Calculating Citric Acid for pH Adjustment

In summary, you would need to increment the H^+ concentration by 10^{-5.2}-10^{-8} in order to change the pH of a solution from 8 to 5.2.
  • #1
Engbryg
2
0
How can I calculate the amount of citric acid to add to a solution of a given pH, to achieve another value of pH?
 
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  • #2
Experimentally, use small increments of citric acid and monitor pH; then scale the ratio upward to the size of solution you want to adjust.

Theoretically, use polyprotic weak acid equilibrium dissociation constants...
... loosing skills here, so hope you want experimental general answer.
 
  • #3
No, I was hoping for a ready-to-use formula, i.e. x mg of citric acid to decrease from pH 8 to pH 5.2.
 
  • #4
Engbryg said:
No, I was hoping for a ready-to-use formula, i.e. x mg of citric acid to decrease from pH 8 to pH 5.2.

You best probably cannot find such a formula to be too simple. You may need to know the source of the alkalinity. If the source of alkalinity is just sodium hydroxide, then maybe you could rely on dissociation constant information with equilibrium calculations to derive a formula. Maybe someone who is currently more skilled in this area can comment further, since my proficiency is no longer strong in this area.

Actually, you could even try measured additions of citric acid of known concentration from a buret while monitoring pH; you can then pre-design your proportion formula.
 
  • #5
To be honest, I just threw this out, I am not even 100% sure if any of this maths is right as it seemed to be a slippery slope trying to solve this one.

I just put this here to show that the community here do try and make an effort, but this one is whey out of my range.

pH is:
[tex]pH=-log([H^+])[/tex]

Therefore:
[tex][H^+] = 10^{-pH}[/tex]
[tex]\Delta [H^+]=10^{-pH_2}-10^{-pH_1}[/tex]

Intermediate example you chosen: pH 8 -> pH 5.2
[tex][H^+_1] = 10^{-8}[/tex]
[tex][H^+_2] = 10^{-5.2}[/tex]

So if we have a solution that is at pH8 we need to increase the [tex]H^+[/tex] concentration by [tex]10^{-5.2}-10^{-8}[/tex]

Citric acid isn't a strong acid, so its Ka is < 1. We're aiming for the above mentioned concentration change so:

[tex]K_a(citric) = \frac{[X-][H^+]}{[Citric acid added]-[X^-]}[/tex]

Rearranging, remembering that [X-] = [H+] if no other acids/bases are present otherwise youll get a buffer case concentration wise:
[tex][\Delta H^+]^2+[\Delta H^+]K_a = [Citric acid added]K_a[/tex]

You must remember the volume of liquid already present might not be equal to a [tex]dm^3[/tex] so:

[tex][Citric acid added] = \frac{n}{v} = \frac{m}{192.123v}[/tex]

Volume of solution in [tex]dm^3[/tex]
Mass in grams

So inserting all what we know:
[tex][\Delta H^+]^2+[\Delta H^+]K_a = \frac{mK_a}{192.123V}[/tex]

Rearranging it for m to be the subject

[tex]\frac{192.123V}{K_a}([\Delta H^+]^2 + [\Delta H^+]K_a) = m [/tex]

Since we found [tex][\Delta H^+][/tex] before we can sub that in:

[tex] \frac{192.123V}{K_a}((e^{-2*pH_2}-e^{-2*pH_1})+(e^{-pH_2}-e^{-pH_1})K_a) = m [/tex]

As this is a quadratic equation we make [tex][\Delta H^+][/tex] the subject as such (if your trying to find the pH change on addition of m amount of acid to v):

[tex][\Delta H^+] = \frac{-K_a+\sqrt{K_a^2 + 4*\frac{mK_a}{192.123V}}}{2}[/tex]

If you want to know the pH change from adding mass m to volume V then:

[tex]\Delta pH = log_10 \left[ \frac{-K_a+\sqrt{K_a^2+4*\frac{mK_a}{192.123V}}}{2}\right][/tex]

The left side of the equation is decided by you, then the right side is found out, where:
[tex]K_a[/tex] Ka of the acid in question
[tex]m[/tex] mass of solid acid added that is changing the pH
[tex]V[/tex] Volume of solvent/solution that your adding the solid acid too

To be honest, I just threw this out, I am not even 100% sure if any of this maths is right as it seemed to be a slippery slope trying to solve this one.

This not only goes off the assumption of a monoprotic acid, but a monoprotic acid that is not in a salt solution (buffer possibilities), as you can see i messed my head up trying to calculate this extremely "easy" example (since I thought I'd do this in no time whatsoever) imagine trying to do this under more realistic conditions.
 
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1. How do I calculate the amount of citric acid needed for pH adjustment?

To calculate the amount of citric acid needed for pH adjustment, you will need to know the initial pH of your solution, the desired pH, and the volume of the solution. You can use an online calculator or the Henderson-Hasselbalch equation to determine the amount of citric acid needed.

2. What is the purpose of using citric acid for pH adjustment?

Citric acid is commonly used for pH adjustment because it is a weak acid that can easily be titrated to reach a desired pH. It is also a food-grade acid and is safe to use in various applications such as in food and beverage products.

3. Can I use citric acid for pH adjustment in any type of solution?

Citric acid is suitable for pH adjustment in most aqueous solutions. However, it may not be effective in highly alkaline solutions as it is a weak acid and may not be able to sufficiently lower the pH. In these cases, a stronger acid may be needed.

4. How do I ensure accurate measurements when using citric acid for pH adjustment?

To ensure accurate measurements, it is important to use a precise measuring tool such as a scale or graduated cylinder. It is also recommended to perform multiple trials to confirm the accuracy of your results.

5. Are there any safety precautions I should take when handling citric acid for pH adjustment?

Citric acid is generally safe to handle, but it is still important to wear protective gear such as gloves and goggles when handling concentrated solutions. It is also recommended to work in a well-ventilated area and to avoid inhaling the fumes.

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