Verified calculation capability

Weak-base ICE Calculation Capability

Monoprotic weak-base ICE: B + H2O ⇌ BH+ + OH− from formal C and Kb or pKb. Charge and mass balance; optional water at 25 °C. Reuses math.numerical.root. Not Henderson–Hasselbalch and not weak-acid ICE. · Chemistry · Equilibrium

Capability ID chemistry.equilibrium.weak_base · version 1.0.0

Open calculator REST API MCP Evidence Evidence JSON Review policy

Model

ICE with water

ICE with water: [OH⁻]³ + Kb[OH⁻]² − (Kw + Kb C)[OH⁻] − Kb Kw = 0
ICE neglecting water: Kb = x² / (C − x)

Solve modes: ice · ice no water

Inputs / Outputs

Canonical symbols for this capability. Agent schemas remain the contract.

Symbol	Quantity	Unit	Role
`C`	Formal B concentration in mol/L.	—	input / output
`pKb`	pKb = −log10(Kb). