Q.Calculate pH of a 1.0 × 10⁻⁸ M solution of HCl.
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Hydrogen Ion Concentration and pH
Imagine you have a glass of pure water. It looks simple, but inside, a tiny fraction of water molecules are constantly splitting apart and re-forming. This splitting creates two kinds of charged particles: a hydrogen ion (H+) and a hydroxide ion (OH−). In pure water, these two are perfectly balanced — there are exactly as many H+ as OH−.
Now, if you add something like lemon juice (an acid), you increase the number of hydrogen ions. The balance tips: more H+ than OH−. If you add baking soda (a base), you decrease H+ or increase OH−, and the balance tips the other way.
The question is: how do we measure this imbalance in a simple, practical way? The numbers of H+ ions are incredibly tiny — in pure water, only about 1 in every 10 million water molecules is split at any moment. Writing these numbers directly (like 0.0000001 moles per litre) is clumsy. That's where pH comes in.
The Precise Definition
pH is a mathematical shortcut. It stands for "power of hydrogen" (from the French puissance d'hydrogène).
pH=−log10[H+]
where [H+] is the concentration of hydrogen ions in moles per litre (mol/L).
The logarithm base 10 does two things at once:
- It compresses a huge range of numbers (from 10−14 to 100) into a manageable scale of 0 to 14.
- The negative sign flips the direction: higher [H+] gives a lower pH, and lower [H+] gives a higher pH.
What the Numbers Mean
| [H+] (mol/L) | pH | Example |
|---|---|---|
| 10−1 | 1 | Stomach acid |
| 10−3 | 3 | Lemon juice |
| 10−7 | 7 | Pure water (neutral) |
| 10−9 | 9 | Baking soda solution |
| 10−13 | 13 | Household bleach |
Notice the pattern: each step of 1 in pH means a tenfold change in [H+]. A solution of pH 3 has 10 times more H+ than pH 4, and 100 times more than pH 5.
The Key Insight
pH is not a measure of "how acidic" something is in a vague sense — it is a precise, logarithmic measure of the actual number of hydrogen ions present. The scale runs from 0 (most acidic, highest [H+]) to 14 (most basic, lowest [H+]), with 7 being neutral. …
The key idea is that at very low acid concentrations, the autoionization of water contributes significantly to [H+], so it cannot be ignored.
Step 1: HCl is a strong acid, so it dissociates completely, giving 1.0×10−8M of H+ from the acid.
Step 2: Water also contributes x M of H+ (and OH−). The total [H+]=10−8+x, and [OH−]=x.
Step 3: Use the water dissociation constant:
(10−8+x)(x)=10−14 …
At 10−8 M, the H+ from water is not negligible. A charge balance gives [H+]=1.05×10−7 M, so pH=6.98 — just acidic, not the naïve value of 8.
Taking pH=−log(10−8)=8 is wrong: it would make an acid basic. At this very low concentration the H+ from the autoionisation of water must be included.
1. Charge balance. HCl dissociates fully, so [Cl−]=10−8 M. Electroneutrality requires:
[H+]=[Cl−]+[OH−]=10−8+[OH−]
2. Use Kw. With [OH−]=Kw/[H+] and Kw=10−14:
[H+]=10−8+[H+]10−14⇒[H+]2−10−8[H+]−10−14=0
3. Solve for [H+]. …
Showing the 12 most recent of 25 on this concept.
- CBSE 2026Set ANNUAL1 markMCQQ.NaOH(aq), HCl(aq) and NaCl(aq) have concentration of 10^-3 M each. Their pH will be respectively(a) 10, 6, 2(b) 11, 3, 7(c) 10, 3, 7(d) 10, 4, 7
›Reveal solutionSolution
NaOH and HCl are both strong electrolytes that fully dissociate, giving [OH-] or [H+] equal to the stated concentration; NaCl is a neutral salt (from a strong acid and strong base) and does not affect pH.
NaOH (strong base), 10^-3 M:
Fully dissociates: [OH-] = 10^-3 M
pOH = -log(10^-3) = 3
pH = 14 - pOH = 14 - 3 = 11
HCl (strong acid), 10^-3 M:
Fully dissociates: [H+] = 10^-3 M
pH = -log(10^-3) = 3
…
- CBSE 2026Set ANNUAL1 markMCQQ.The pH value of gastric juice is -(a) -3(b) -1.2(c) -2(d) -4
›Reveal solutionSolution
The pH of gastric juice is commonly quoted as approximately 1.2 (highly acidic); of the given options, (b) -1.2 matches this value in magnitude.
Gastric juice, secreted by the stomach's gastric glands, contains hydrochloric acid (HCl) at a concentration that gives it a strongly acidic pH, essential for activating pepsin and digesting food. NCERT's own table of pH of some common fluids lists gastric juice at pH ≈ 1.2.
…
- CBSE 2026Set ANNUAL1 markMCQQ.A solution with a pH value less than 7 is:(a) Basic(b) Acidic(c) Saline(d) Neutral
›Reveal solutionSolution
pH < 7 = acidic, pH = 7 = neutral, pH > 7 = basic, on the standard 0-14 pH scale.
pH is defined as pH = -log10[H3O+]. A lower pH corresponds to a higher concentration of hydronium (H3O+) ions. Pure water at 25°C has pH = 7 and is neutral. Solutions with pH less than 7 have a higher H+ concentration than pure water and are called acidic; solutions with pH greater than …
- CBSE 2026Set ANNUAL1 markMCQQ.The pH of an aqueous solution is 4.0, the value of its pOH would be(a) 4.0(b) 6.0(c) 8.0(d) 10.0
›Reveal solutionSolution
pOH = 14 − pH = 14 − 4 = 10.
