JEE Main · 2023 · Shift-IIeasyIEQ-009

When the hydrogen ion concentration [H+] changes by a factor of 1000, the value of pH of the solution

Ionic Equilibrium · Class 11 · JEE Main Previous Year Question

Question

When the hydrogen ion concentration [H+][\mathrm{H^+}] changes by a factor of 1000, the value of pH of the solution

Options
  1. a

    Increases by 1000 units

  2. b

    Decreases by 3 units

    ✓
  3. c

    Decreases by 2 units

  4. d

    Increases by 2 units

Correct Answerb

Decreases by 3 units

Detailed Solution

Definition: pH=−log⁡[H+]\mathrm{pH} = -\log[\mathrm{H^+}]

Step 1 — Effect of 1000-fold change in [H+][\mathrm{H^+}]:

If [H+][\mathrm{H^+}] increases by factor 1000: pHnew=−log⁡(1000×[H+])=−log⁡[H+]−log⁡1000=pHold−3\mathrm{pH_{new}} = -\log(1000 \times [\mathrm{H^+}]) = -\log[\mathrm{H^+}] - \log 1000 = \mathrm{pH_{old}} - 3

So pH decreases by 3 units.

Step 2 — Verify: If [H+][\mathrm{H^+}] goes from 10−710^{-7} to 10−410^{-4} (×1000), pH goes from 7 to 4 →\rightarrow decrease of 3 ✓

Answer: Option (2) — Decreases by 3 units

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