General Chemistry · Environmental Chemistry · ACID RAIN

The pH of rainwater
natural acidity (CO₂) and acid rain (SO₂)

What sets the pH of rainwater? Change the atmospheric CO₂ level and the amount of strong acid (H₂SO₄, HNO₃) formed from SO₂ and NOₓ. The simulation calculates the pH of rainwater and the source of its [H⁺] (carbonic acid vs strong acid) with exact equations from Henry's law and the charge balance. Predict first.

Learning objectives After this activity you can …
find and explain the pH of unpolluted rainwater from the dissolution of CO₂ (Henry's law) and the ionization of carbonic acid.explain why unpolluted rainwater is weakly acidic, using the dissolution of CO₂ (Henry's law) and the ionization of carbonic acid.
calculate the dissolved CO₂ concentration and the pH of rainwater from the atmospheric CO₂ level.
compare the effects of more CO₂ and of strong acids (H₂SO₄, HNO₃) on rainwater pH by splitting [H⁺] into its sources.compare how much more CO₂ and strong acids (H₂SO₄, HNO₃) lower the pH by splitting [H⁺] into its sources.
Progress 0% · Predict → Observe → Check → Complete
Estimated time 20–25 minPrerequisites: Henry's law · Ka of a weak acid · pH = −log[H⁺]—
Level Basic Standard Advanced
Key summary Three key ideas
  1. Atmospheric CO₂ dissolves in rainwater in proportion to its partial pressure (Henry's law).Atmospheric CO₂ dissolves in rainwater in proportion to its partial pressure (Henry's law), and the dissolved CO₂ (H₂CO₃) ionizes as a weak acid and releases H⁺.
  2. In the atmosphere, SO₂ and NOₓ become strong acids such as H₂SO₄ and HNO₃, which dissolve in rainwater.In the atmosphere, SO₂ and NOₓ become strong acids such as H₂SO₄ and HNO₃, and a strong acid releases almost all of its H⁺ for the amount dissolved.
  3. pH is the negative common (base-10) logarithm of [H⁺] (pH = −log[H⁺]).pH is the log of [H⁺], so how many times [H⁺] is multiplied sets the size of the pH change.

Rainwater conditions

CO₂ 400 ppm · no strong acid
CO₂(g) ⇌ CO₂(aq) · CO₂(aq) + H₂O(l) ⇌ H⁺(aq) + HCO₃⁻(aq)
k_H 3.4×10⁻⁴ mol L⁻¹ kPa⁻¹ (= 3.4×10⁻⁴ mol/m³·Pa) · Ka1 4.3×10⁻⁷
P_CO₂ = 0.0405 kPa (total 101.3 kPa)
The pH and the split of [H⁺] into sources are shown after you submit your prediction.
Dissolved CO₂ [CO₂(aq)]— Rainwater pH (exact)— [H⁺]— Strong-acid share (SO₄²⁻, HSO₄⁻, NO₃⁻ charge)— Carbonic-acid share (HCO₃⁻, CO₃²⁻ charge)— Water autoionization share (OH⁻)— ΔpH vs clean rainwater at CO₂ 400 ppm—

Rainwater pH vs strong-acid concentration

The pH curve is shown after you submit your prediction.

How to use: focus the graph and change the strong-acid concentration with the arrow keys. The strong-acid slider does the same.

Solid: current CO₂ level · dotted: CO₂ 280 ppm (pre-industrial) · thin lines: pH 7 and 5.6—
Entry check Before you start — prerequisites and key terms

According to Henry's law, at constant temperature the amount of a gas that dissolves in water is proportional to what?

The partial pressure of that gasIt is always constant, whatever the volume of waterThe molar mass of that gas
Key terms

Henry's law: S = k_H·P; the dissolved gas concentration is proportional to the partial pressure of that gas. · ppm (parts per million): for gases, mole fraction × 10⁶; partial pressure = mole fraction × total pressure. · Carbonic acid: H₂CO₃ formed from dissolved CO₂ and water; a weak acid (Ka1 4.3×10⁻⁷). · Acid rain: rain whose pH is lowered by sulfuric and nitric acids formed from SO₂ and NOₓ. · Charge balance: total positive charge = total negative charge in the solution.

Predict Think first, before you observe

Start with rainwater in equilibrium with air at CO₂ 400 ppm. (a) The atmospheric CO₂ doubles to 800 ppm. (b) 5.0×10⁻⁵ M H₂SO₄ dissolves in the rainwater. What happens to the pH in each case?

(a) lowers it much more; (b) lowers it only a little (b) lowers it much more; (a) does not lower it even by 0.2 Both lower it by a similar amount, about 0.5 each (a) does not change the pH; only (b) lowers it
ConfidenceMedium
The explanation opens after you lock in a prediction
H₂SO₄ (from SO₂)HNO₃ (from NOₓ)
280 ppm800 ppm
0 · 1.0×10⁻⁷ M1.0×10⁻⁴ M

Rainwater is in equilibrium with CO₂ (open system), so [CO₂(aq)] = k_H·P_CO₂ is fixed. The pH is found by solving the charge balance [H⁺] = [HCO₃⁻] + 2[CO₃²⁻] + [OH⁻] + (strong-acid anion charge) without approximation. The first step of H₂SO₄ ionizes completely; the second step is calculated with Ka2. Total pressure 101.3 kPa, 25 °C.

