How Do You Calculate the Acid Dissociation Constant from a pH Value?

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Discussion Overview

The discussion revolves around calculating the acid dissociation constant (Ka) for the equilibrium between HCrO4(-) and CrO4(2-) based on a given pH value of a KHCrO4 solution. Participants explore various approaches to derive Ka, including using pH to find [H+] and applying equilibrium expressions.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related
  • Debate/contested

Main Points Raised

  • One participant presents a specific problem involving a 0.0025 mol/L solution of KHCrO4 with a pH of 3.50 and requests assistance in calculating Ka.
  • Several participants suggest starting with the expression for Ka and using the known [H+] concentration derived from the pH.
  • One participant provides a dissociation reaction and discusses the stoichiometry needed to find concentrations of HCrO4(-) and CrO4(2-).
  • Another participant calculates [H+] as 3.16*10^(-4) mol/L and attempts to derive Ka but questions their result when it does not match the textbook answer.
  • Discussion includes the relationship between [HCrO4(-)] and [CrO4(2-)] and how the initial concentration of HCrO4(-) is affected by the dissociation.
  • A participant mentions the existence of two pKa values related to the system and provides external resources for further reading.
  • Another participant derives an expression for Ka and applies logarithmic manipulation to relate pH, pKa, and the ratio of concentrations.
  • Participants express uncertainty about the textbook answer and suggest consulting a teacher for clarification.

Areas of Agreement / Disagreement

Participants generally agree on the method of calculating Ka using the pH value and the equilibrium expression, but there is no consensus on the correctness of the textbook answer, leading to uncertainty about the final value of Ka.

Contextual Notes

Participants note the importance of stoichiometry and the relationships between species in the equilibrium, but there are unresolved aspects regarding the calculations and assumptions made about concentrations.

Who May Find This Useful

Students studying acid-base equilibria, particularly in the context of polyprotic acids, and those seeking to understand the application of pH in calculating dissociation constants.

Akousmatikos
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A 0.0025 mol/L solution of KHCrO4 has a pH of 3.50.
Calculate the acid dissociation constant (Ka) for the equilibrium between HCrO4(-) and CrO4(2-).

Thanks!:smile:
 
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Any attempt at the problem?
 
Stevedye56 said:
Any attempt at the problem?

You took the words right off of my keyboard!

Why don't you try writing down the expression for Ka in general form and see where that leads you.

Hint: You know the [H+] concentration from the pH.
 
Haha beat you right to it! At school too! Akousmatikos, have you done any problems like this before chemisttree is right just use log rules and you'll be all set.
 
He'll need dissociation reaction and its stoichiometry as well to calculate HCrO4- and CrO4-2 concentrations.
 
Ok. This is what I know.
1. The concentration of [H+]= 3.16*10^(-4) mol/L
2. KHCrO4 -> H(+) + KCrO4(-)
KHCrO4 -> H(+) + K(+) + CrO4(2-)
3. Add them?
2KHCrO4 -> 2H(+) + K(+) + Cro4(2-) + KCrO4(-)
Is this right so far?
4. Ka
= [H+]^2 * [K(+)] * [CrO4(2-)] * [KCrO4(-)] / [KHCrO4]^2
= [3.16*10^(-4)]^2 * [0.5*3.16*10^(-4)]^3 / [0.0025-3.16*10^(-4)]^2
= 8.257 *10^(-14) mol/L
But this is wrong. The answer in the back of textbook is 4.1 * 10^...
What did I do wrong?
 
Last edited:
For the reaction:

HCrO4- <---------> H+ + CrO4-2

You can calculate the Ka with the equation:

Ka = [H+] [CrO4-2]/[HCrO4-]

You are given the pH (pH = -log[H+]) and you can calculate the [H+]. This is also the concentration of [CrO4-2]. Can you see why? The original concentration of [HCrO4-] has been decreased by the same amount of [H+] that forms.

Can you put this information into the expression for Ka and solve?
 
Wait...
Does [HCrO4-]=[KHCrO4]=0.0025mol/L ?

Ka = [H+] [CrO4 2-] / [HCrO4-]
= [3.16*10^(-4)]^2 / [0.0025 - 3.16*10^(-4)]
= 4.57*10^(-5) mol/L

Well that's close to the answer in the textbook, but I don't think it's right.
 
Last edited:
  • #10
Thanks for the sites.
What about the equilibrium between HCrO4(-) and CrO4(2-)?
Sorry if these questions are too basic. I'm just having trouble understanding.
:P
 
  • #11
for Ka = [H+][CrO4-2]/[HCrO4-], rearranging we get:

[H+] = Ka[HCrO4-]/[CrO4-2]

applying log to both sides gives us:

log[H+] = log(Ka) + log[HCrO4-]/[CrO4-2]

multiplying by -1 gives us

-log[H+] = -log(Ka) + log[CrO4-2]/[HCrO4-]

which is pH = pKa + log[CrO4-2]/[HCrO4-]

pH is 3.5 and [CrO4-2] is equal to [H+] or 3.16X10^-4.

[HCrO4] is 0.0025 - 3.16 X 10^-4 or 0.00218

The ratio of [CrO4-2]/[HCrO4-] is 3.16X10^-4/0.00218 = 0.145

Soooo,

3.5 = pKa + log(0.145)
3.5 - log(0.145) = pKa
4.339 = pKa
4.58X10-5 = Ka

Same answer by Henderson-Hasselbalch equation as by the method you described. How far off is the answer from that in your book?
 
  • #12
The answer in the book is 4.1 * 10^..
But now I think their answer is wrong.
Anyway, I'll ask my teacher next week.
Thank you for all the help. :approve:
 

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