For any aqueous solution at 25°C, the ionic product of water gives pH + pOH = 14. …
- CBSE 2026Set ANNUAL1 markQ.What is the value of Kw at 25 C ?
›Reveal solutionSolution
The ionic product of water Kw at 25 C is 1.0 x 10^-14.
Water self-ionises: H2O ⇌ H+ + OH-. The ionic product Kw = [H+][OH-]. At 25 C pure water has [H+] = [OH-] = 1.0 x 10^-7 mol L^-1, so:
Kw = (10^-7)(10^-7) = 1.0 x 10^-14 mol^2 L^-2. …
- CBSE 2025Set ANNUAL1 markMCQQ.With increase in temperature, ionic product of water(a) Increases(b) Decreases(c) Remains unaffected(d) Zero
›Reveal solutionSolution
Kw (the ionic product of water) increases with rising temperature.
Water's self-dissociation (2H2O ⇌ H3O+ + OH-) is an endothermic process. By Le Chatelier's principle, increasing temperature shifts an endothermic equilibrium further towards the products, increasing the concentrations of H3O+ and OH-, a …
- CBSE 2025Set ANNUAL1 markMCQQ.Which of the following has lowest pH value?(a) 1M HCl(b) 1M NaOH(c) 1M H2SO4(d) 1M C2H5OH
›Reveal solutionSolution
1M H2SO4 has the lowest pH because, being diprotic, it furnishes roughly twice the [H+] of 1M HCl.
HCl and H2SO4 are both strong acids, but HCl is monoprotic (1M HCl gives [H+] ≈ 1M, pH = 0) while H2SO4 is diprotic (1M H2SO4 gives [H+] ≈ 2M, since both protons ionise essentially completely, pH = -log(2) ≈ -0.3). NaOH is a strong base (high pH, ~14), and ethanol (C2H5OH) i …
- CBSE 2025Set ANNUAL1 markMCQQ.If 50 ml of 0.1 M HCl and 50 ml of 0.2 M NaOH are mixed then the pH of the resulting solution will be(a) 1.30(b) 4.2(c) 12.70(d) 11.70
›Reveal solutionSolution
Mixing 50 mL of 0.1M HCl with 50 mL of 0.2M NaOH leaves excess NaOH, giving pH = 12.70.
Moles of HCl = 0.050 L x 0.1 mol/L = 0.005 mol.
Moles of NaOH = 0.050 L x 0.2 mol/L = 0.010 mol.
HCl + NaOH → NaCl + H2O consumes 0.005 mol of each, leaving excess NaOH = 0.010 - 0.005 = 0.005 mol.
…
- CBSE 2025Set ANNUAL1 markMCQQ.The value of pH of 0.1 M NaOH solution is equal to(a) 13(b) 1.2(c) 5.0(d) 1.0
›Reveal solutionSolution
NaOH is a strong base (100% dissociated); its [OH-] equals its molarity, so pOH = 1 and pH = 14 - pOH = 13.
Step 1 — Dissociation: NaOH is a strong base, meaning it dissociates completely in water:
NaOH -> Na+ + OH-
Since dissociation is 100%, the hydroxide ion concentration equals the given molarity:
[OH-] = 0.1 M = 10^-1 M
Step 2 — Calculate pOH:
pOH = -log10[OH-] = -log10(10^-1) = 1
…
- CBSE 2025Set ANNUAL1 markMCQQ.If concentration of hydrogen ion [H+] changes by a factor of 100, then the value of pH changes by:(a) one unit(b) 2 unit(c) 10 unit(d) 100 unit
›Reveal solutionSolution
Since pH is a logarithmic (base 10) scale, multiplying [H+] by 100 shifts pH by exactly log10(100)=2 units.
By definition:
pH=−log10[H+]
Let the initial concentration be [H+]1 and the new concentration be [H+]2=100×[H+]1 (changed by a factor of 100).
pH1=−log[H+]1
pH2=−log(100×[H+]1)=−log(100)−log[H+]1=−2+pH1
ΔpH=pH1−pH2=2
…
- CBSE 2025Set hz1 markMCQQ.Select the correct one: The hydronium ion concentration i.e. [H3O+] of a solution is 2x10^-5 M, its pH is:(a) 5(b) 7(c) 4.7(d) 3
›Reveal solutionSolution
pH = -log[H3O+]; substituting [H3O+] = 2x10^-5 M gives pH = 4.7.
By definition: pH = -log10[H3O+]
Given [H3O+] = 2 x 10^-5 M.
pH = -log(2 x 10^-5)
= -[log 2 + log 10^-5] …
- CBSE 2024Set ANNUAL1 markMCQQ.The pH of 10^-4 M NaOH solution is(a) 4(b) 10(c) 12(d) 2
›Reveal solutionSolution
10⁻⁴ M NaOH has pOH = 4, so pH = 10.
NaOH is a strong base, fully dissociated, so [OH−]=10−4 M.
…
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