Calculate CO2 for Water Equilibrium at pH 7.2

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Discussion Overview

The discussion revolves around calculating the amount of CO2 that needs to be removed from water at a pH of 7.2 to achieve equilibrium, particularly in the context of water treatment. Participants explore the implications of pH, concentrations of bicarbonate and carbon dioxide, and relevant equations.

Discussion Character

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

Main Points Raised

  • One participant questions the definition of equilibrium in this context and seeks clarification on how to approach the problem.
  • Another participant notes the absence of critical parameters such as temperature and pressure, suggesting that the problem may refer to previously mentioned information.
  • A different viewpoint suggests assuming that the concentration of CO2 is equivalent to that of carbonic acid (H2CO3) and proposes treating the solution as a buffer to find the required final concentration.
  • After clarifying that the temperature is 12°C, a participant asks for applicable formulas to use in the calculations.
  • One participant introduces the acid dissociation constant and the Henderson-Hasselbalch equation as relevant tools for the calculation.
  • Another participant presents a detailed calculation based on the equilibrium pH and the concentrations of CO2 and HCO3-, arriving at a conclusion about the amount of CO2 to be removed.
  • A later reply acknowledges a mistake in interpreting the original question, indicating that if the initial pH is indeed 7.2, acid would need to be added to lower the pH, not removed.
  • Participants engage in correcting each other's calculations and clarifying units, with some expressing uncertainty about the accuracy of the values presented.
  • One participant expresses gratitude for assistance and poses a new question regarding the calculation of lime dosage in water softening, prompting a suggestion to start a new thread.

Areas of Agreement / Disagreement

There is no clear consensus on the calculations or the interpretation of the problem. Participants express differing views on the initial conditions and the necessary actions to achieve equilibrium.

Contextual Notes

Participants highlight limitations in the problem statement, including missing parameters and the need for clarity on units and definitions. Some calculations are presented with assumptions that may not be universally accepted.

Who May Find This Useful

This discussion may be useful for individuals interested in water treatment processes, acid-base chemistry, and the application of mathematical reasoning in environmental science contexts.

alex5d1
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Hi,
I must calculate how much CO2 has to be removed from the water (pHs=7.2) to obtain equilibrium

Given concentrations:
HCO3-: 223 mg/L
CO2: 60 mg/L
pH: unknown
SI: unknown

What is meant by equilibrium? (ph=7?) Please advise how to tackle this problem
 
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There are missing parameters: temperature, pressure, other solutes. Check the problem statement and see if isn't referring you to something previously mentioned.
 
My bet is that they want you to assume concentration of CO2 is equivalent to the concentration of H2CO3. Then it is just a matter of treating the solution as a buffer, finding the required final concentration of carbonic acid, and comparing it with the initial (60 mg/L) CO2 concentration.
 
Sorry, I forgot to mention that this is a water treatment problem. Temperature is 12C.
What formula is applicable?
 
Acid dissociation constant definition, or Henderson-Hasselbalch equation (which is actually the same, just rearranged to a more convenient form).
 
Well, after some research I came up with this, what do you think?

pHs = 7.2 = equilibrium of CO2 (= H2CO3 ) and HCO3-

pHs = pK1 – log ([CO2] / [HCO3-])

pK1 = 6.45 @12C

log ([CO2] / [HCO3-]) = -0.750

log ([CO2] / [HCO3-]) = 0.178

[HCO3-] = 223/61 = 3.656 mol/L

[CO2] = 0.178 * 3.656 = 0.650 mol/L

CO2 = 0.650 * 44 = 28.6 mg/L

We need to remove 60 – 28.6 = 31.4 mg/L
 
Actually I did a mistake reading the original question, and it doesn't make sense to me now. Sorry about that. I missed the part about initial pH being 7.2. If the initial pH is 7.2 and you are asked to change the pH of the solution to 7.0, you have to ADD acid, not remove it from the solution.

However, if you use concentrations given to calculate pH (which I did) you will find that pH of the initial solution is around 6.8, not 7.2.

alex5d1 said:
log ([CO2] / [HCO3-]) = 0.178

Youdon't mean a log here, but OK.

[HCO3-] = 223/61 = 3.656 mol/L

223 mg, not g. Besides, don't ignore units, as you force others to guess what is 61.
 
Sorry for my typo's in the units. The question as I understand it is to obtain Carbonic acid equilibrium given the equilibrium pH = pHs = 7.2

Then:

pHs = 7.2 = equilibrium of CO2 (= H2CO3 ) and HCO3-

pHs = pK1 – log ([CO2] / [HCO3-])

pK1 = 6.45 @12C

log ([CO2] / [HCO3-]) = -0.750

[CO2] / [HCO3-] = 0.178

[HCO3-] = 223/61 = 3.656 mmol/L

[CO2] = 0.178 * 3.656 = 0.650 mmol/L

CO2 = 0.650 * 44 = 28.6 mg/L

We need to remove 60 – 28.6 = 31.4 mg/L. Do you think this is correct?
 
At least logic behind looks OK, I have not checked the exact value (but it is definitely in a correct ballpark).
 
  • #10
Hi Borek,
That calculation was correct!
many thanks for your assistance.

One more question, how do I calculate this one?:
Lime (calcium hydroxide) is used in softening. How much lime (mmol/L) needs to be dosed in the softening step?
 
  • #11
Please start another thread (and follow the template).
 

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