How Do You Calculate the Equilibrium Constant for a Weak Acid in Water?

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SUMMARY

The equilibrium constant, Ka, for a monoprotic weak acid in a 0.0153 M solution with a pH of 6.31 can be accurately calculated by considering the initial H+ concentration from water's autodissociation, which is 10^-7 M. A systematic approach is essential, involving the use of mass balances, charge balances, and the equilibrium equations for Ka and Kw. Relying solely on ICE tables is insufficient for this calculation, as it does not provide a comprehensive understanding of the underlying chemistry.

PREREQUISITES
  • Understanding of weak acid dissociation and equilibrium constants
  • Familiarity with the concept of pH and its relationship to H+ concentration
  • Knowledge of mass balance and charge balance in chemical systems
  • Proficiency in writing and solving equilibrium equations, including Ka and Kw
NEXT STEPS
  • Study the derivation and application of the equilibrium constant, Ka, for weak acids
  • Learn how to construct and interpret mass and charge balance equations in chemical equilibria
  • Explore the effects of water's autodissociation on weak acid solutions
  • Review advanced techniques for solving equilibrium problems beyond ICE tables
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Chemistry students, educators, and professionals involved in acid-base chemistry, particularly those focusing on equilibrium calculations and weak acid behavior in aqueous solutions.

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Homework Statement


If enough of a monoprotic acid is dissolved in water to produce a 0.0153 M solution with a pH of 6.31, what is the equilibrium constant, Ka, for the reaction?

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The Attempt at a Solution


I have attempted to solve this problem using ICE tables, but keep getting the incorrect answer. One feedback stated that I needed to account for the initial H+ concentration due to water, which is 10^-7 M, but I'm not sure how to go about putting this into the ICE table. Thanks in advance for any help
 
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Please show your work and the result you got, hard to comment on the problem not seeing what you did.

In general concentration of H+ from the water autodissociation is not 10-7 M, as its concentration changes when the acid dissociates shifting the water dissociation equilibrium. This can be still solved, but not with just an ICE table. You would need a full, systematc approach, which requires writing all equations describing the system (Ka, Kw, mass balances, charge balance) and solving for Ka.
 
Instead of tables which IMHO will leave you with no knowledge or ability a year after the last time you've used them, I would use the simple fundamentals which you will be able to call on any time needed.

What are the relevant equations for this question?
 

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