Clean rainwater has a pH of about 5.6

At CO₂ 400 ppm, P_CO₂ = 0.0405 kPa and the dissolved CO₂ is 1.38×10⁻⁵ M. Carbonic acid is a weak acid, so [H⁺] ≈ √(Ka1·[CO₂(aq)]) = 2.4×10⁻⁶ M, pH 5.61. Doubling CO₂ makes [H⁺] only √2 times (about 1.4 times) larger, so the pH drops by only 0.15. The amount dissolved is proportional to pressure, but the fraction that ionizes becomes smaller.

[H⁺]² ≈ Ka1·k_H·P_CO₂ (Kw neglected)

Acid rain has a pH of about 4 · strong-acid share

5.0×10⁻⁵ M H₂SO₄ releases about 1.0×10⁻⁴ M H⁺ and lowers the pH to 4.0 (a drop of 1.6 units). With more strong acid, [H⁺] rises and suppresses the ionization of carbonic acid (common-ion effect), so the carbonic-acid share becomes almost 0 and most of the [H⁺] comes from the strong acid. At the same molarity, H₂SO₄ releases about twice as much H⁺ as HNO₃. In the same way, soils with few basic ions are acidified more easily by acid rain.

[H⁺] = [HCO₃⁻] + 2[CO₃²⁻] + [OH⁻] + [HSO₄⁻] + 2[SO₄²⁻]
Limits Limits of this model

The model uses 25 °C, a total pressure of 101.3 kPa and activity coefficients of 1 (dilute solution). Real rainwater contains cations such as NH₄⁺ and Ca²⁺ and organic acids, which can change the pH. At lower temperature more CO₂ dissolves (temperature dependence is not in this model). Constants are reference values (k_H 3.4×10⁻⁴ mol L⁻¹ kPa⁻¹ (= 3.4×10⁻⁴ mol/m³·Pa), H₂CO₃ Ka1 4.3×10⁻⁷ and Ka2 5.6×10⁻¹¹, HSO₄⁻ Ka2 1.2×10⁻²). Compared with literature values, Ka1 is 4.5×10⁻⁷ (3% difference); H₂CO₃ Ka2 4.7×10⁻¹¹ and HSO₄⁻ Ka2 1.0×10⁻² differ by more than 5%, but the calculated pH in this range agrees within 0.01.

Check Formative check — pass all items to complete
Q1—
— — —
Hint

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Q2 · Task—
Now: — · Goal: —
Q3—
Hint

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Q4 · Fill in the blank—
Hint

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Q5 · Apply (advanced, not required for completion)Rainwater in one region has a pH of 4.30. How many times larger is its [H⁺] than that of clean rainwater at CO₂ 400 ppm (pH 5.61)? (whole number)
Reflect Reflect — metacognition · completion

My prediction result: Not predicted yet

Explain in one sentence why the idea "the main cause of acid rain is the increase in CO₂" or "clean rainwater has pH 7" is wrong. Use a concept word (carbonic acid, strong acid, Henry's law, [H⁺]) and a reason word ("because", "so"):

Apply Use the idea in a new context (not required for completion)

Lakes in limestone areas keep their pH even when acid rain falls, but lakes in granite areas become acidic easily. Explain this in one or two sentences, linking it to the role of basic ions such as HCO₃⁻.

Next up: ocean acidification and carbonate equilibria (seawater with HCO₃⁻ buffering), gas solubility and Henry's law, buffer capacity.

COMPLETE · Completed — all checks passed.

Worksheet — The pH of rainwater: natural acidity (CO₂) and acid rain (SO₂)

Name ________ Class ________ Date ________

1. Predict — How much does the rainwater pH drop when CO₂ doubles from 400 ppm to 800 ppm, and when 5.0×10⁻⁵ M H₂SO₄ dissolves in it? Reason for your choice:

2. Calculate — Fill in the table using Henry's law (k_H = 3.4×10⁻⁴ mol L⁻¹ kPa⁻¹ (= 3.4×10⁻⁴ mol/m³·Pa), total 101.3 kPa) and [H⁺] ≈ √(Ka1·[CO₂(aq)]) (Ka1 = 4.3×10⁻⁷).

CO₂ (ppm)P_CO₂ (kPa)[CO₂(aq)] (M)[H⁺] (M)pH
280
400
800

3. Observe — On the axes below (horizontal: log[H₂SO₄], vertical: pH), sketch the pH curves of rainwater at CO₂ 280 ppm and 800 ppm, and mark where the two curves meet.

4. Fill in the blank — Unpolluted rainwater is weakly acidic because [＿＿＿] from the air dissolves in it and forms carbonic acid.

