For 0.010 M hydrofluoric acid at 25 °C

MATHEMATICS · Subjective · AoPS · Mathematics · Introduction to Inequalities · Which Is Greater?

Problem

For 0.010 M hydrofluoric acid at 25 °C, the small-x approximation gives [H3O+]approx=2.6×10−3 M[H_3O^+]_{\text{approx}} = 2.6 \times 10^{-3}\,\text{M}, whereas solving the exact quadratic yields [H3O+]exact=2.3×10−3 M[H_3O^+]_{\text{exact}} = 2.3 \times 10^{-3}\,\text{M}. Calculate the percent error of the approximation relative to the exact value, and indicate whether the approximation satisfies the 5 % acceptance criterion.

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