# pH calculator for acids, bases and buffers

> Calculate pH, pOH, [H⁺] and [OH⁻] from a concentration, a strong acid or base, a weak acid's Ka or pKa, or a Henderson–Hasselbalch buffer.

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pH is the negative base-10 logarithm of the hydrogen-ion concentration, pH = −log₁₀[H⁺]. At 25 °C the ion product of water, Kw, is 1.0 × 10⁻¹⁴, so pH + pOH = 14. Strong acids and bases are treated as fully dissociated, with water's own ions included; weak acids are solved exactly from Ka with the quadratic x² + Ka·x − Ka·C = 0; buffers use the Henderson–Hasselbalch equation.

The default, 0.1 mol/L acetic acid with Ka = 1.8 × 10⁻⁵, gives pH 2.88 with 1.33 % of the acid ionised. The √(Ka·C) shortcut taught in class gives pH 2.872, because it overstates [H⁺] by 0.67 %.

Concentrations stand in for activities, which works best for dilute solutions. Results below pH 0 or above 14 are possible for concentrated acids and bases, but there the simple formula is only an estimate.

## 입력

- **Start from** (선택 항목: [H⁺] concentration, [OH⁻] concentration, pH value, Strong acid concentration, Strong base concentration, Weak acid (Ka), Buffer (Henderson–Hasselbalch))
- **Concentration**
- **Concentration unit** (선택 항목: µmol/L, mmol/L, mol/L)
- **H⁺ or OH⁻ released per formula unit**: 2 for Ba(OH)₂; H₂SO₄'s second proton is only partly dissociated
- **pH**
- **Acid strength given as** (선택 항목: Ka, pKa)
- **Ka**
- **pKa**
- **Conjugate base [A⁻]**
- **Weak acid [HA]**

## 결과

- pH — 주요 결과
- pOH
- [H⁺] (mol/L)
- [OH⁻] (mol/L)
- Solution is
- pH with the √(Ka·C) shortcut
- Shortcut error in [H⁺]
- Fraction ionised

## 공식

$$
\text{pH} = -\log_{10}[\mathrm{H^+}],\ \text{pH} + \text{pOH} = 14;\quad x^2 + K_a x - K_aC = 0;\quad \text{pH} = \text{p}K_a + \log_{10}\frac{[\mathrm{A^-}]}{[\mathrm{HA}]}
$$

## 계산 예제

### [H⁺] = 0.001 mol/L

- Start from: [H⁺] concentration
- Concentration: 0.001
- Concentration unit: mol/L
- **pH: 3.00**
- **pOH: 11.00**
- **Solution is: Acidic**
- 검증 출처: −log₁₀(10⁻³) = 3; pOH = 14 − 3

### pH 7 is neutral

- Start from: pH value
- pH: 7
- **[H⁺]: 1 × 10⁻⁷ mol/L**
- **[OH⁻]: 1 × 10⁻⁷ mol/L**
- **Solution is: Neutral**
- 검증 출처: 10⁻⁷ mol/L at 25 °C (Kw = 10⁻¹⁴)

### 0.01 M HCl

- Start from: Strong acid concentration
- Concentration: 0.01
- Concentration unit: mol/L
- H⁺ or OH⁻ released per formula unit: 1
- **pH: 2.00**
- 검증 출처: Python 3.8 decimal: [H⁺] = (C + √(C² + 4Kw))/2 = 0.010000000001 ⇒ pH 2.0000

### Very dilute HCl (1e-8 M) is still acidic

- Start from: Strong acid concentration
- Concentration: 1e-8
- Concentration unit: mol/L
- H⁺ or OH⁻ released per formula unit: 1
- **pH: 6.98**
- **[H⁺]: 1.05125 × 10⁻⁷ mol/L**
- 검증 출처: Python 3.8 decimal: [H⁺] = (10⁻⁸ + √(10⁻¹⁶ + 4×10⁻¹⁴))/2 = 1.0512492×10⁻⁷ ⇒ pH 6.97829 (not 8)

