A square-root estimate for a weak acid neglects part of the material balance. Its own result should be checked against the assumption that made it possible.
State the equilibrium model
For a dilute idealized monoprotic acid with negligible initial hydrogen concentration, let x be the dissociated concentration and c the initial acid concentration. Use the concentration-form coefficient Kc = x²/(c − x), with units mol/L and fixed stated solution conditions. Replacing c − x with c requires x to be small relative to c. Primary reference.
Compare exact and approximate fictional results
Choose hypothetical inputs c = 0.100 mol/L and Kc = 1.00 × 10⁻⁵ mol/L, with activity coefficients neglected. The square-root estimate gives x = √(Kc c) = 0.00100 mol/L. Solving x² + Kc x − Kc c = 0 gives the positive root x ≈ 0.000995 mol/L.
The exact model result is about 0.995% of the initial acid concentration. The estimate is about 0.501% above that exact result. These are different percentage comparisons, and neither is a universal acceptance rule for approximations. The chosen numbers are invented rather than measured.
Retain the assumption check
Prepare an original calculation record with the balance equation, assumed neglected terms and the root retained. A negative concentration root is physically inadmissible for this constructed inventory. If another acid, salt or significant water contribution is present, the one-equilibrium model may be incomplete.
This guide evaluates a mathematical approximation, not a validated pH prediction or reagent instruction. Keep the selected model separate from actual sample conditions. The reader decision is whether an approximate result remains consistent with its stated small-dissociation assumption and the intended precision.
Solution review worksheet
This blank worksheet is for your own project. It contains no H M machine trial result.
| Question | Record to retain |
|---|---|
| Which equilibrium is modeled? | One specified monoprotic acid |
| What was neglected? | Initial hydrogen, activity effects and other stated terms |
| What compares with c? | The calculated dissociation x and its fraction of the initial inventory |
Customer Questions
What is the fictional square-root result?
0.00100 mol/L.
What is the positive quadratic result?
Approximately 0.000995 mol/L.
Does a small fraction establish a universal approval criterion?
No. Required precision and model validity must be assessed separately.
Primary References
These references support the technical principles discussed in this guide. The worked examples and review questions are educational.
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