For weak acids at low concentration, the approximation 0.1−x≈0.1 is excellent because α≪1. This avoids solving a quadratic. The key check: α<5% means the approximation is safe.
The textbook value of Ka for acetic acid at 25°C is 1.8×10−5 — our answer matches almost exactly. NEET often quotes this number as a sanity check.
Alternative Method
Use Ostwald’s dilution law: Ka=cα2/(1−α). With c=0.1 M and α=0.01349: Ka=0.1×(0.01349)2/(1−0.01349)≈1.82×10−5. Same answer.
Ostwald’s dilution law in shortcut form: α=Ka/c for weak acids when α<5%. Memorise — saves a quadratic.
Common Mistake
Solving the full quadratic when the approximation is fine. For weak acids (Ka≪c), the linear approximation gives the same answer to 3 significant figures and saves time.
Forgetting to take antilog of pH correctly. pH=2.87 → [H+]=10−2.87, not 10−3 or 0.287. Use a log table or memorise 10−0.87≈0.135.
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