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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.

Cập nhật Ví dụ đã kiểm tra: 8

= 0.000018
Thử
pH
pH: 2.88
Số chữ số thập phân: 2; Gần nhất; nếu cách đều thì về chữ số chẵn
pOH
11.12
[H⁺]
0.00133267mol/L
[OH⁻]
7.50373 × 10⁻¹²mol/L
Solution is
Acidic
pH with the √(Ka·C) shortcut
2.872
Shortcut error in [H⁺]
0.67%
Fraction ionised
1.33%
Uses Kw = 1.0 × 10⁻¹⁴ (25 °C) and concentrations in place of activities.

pH 2.88 (acidic): [H⁺] = 0.001333 mol/L and [OH⁻] = 7.504 × 10⁻¹² mol/L; the acid is 1.33% ionised, and the √(Ka·C) shortcut would be off by 0.67%.

pH scale

Strongly acidicAcidicNear neutralBasicStrongly basic03681114neutral, pure waterpH 2.88
Cách tính S

  1. Equilibrium HA ⇌ H⁺ + A⁻

    Ka=x2C−x⇒x2+Kax−KaC=0,Ka=0.000018, C=0.1K_a = \frac{x^2}{C - x} \Rightarrow x^2 + K_a x - K_aC = 0,\quad K_a = 0.000018,\ C = 0.1

  2. Exact root

    x=−Ka+Ka2+4KaC2=0.00133267 mol/Lx = \frac{-K_a + \sqrt{K_a^2 + 4K_aC}}{2} = 0.00133267\ \mathrm{mol/L}

    Water's own ionisation is neglected — fine while [H⁺] ≫ 10⁻⁷ mol/L.

  3. Compare the shortcut

    KaC=0.00134164⇒pH≈2.8724 (0.673% high in [H+])\sqrt{K_aC} = 0.00134164 \Rightarrow \text{pH} \approx 2.8724\ (0.673\%\ \text{high in }[\mathrm{H^+}])

  4. pOH and [OH⁻] at 25 °C

    pH=2.87528,pOH=14−pH=11.1247,[OH−]=7.50373×10−12 mol/L\text{pH} = 2.87528,\quad \text{pOH} = 14 - \text{pH} = 11.1247,\quad [\mathrm{OH^-}] = 7.50373 \times 10^{-12}\ \mathrm{mol/L}

Giới thiệu pH calculator for acids, bases and buffers

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.

Ví dụ có lời giải

[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

Nguồn đối chiếu: −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

Nguồn đối chiếu: 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

Nguồn đối chiếu: 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

Nguồn đối chiếu: Python 3.8 decimal: [H⁺] = (10⁻⁸ + √(10⁻¹⁶ + 4×10⁻¹⁴))/2 = 1.0512492×10⁻⁷ ⇒ pH 6.97829 (not 8)

Câu hỏi

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” chính xác đến mức nào?

Độ chính xác phụ thuộc vào dữ liệu nhập và giả định của phương pháp. Phép tính thập phân dùng 50 chữ số có nghĩa, nhưng ước lượng, phương pháp số và dữ liệu nguồn có thể kém chính xác hơn; làm tròn khi hiển thị không loại bỏ các giới hạn đó. Ví dụ có lời giải đã đối chiếu với nguồn độc lập: 8. Ví dụ, “[H⁺] = 0.001 mol/L” được kiểm tra bằng −log₁₀(10⁻³) = 3; pOH = 14 − 3.

Phương pháp này lấy từ đâu?

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).

Về công cụ tính này

pH=−log⁡10[H+], pH+pOH=14;x2+Kax−KaC=0;pH=pKa+log⁡10[A−][HA]\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}]}

Nguồn

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

Đã đối chiếu nguồn tham khảo

Công cụ tính này có 8 ví dụ đã giải với đáp án từ các nguồn độc lập. Chúng được chạy trong bộ kiểm thử và bạn cũng có thể chạy tại đây.

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