Chemistry calculator

Weak-Base Equilibrium Calculator

Solve monoprotic weak-base ICE from formal C and Kb or pKb. Charge and mass balance; optional water at 25 °C. Runs locally. Not Henderson–Hasselbalch and not weak-acid ICE.

Instant result

Result

—

Enter values to calculate.

Inputs—

Mode—

Formula—

Trust summary Engine tested · Source checked · 13/13 tests · Production surface contract 4/4 · v1.0.0

Input interpretation: Enter values to calculate.
Result: —
Model: Monoprotic weak-base ICE pH and species from formal C and Kb or pKb.
Scope: Monoprotic B + H2O ⇌ BH+ + OH−
Verification: Engine tested · 13/13 tests · Production surface contract 4/4 · Source checked · v1.0.0
Named expert review: Optional · Not performed
Sources: OpenStax Chemistry 2e — Weak Bases — Equilibrium of a weak base
IUPAC Gold Book — basicity constant — basicity constant
Sources
Evidence: 2 golden · 6 boundary · 5 property · Production surface contract 4/4 · Artifact integrity PASS
Production: Embedded snapshot: STALE · Last attested schema matched 1.0.0 snapshot / local build · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · Public/cache ✓ · Origin ✓ · Live production status PASS (0 stale; 163 CURRENT) @ 2026-09-17T06:27:56.932Z
Semantic contract: PASS

Formulas

Core equations used by this calculator.

ICE with water[OH⁻]³ + Kb[OH⁻]² − (Kw + Kb C)[OH⁻] − Kb Kw = 0

ICE neglecting waterKb = x² / (C − x)

iKw = 1.0×10⁻¹⁴ at 25 °C. This page is not Henderson–Hasselbalch and not weak-acid ICE HA ⇌ H+ + A−.

How to use

Enter formal concentration C

C is the analytical B concentration in mol/L. It must be greater than zero.

Enter pKb or Kb

Give one basicity encoding. Sending both, or sending Ka/pKa, is rejected.

Choose whether to include water

ICE (default) includes Kw at 25 °C. ICE, no water uses the quadratic approximation for [OH−].

Read pH and the ICE species

The solver reuses math.numerical.root. Outputs [OH−], [B], [BH+], [H+], pOH, and α = [BH+]/C.

Example calculations

Common configurations with formula and result.

Ammonia, water neglected

C=0.1 mol/L, Kb=1.8e-5

x = (−Kb + √(Kb² + 4 Kb C)) / 2

[OH−]≈1.333e-3, pH≈11.125

From pKb

C=0.1 mol/L, pKb=5

Kb = 10^(−pKb)

Kb=1e-5; ICE pH from the cubic or quadratic

Weak-Base Equilibrium calculator specification

Version 1.0.0 · Engine tested

Calculation status

Engine tested 13/13 tests · Production surface contract 4/4
Named expert review Not performed
Calculation version 1.0.0

Review policy · Evidence

Definition: Monoprotic B + H2O ⇌ BH+ + OH−. With water: [OH−]³ + Kb[OH−]² − (Kw + Kb C)[OH−] − Kb Kw = 0. Without water: Kb = x²/(C−x).
What it calculates: Monoprotic weak-base ICE pH and species from formal C and Kb or pKb.
Inputs: mode?
C | c | concentration
pKb | Kb
Outputs: pH
pOH
h
oh
B
BH
C
Kb
pKb
fraction_ionized
Formula: [OH−]³ + Kb[OH−]² − (Kw + Kb C)[OH−] − Kb Kw = 0 (mode=ice)
Assumptions: Monoprotic B + H2O ⇌ BH+ + OH−
Activity coefficients ≈ 1
Kw = 1e-14 at 25 °C when mode=ice
Not Henderson–Hasselbalch
Not weak-acid ICE
Not pH = −log10[H+] identities
Not polyprotic, not titration
Units: mol/L
pH
pKb
Boundary conditions: missing C → MISSING_REQUIRED_INPUT
C ≤ 0 or Kb ≤ 0 → VALUE_MUST_BE_POSITIVE
pKb and Kb together, or Ka/pKa, or HA/A → MIXED_INPUT_ENCODING
hh_ph is not a mode on this page
Example: C=0.1 Kb=1.8e-5 mode=ice_no_water → x=(−Kb+√(Kb²+4 Kb C))/2
Validation cases: 3 published on this page · 13/13 tests · Production surface contract 4/4 · View evidence
C=0.1 Kb=1.8e-5 mode=ice_no_water → oh = (−Kb+√(Kb²+4 Kb C))/2
C=0.1 pKb=5 → pKb=5, model=weak_base_ice
Kb=1e-5 → MISSING_REQUIRED_INPUT
Sources: OpenStax Chemistry 2e — Weak Bases — Equilibrium of a weak base
Supports: Kb = [BH+][OH−]/[B]; ICE from formal C; dilute water may include Kw
IUPAC Gold Book — basicity constant — basicity constant
Supports: Kb is the equilibrium constant for B + H2O ⇌ BH+ + OH−
Calculation version: 1.0.0

Background

Interpretation and common distinctions.

Compute monoprotic weak-base ICE from formal concentration and Kb.

Supported and not supported

Supported — B + H2O ⇌ BH+ + OH− from C and Kb or pKb; optional Kw at 25 °C · API chemistry.equilibrium.weak_base

Not supported — weak-acid ICE, Henderson–Hasselbalch, pH=−log10[H+] identities, polyprotic, activity coefficients, titration

Agent / API notes

Capability id: chemistry.equilibrium.weak_base · tool id: weak-base-equilibrium · pin 1.0.0.

{ "mode": "ice", "C": 0.1, "Kb": 1.8e-5 }

Alternate encoding: { "C": 0.1, "pKb": 4.75 }. Modes: ice (default, includes water), ice_no_water. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE, MIXED_INPUT_ENCODING, INVALID_MODE, NO_PHYSICAL_ROOT.

Calculator URL is /calc/chemistry/weak-base-equilibrium. Weak-acid ICE stays on /calc/chemistry/weak-acid-equilibrium. Buffer pH stays on /calc/chemistry/henderson-hasselbalch. Water-ion identities stay on /calc/chemistry/ph.

Other calculators in this family: Weak-acid ICE, Henderson–Hasselbalch, pH .

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Frequently asked questions

Key distinctions behind the calculation.

Is this a weak-acid ICE?

No. HA ⇌ H+ + A− from formal C and Ka is /calc/chemistry/weak-acid-equilibrium. This page is B + H2O ⇌ BH+ + OH− from C and Kb. Sending Ka or pKa is MIXED_INPUT_ENCODING.

Is this Henderson–Hasselbalch?

No. Buffer pH from a given pair is /calc/chemistry/henderson-hasselbalch. This page solves ICE from formal C and Kb.

Is this pH = −log10[H+]?

No. That identity is /calc/chemistry/ph. This page finds [OH−] from charge and mass balance, then reports pH = 14 − pOH at 25 °C.

Where does this run?

Locally in the browser by default. REST and MCP call the same chemistry-engine weak-base ICE wrapper, which reuses math.numerical.root.