Curve key (teacher copy): solid CO₂ 800 ppm · dashed CO₂ 280 ppm.

Answer key (teacher only · not in the student printout) — 1. doubling CO₂ lowers it by about 0.15; 5.0×10⁻⁵ M H₂SO₄ lowers it by about 1.6 · 2. 280 ppm: 0.0284 kPa, 9.65×10⁻⁶ M, 2.04×10⁻⁶ M, pH 5.69 / 400 ppm: 0.0405 kPa, 1.38×10⁻⁵ M, 2.43×10⁻⁶ M, pH 5.61 / 800 ppm: 0.0811 kPa, 2.76×10⁻⁵ M, 3.44×10⁻⁶ M, pH 5.46 · 3. above 10⁻⁵ M strong acid the two curves almost overlap (the strong acid dominates) · 4. CO₂ (carbon dioxide)
Teacher notes — open the lesson plan

Lesson plan · 5E phase and time

  • Explore and Explain, 20–25 min. Right after the topic of SO₂ and acid rain; a link activity that reviews Henry's law and the pH of weak acids. Whole-class demonstration (?mode=teacher) or individual work.

Demonstration in 3 steps

  • ① No strong acid, CO₂ 280 → 400 → 800 ppm: pH 5.69 → 5.61 → 5.46. Dissolved CO₂ doubles, but the pH changes by only 0.15.
  • ② At CO₂ 400 ppm, H₂SO₄ from 10⁻⁶ → 5×10⁻⁵ M: pH 5.4 → 4.0, strong-acid share above 99%.
  • ③ Switch to HNO₃ at the same concentration: it releases only half as much H⁺, so the pH is about 0.3 higher.

Three key questions

  • "Dissolved CO₂ doubles. Why does [H⁺] not double?"
  • "Why does carbonic acid release almost no H⁺ when there is a lot of strong acid?"
  • "To reduce acid rain, which should be reduced first: CO₂ or SO₂?"

Common misconceptions

  • MC-AR-01 "clean rainwater has pH 7" → confuses pure water with water in equilibrium with air. With no strong acid, even at CO₂ 280 ppm the pH stays near 5.7; show this to correct it.
  • MC-AR-02 "the main cause of acid rain is CO₂" → confuses weak and strong acids. Compare the ΔpH of the two prediction cases side by side (0.15 vs 1.6).

Calculation method (E2 exact equations)

  • [CO₂(aq)] = S = k_H·(ppm × 10⁻⁶)·101.325 kPa (open system). The charge balance h = (Ka1·S + Kw)/h + 2Ka1Ka2·S/h² + A(h), with A = C(h + 2Ks)/(h + Ks) for H₂SO₄ (Ks = 1.2×10⁻²) or C for HNO₃, is solved without approximation by bisection in log space (200 steps). The source split is each term on the right side of the charge balance divided by h.

Reference values and sources

  • Acid rain: unpolluted rain pH about 5.6, acid rain about pH 4, SO₃ + H₂O → H₂SO₄. The exact solution gives 5.61 at 400 ppm and 4.00 with 5.0×10⁻⁵ M H₂SO₄, in agreement.
  • The Henry's law constant of CO₂, 3.4×10⁻⁴ mol m⁻³ Pa⁻¹ (= 3.4×10⁻⁴ mol L⁻¹ kPa⁻¹ (= 3.4×10⁻⁴ mol/m³·Pa)), is used as the reference. Some worked examples imply 3.65×10⁻⁴ (7% higher); this simulation uses the single value 3.4×10⁻⁴ throughout.
  • H₂CO₃ Ka1 4.3×10⁻⁷, Ka2 5.6×10⁻¹¹; H₂SO₄ Ka2 1.2×10⁻².

Literature check (2 sources, checked 2026-10-03)

  • CO₂ k_H: JPL Publication 19-5 (Burkholder et al. 2019) 3.4×10⁻⁴ mol m⁻³ Pa⁻¹; NIST Chemistry WebBook Henry's law table, mol kg⁻¹ bar⁻¹. Agrees with the reference value.
  • H₂CO₃ Ka1: Harned and Davis (1943, J. Am. Chem. Soc. 65, 2030) pK1 6.352; CRC Handbook 84th ed. (reprinted in LibreTexts Table E1) pKa1 6.35 → 4.5×10⁻⁷. 3% difference from the reference 4.3×10⁻⁷.
  • H₂CO₃ Ka2: CRC 84th ed. 4.7×10⁻¹¹ (16% difference from the reference 5.6×10⁻¹¹, both listed). HSO₄⁻ Ka2: CRC 84th ed. 1.0×10⁻², Pitzer, Roy and Silvester (1977, J. Am. Chem. Soc. 99, 4930) 1.05×10⁻² (13–17% difference from the reference 1.2×10⁻², both listed). Using the literature values changes the pH in this range by less than 0.01.
University general chemistry · atmospheric chemistryEngine E2 equation-driven (exact charge balance)Verified: independent Python (mpmath) multi-point comparison
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