq
    Jan 30 at 15:10
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Regarding your degree of hydrolysis expression in the textbook, we have to keep charge balance in mind. It is not an assumption, it is a charge balance fundamental requirement because a solution can never have a uncharged specie without its counter ion. A solution is always electrically neutral. For example, $\ce{Na+}$ cannot exist alone in a solution, it also needs one singly charge anion like $\ce{Cl-}$ or $\ce{NO3-}$ to balance the charge. Same is the case of hydrolysis, if you lose one ammonium ion on the left hand side you must also lose a single formate ion.

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  • $\begingroup$ but I think that the net charge is balanced even in my answer that I have written above,,,,as CH3COO- ion gives ch concetration of OH^- ion ,,,and NH4+ gives c*alpha concentration of H+ ions if you write the concentration of all ions and balance then you will notice the charge is balanced $\endgroup$ Jan 30 at 8:48
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LOL - I spent so much time trying to decipher your handwriting I missed what you question was.

You actually asked a very pertinent question. It is very very wise to wonder about the boundary conditions of some derived formula.

First let me point out that chemistry problems aren't like pure math problems. In math pi has been calculated to millions of decimal places. In chemistry 2-4 significant figures is typically the best that can be done.

You are absolutely right. For ammonium formate there are two hydrolysis reactions.

$$\ce{NH4+ + H2O <=> NH3 + H3O+}\tag{1}$$

$$\ce{HCOO- + H2O <=> HCOOH + OH-}\tag{2}$$

Now the solution must be electrically neutral so for the charge balance we have:

$$\ce{[NH4+] + [H+] = [HCOO-] + [OH-]}\tag{3}$$

However let's consider making a strong ammonium formate solution say 0.1 molar. The ammonium cation is a weak acid, and the formate anion is a weak base. Thus little of either will hydrolyze. So we can assume:

$$\ce{[NH4+] \gg [H+]}\tag{4}$$

and

$$\ce{[HCOO-] \gg [OH-]}\tag{5}$$

thus for charge balance we can assume:

$$\ce{[NH4+] = [HCOO-] }\tag{6}$$

This in turn implies that the majority of ammonia and formic acid in solution are not formed by the reactions (1) and (2) but rather by the reaction:

$$\ce{[NH4+] + [HCOO-] <=> [NH3] + [HCOOH]}\tag{7}$$

Thus the two ions from the salt are hydrolyzed by same amount.

Now if we have instead made a weak solution of ammonium formate, say $1.0\cdot 10^{-5}$ molar, then equations (4) and (5) wouldn't be valid and the individual hydrolysis reactions would have to be considered making the formula to calculate the pH much more complicated.

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  • $\begingroup$ I have one more question that, by assuming the degree of hydrolysis of both cations and anions to be same,, don't we indirectly assuming the concentrations of H+ and OH- to be same? as they will be produced in smae amount and will react in same amount to form water $\endgroup$ Feb 2 at 9:46

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