BPSC 71st CCE Prelims General Studies · Question 131 of 150

Correct — A, 1.0. Hydrochloric acid is a strong, monoprotic acid: in dilute aqueous solution it dissociates essentially completely, HCl → H⁺ + Cl⁻. Normality counts equivalents per litre, and for an acid one equivalent is one mole of donatable H⁺, so a 0.1 N solution of any strong acid delivers 0.1 mol of hydrogen ions per litre. For HCl there is not even a conversion to do — it has a single ionisable hydrogen, so its n-factor is 1 and 0.1 N is simply 0.1 M. Put [H⁺] = 0.1 = 1 × 10⁻¹ mol/L into Sørensen's definition, pH = −log₁₀[H⁺] = −log₁₀(10⁻¹) = 1.0. The Commission published exactly this working when it disposed of candidate objections on 31 October 2025: −log(0.1) = −log(10⁻¹) = 1. Two independent checks confirm it. First, at 25 °C pOH = 14 − 1 = 13, so [OH⁻] = 10⁻¹³ mol/L — vanishingly small, as it must be in a decinormal strong acid. Second, the physical analogue: human gastric juice is roughly 0.1 M hydrochloric acid and measures about pH 1.5–3.5, the same order of magnitude as this solution. The word 'approximately' in the stem is doing honest work, because pH is strictly defined on hydrogen-ion activity rather than concentration, and the mean ionic activity coefficient of 0.1 molal HCl is about 0.80 — so a real electrode reads close to 1.1, not an exact 1.00. Note also what the arithmetic quietly assumes: complete dissociation, which is legitimate only because HCl is strong. Had the stem said 0.1 N acetic acid (Ka = 1.8 × 10⁻⁵), [H⁺] would be √(Ka·C) ≈ 1.3 × 10⁻³ M and the pH about 2.9.

• (b)11.0 — pH 11 is alkaline — a solution with [H⁺] = 10⁻¹¹ mol/L, ten billion times poorer in hydrogen ions than this one. It is roughly the pH of 0.001 M sodium hydroxide or of household ammonia. No acid can read above 7 at 25 °C, and no arithmetic on 0.1 produces 11: even the pOH of this solution, for the candidate who subtracts on the wrong side of pH + pOH = 14, is 13.
• (c)10 — Also alkaline, and the sharpest trap in the set, because it differs from the correct option only in where the decimal point sits — '1.0' against '10'. A candidate racing through a block of ten numericals can do the sum perfectly and still tick the wrong box. pH 10 means [H⁺] = 10⁻¹⁰ mol/L, about a billion-fold less acidic than 0.1 N HCl; milk of magnesia sits near it at about 10.5.
• (d)2.0 — The intelligent wrong answer. pH 2 belongs to 0.01 N (10⁻² M) HCl — exactly one ten-fold dilution away. You land on it by miscounting the exponent, by reading 0.1 as 0.01, or by recalling a school demonstration in which 'dilute HCl' happened to be 0.01 M. A fourth route is to invent a normality-to-molarity halving that HCl never needs: 0.1 N H₂SO₄ is indeed 0.05 M, but it still carries 0.1 mol H⁺ per litre and its pH is also 1.0.

pH is a compressed way of writing hydrogen-ion concentration. The Danish chemist S. P. L. Sørensen introduced it at the Carlsberg Laboratory in Copenhagen in 1909, working on brewing enzymes, to spare chemists from writing numbers like 0.00000001 mol/L; he defined pH = −log₁₀[H⁺], and modern IUPAC practice refines the bracket to hydrogen-ion activity, which departs from concentration only in strong or concentrated solutions. Because the definition is a base-ten logarithm, one pH unit is a ten-fold change in acidity: pH 3 is ten times more acidic than pH 4 and a hundred times more acidic than pH 5. The familiar 0–14 range is not a law of nature but a consequence of water's own self-ionisation. At 25 °C the ionic product Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴, so pH + pOH = 14, and pure water — where [H⁺] = [OH⁻] = 10⁻⁷ M — is neutral at pH 7. Both boundaries leak: concentrated hydrochloric acid at about 12 M has a negative pH, and because Kw rises with temperature to 5.1 × 10⁻¹³ at 100 °C, boiling water is neutral at pH 6.14 while remaining perfectly neutral. The second half of the question is a units question. Normality is equivalents per litre; molarity is moles per litre; normality = molarity × n-factor, where the n-factor of an acid is the number of replaceable hydrogens. HCl, HNO₃ and CH₃COOH are monoprotic, so N = M; H₂SO₄ is diprotic, so 0.1 M H₂SO₄ is 0.2 N.

