In a 1.2 M solution of KOH, a strong base, [H3O+] = _____, and [OH−] = _____.

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Question restatement: In a 1.2 M solution of KOH, a strong base, [H3O+] = _____, and [OH−] = _____.

Option-by-option analysis:
Option 1: 8.3 × 10−15 M; 1.2 M. This aligns with the chemistry of a strong base parent solution. For a strong base like KOH, it dissociates completely, so [OH−] equals the concentration of KOH, i.e., 1.2 M. The corresponding hydronium ion concentration is found from Kw = [H3O+][OH−] ≈ 1.0 × 10−14. Therefore [H3O+] = Kw / [OH−] = (1.0 × 10−14) / (1.2) ≈ 8.3 × 10−15 M. So this option matches both the expected [OH−] and the calculated [H3O+].
Option 2: 8.3 × 10−15 M; 1.0 × 10−14 M. Here, [H3O+] is computed correctly from Kw and the listed [OH−], but the stated [OH−] value (1.0 × 10−14 M) is far too small for a full dissociation of 1.2 M KOH; a strong base at 1.2 M would yield a much larger [OH−], specifically 1.2 M, not a fraction of a mole per liter. This reflects a misunderstanding of strong-base dissociation and ionic strength in solution. 
Option 3: 1.2 M; 1.2 M. This would imply [H3O+] equals [OH−], which would give Kw = [H3O+][OH−] = (1.2)(1.2) = 1.44,000, which is not physically meaningful for aqueous solution at standard conditions; moreover, for a basic solution with a strong base, [H3O+] should be much smaller than 1, and certainly not equal to [OH−] when the base concentration is 1.2 M. This option mixes up the fundamental relationship between [H3O+] and [OH−] and misapplies Kw. 
Option 4: 1.2 M; 8.3 × 10−15 M. This reverses the expected roles: [OH−] should be the large value around 1.2 M for a 1.2 M KOH solution, while [H3O+] should be the very small Kw-derived value near 10−14 divided by 1.2, i.e., ~8 × 10−15 M; placing 1.2 M as [H3O+] and the tiny number as [OH−] contradicts the chemistry of a strong base in water and would imply an improbable proton-rich basic solution. This option flips the correct magnitudes and is inconsistent with the established expression Kw = [H3O+][OH−].

Synthesis of the underlying concept: In a solution of a strong base like KOH, dissociation is complete, so [OH−] equals the base concentration (1.2 M). The hydronium concentration is determined by Kw, yielding a very small value around 8 × 10−15 M. The incorrect options fail because they either misstate the extent of dissociation, miscalculate Kw, or invert the expected concentrations, reflecting common conceptual mistakes about acid-base equilibrium.

CHM-1020-LD01.2025SU Quiz 4-Acids and bases

In a 1.2 M solution of KOH, a strong base, [H3O+] = _, and [OH−] = _.

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