Weak acid-base solution assumption

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Discussion Overview

The discussion revolves around the assumptions made in calculating the pH of a weak acid-base solution, specifically when mixing NaOH with HNO2. Participants explore various methods for determining concentrations and the impact of additional hydroxide ions on the equilibrium of the acid-base reaction.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant proposes a method involving simultaneous equations to account for the interaction between added OH- and H+ ions, suggesting that this interaction is significant in certain scenarios.
  • Another participant questions the origin of the equations and values used, indicating a need for clarification on the assumptions made in the calculations.
  • A different participant explains their approach to calculating the initial concentrations of NO2- and HNO2, emphasizing the importance of equilibrium constants in their calculations.
  • Concerns are raised about mixing HNO3 with NO2- and the validity of the approximations used, with a suggestion to refer to external resources for a more rigorous approach.
  • One participant asserts that their method has been validated through multiple applications with weak acid reactions, seeking confirmation of its correctness.
  • Another participant emphasizes that the concentrations of H+ and OH- should not be assumed to be the only sources, as further dissociation can occur when their concentrations change.
  • A later reply mentions that both methods tried yielded the same results, suggesting that both approaches may be valid.

Areas of Agreement / Disagreement

Participants express differing views on the validity of the methods used for calculations, with some supporting the proposed approach while others challenge its assumptions and rigor. The discussion remains unresolved regarding the best method to use.

Contextual Notes

Participants note that certain assumptions, such as the neglect of additional dissociation of acids and bases, may not hold in all scenarios, particularly in extreme cases. The discussion highlights the complexity of the calculations involved and the potential for significant errors if certain interactions are overlooked.

Conductivity
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I have been using a way to verify the assumptions.

For example let's say, If we add 200 mL of NaOH to 400 mL of HNO2 2M, The pH become 1.5 + (##pH_i##)
calculate the concentration of NaOH.

The usual way of doing is this:
## K_a = (0.02+x)[H^+]/(4/3-x) ## then find the x which most of the time is equal to the initial concentration of OH- after addition which you can convert back to the original solution and find the required information.

But the way I see how these approximations work is that you have to also think about how the additional OH can interact with H+ (or H3O+ if you like) to form water. So you really need simultaneous equations
##K_w = ([H+]_i -y)([OH-]_i-x-y) ##
Where X is from the original acid reaction and Y comes from forming water reaction.

Now usually Y is negligible so I can assume the OH- fully reacts with the acid but here in this situation Y isn't

I did the math and found that x = 0.41345 and y = 0.01917811 which is not negligible ( about 4.63% mistake, However I am talking about more extreme version of this) . Is this way of thinking is true?
 
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Conductivity said:
The pH become 1.5 + (##pH_i##)

Conductivity said:
## K_a = (0.02+x)[H^+]/(4/3-x) ##

No idea where these equations and numbers come from nor what the i means, care to elaborate?

In general when it comes to dealing with such calculations it is best to approach the system in a way described here: http://www.chembuddy.com/?left=pH-calculation&right=toc
 
Sure sorry,
First the concentration of NO2- in the acid solution alone is
## Ka * [HNO3]_i = x^2 ## solve for x, I get x = 0.03 (assuming [HNO3] doesn't change)

initial [NO2-] in the combined solution is 0.02 M
Initial [HNO3] let's assume it doesn't change so it is 4/3 M
Now when you add OH- the reaction will go to the right:
HNO2 (-----) H+ + NO2-
4/3-x ##[H+]_f## 0.02+x
Using the equilibrium constant equation we get the first equation.
After finding x which is 0.41345 M, It means that we had 0.41345 M of OH- from NaOH in the combined solution. Going back to the NaOH solution alone we get 0.620175

Note: Prepare for the mess! I know there are much simpler ways.

The other way that I am concerned about is this:
##[OH-]_i## represents the initial concentration of OH- that comes from NaOH in the combined solution
##[H+]_i## represents the initial concentration of H+ that comes from the disassociation of HNO2 in the combined solution before any reaction happen in the combined solution
If I form two simultaneous equation concerning that OH- might react with H+ or HNO2, I get
##\frac{K_a}{K_w} = \frac{(0.02+x)}{(4/3-x)([OH-]_i -x -y)}##
Where x results from HNO2 and OH- reaction

and Y results from this

##K_w = ([H+]_i -y)([OH-]_i-x-y) ##

Usually, Y is negligible but in this specific question it is not entirely negligible.
I found X = 0.41345 and Y = 0.019178
First, Is all this true?
and I am asking about if there was a extreme version of this, Where Y is not negligible at all. I have to do this in order to get an exact solution right.
 
Conductivity said:
Sure sorry,
First the concentration of NO2- in the acid solution alone is
## Ka * [HNO3]_i = x^2 ## solve for x, I get x = 0.03 (assuming [HNO3] doesn't change)

That is already based on an approximation, and you are mixing HNO3 with NO2- as if these were related - basically they are not.

I strongly suggest you read the linked pages before digging deeper, as it seems like you are just juggling equations, no wonder you are getting strange results.
 
Ah, I meant HNO2 with a ka of 4.8 * 10^(-4)
I made 2 parts one with an approximation and one without

Please see the second part. It must be true because I used it multiple times on very weak acid reaction and it gave exact answer. I want to know if this approach is true.

Yes I have seen some of topics you provided before. I also said in the beginning there is another way
Thanks in advance
 
You can't assume your[OH-]i (nor [H+]i) to be the only source of OH- (H+), once their concentrations go down acid (and base) will dissociate further (even if you ignore base dissociation here).

I told you to approach the problem in a more rigorous way, you are wasting time ATM.
 
I tried both ways and it gave the same answer.
So I guess both ways are true

I also found a way to simplify all what I wrote to 2 lines.
and I derived a equation to solve these kind of questions from your link

Thanks borek
 
Last edited:

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