Attack this in three moves and it takes under ten seconds. Move one: it is an acid, so at 25 °C its pH must be below 7. That deletes (b) 11.0 and (c) 10 outright without a single calculation — and notice how the option set is built, two acidic values against two alkaline ones, so half the paper falls to one line of reasoning. Move two: settle the concentration unit. This is where the stem hides its work, because the normality-to-molarity step is a trap only for a polyprotic acid; HCl donates one proton, so 0.1 N = 0.1 M and no factor appears anywhere. Move three: express the concentration as a power of ten. 0.1 = 10⁻¹, and for a strong acid pH is just that exponent with the sign flipped, so pH = 1. The single fact that discriminates between the two surviving options is the exponent itself — whether 0.1 is 10⁻¹ or 10⁻². Everything else in the question is scenery. The deeper reason (d) tempts is memory beating reading: many candidates carry 'dilute HCl is about pH 2' from a school lab that used 0.01 M acid, and recall of a remembered number is faster than reading a stem. The durable habit to build is the opposite one — whenever a pH item quotes a strong acid at a clean power of ten, do not calculate at all, just read the exponent; and whenever it names a weak acid, stop, because the shortcut collapses.

• pH was defined by S. P. L. Sørensen at the Carlsberg Laboratory, Copenhagen, in 1909 as pH = −log₁₀[H⁺]; because it is a base-ten logarithm, every whole pH unit is a ten-fold change in hydrogen-ion concentration.
• At 25 °C the ionic product of water Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴, which is why pH + pOH = 14 and pure water is neutral at pH 7; Kw climbs to 5.1 × 10⁻¹³ at 100 °C, where neutral water reads pH 6.14.
• Normality is equivalents per litre and one acid equivalent is one mole of donatable H⁺, so for any strong acid pH = −log(Normality): 0.1 N H₂SO₄ (= 0.05 M) also has pH 1.0. The N-versus-M distinction bites only when the stem quotes molarity — 0.1 M H₂SO₄ is 0.2 N and its pH is about 0.7.
• 0.1 N HCl — 'decinormal', N/10 — is a standard laboratory titration strength: pH 1.0, pOH 13, [OH⁻] = 10⁻¹³ mol/L. Human gastric juice is roughly 0.1 M HCl and measures about pH 1.5–3.5.
• The strong-acid shortcut fails for weak acids, where [H⁺] = √(Ka × C): 0.1 M acetic acid (Ka = 1.8 × 10⁻⁵) gives [H⁺] ≈ 1.3 × 10⁻³ M and pH ≈ 2.9 — almost two whole units away from 0.1 M HCl at the same concentration.

• Reading 0.1 as 10⁻² instead of 10⁻¹ and answering pH 2 — the error the option set is built to catch
• Ticking '10' instead of '1.0' in a hurry; the two options differ only by the position of a decimal point
• Applying the strong-acid shortcut to a weak acid — 0.1 M acetic acid is pH ≈ 2.9, not 1.0

BPSC sets this as a bare one-step numerical inside a run of physics-and-chemistry sums (Q121–Q131 of this very paper) — substitute, read the exponent, one mark in ten seconds — and the Commission even published the arithmetic itself in its remarks. UPSC has not set a pH computation in Prelims for decades; when it touches the same syllabus line it tests the consequence instead of the calculation: the 7.35–7.45 range of human blood in 2008, why an aqueous copper sulphate solution is acidic in 2001, or acidophile microbes surviving below pH 3 in 2023.

• practice — not a real PYQ

  At 25 °C, the pH of a 0.01 M aqueous solution of NaOH is approximately

  • (a)2
  • (b)10
  • (c)12
  • (d)14

  Answer(c) 12 — NaOH is a strong base, so [OH⁻] = 10⁻² M and pOH = 2; since pH + pOH = 14 at 25 °C, pH = 12. Answering 2 is the classic slip of quoting the pOH instead of the pH.

• practice — not a real PYQ

  Assuming complete dissociation of both protons, the pH of a 0.1 M solution of H₂SO₄ at 25 °C is closest to

  • (a)0.7
  • (b)1.0
  • (c)1.3
  • (d)2.0

  Answer(a) 0.7 — 0.1 M H₂SO₄ is 0.2 N, so [H⁺] = 0.2 mol/L and pH = −log(0.2) ≈ 0.70. The answer is 1.0 only if the stem says 0.1 N, because normality already counts hydrogen-ion equivalents.