### 0.1 M acetic acid, Ka = 1.8e-5

- Start from: Weak acid (Ka)
- Concentration: 0.1
- Concentration unit: mol/L
- Acid strength given as: Ka
- Ka: 1.8e-5
- **pH: 2.88**
- **pH with the √(Ka·C) shortcut: 2.872**
- **Shortcut error in [H⁺]: 0.67%**
- 검증 출처: Python 3.8 decimal: x = (−Ka + √(Ka² + 4KaC))/2 = 1.33267×10⁻³ ⇒ pH 2.87528; √(KaC) ⇒ 2.87236

### Buffer with [A⁻] = 2[HA]

- Start from: Buffer (Henderson–Hasselbalch)
- pKa: 4.76
- Conjugate base [A⁻]: 0.2 mol/L
- Weak acid [HA]: 0.1 mol/L
- **pH: 5.06**
- 검증 출처: Python 3.8 decimal: 4.76 + log₁₀2 = 5.0610300

## 자주 묻는 질문

### How do you calculate pH from concentration?

For a strong acid, [H⁺] equals the acid concentration times the protons each unit releases, and pH = −log₁₀[H⁺]: 0.01 M HCl has pH 2.00. For a strong base, take pOH = −log₁₀[OH⁻] and subtract it from 14: 0.005 M Ba(OH)₂ releases 0.01 M OH⁻, so pOH is 2 and pH is 12. Weak acids only partly ionise, so they also need Ka.

### Why is the pH of pure water 7?

Water ionises slightly, H₂O ⇌ H⁺ + OH⁻, and at 25 °C the product [H⁺][OH⁻] equals Kw = 1.0 × 10⁻¹⁴. In pure water the two concentrations are equal, so each is 10⁻⁷ mol/L and the pH is 7. Kw grows with temperature: at 50 °C pKw is 13.26, so neutral water has pH 6.63. This calculator uses the 25 °C value.

### What is the difference between Ka and pKa?

Ka is the acid dissociation constant, [H⁺][A⁻]/[HA] at equilibrium, and pKa = −log₁₀Ka. A lower pKa means a stronger acid, and each unit of pKa is a factor of 10 in Ka. Acetic acid has pKa 4.76, so Ka = 1.74 × 10⁻⁵ (often rounded to 1.8 × 10⁻⁵); hydrofluoric acid, Ka = 6.8 × 10⁻⁴, has pKa 3.17.

### When is the Henderson–Hasselbalch equation accurate?

pH = pKa + log₁₀([A⁻]/[HA]) holds when the acid and its conjugate base are both far more concentrated than Ka and [H⁺], and their ratio lies between 0.1 and 10, which keeps the pH within one unit of pKa. Outside that ratio the buffer has little capacity left, and the calculator warns you. Equal concentrations give pH = pKa, so a 1:1 acetate buffer sits at 4.76.

### Can pH be negative?

Yes. A 2 mol/L solution of a strong acid such as HCl has [H⁺] of about 2 mol/L, and −log₁₀2 gives pH −0.30. At concentrations like this, ion activities differ markedly from concentrations, so a pH electrode reads a different value. Treat any calculated pH below 0 or above 14 as an estimate rather than a measurement.

### “pH calculator for acids, bases and buffers”의 정확도는 어느 정도인가요?

정확도는 입력값과 계산 방법의 가정에 따라 달라집니다. 십진 연산은 유효숫자 50자리를 사용하지만, 추정값·수치해석 방법·원본 데이터의 정밀도는 더 낮을 수 있습니다. 표시값을 반올림해도 이러한 한계는 사라지지 않습니다. 독립적인 출처의 풀이와 대조한 계산 예시: 8. 예를 들어 “[H⁺] = 0.001 mol/L”은 −log₁₀(10⁻³) = 3; pOH = 14 − 3와 대조해 확인합니다.

### 이 계산 방법의 출처는 무엇인가요?

OpenStax Chemistry 2e, §14.2 pH and pOH; §14.3 Relative strengths of acids and bases; §14.6 Buffers; IUPAC Gold Book — pH; ionic product of water (Kw = 1.0 × 10⁻¹⁴ at 25 °C).

## 출처

- [OpenStax Chemistry 2e, §14.2 pH and pOH; §14.3 Relative strengths of acids and bases; §14.6 Buffers](https://openstax.org/books/chemistry-2e/pages/14-2-ph-and-poh)
- [IUPAC Gold Book — pH; ionic product of water (Kw = 1.0 × 10⁻¹⁴ at 25 °C)](https://goldbook.iupac.org/terms/view/P04524)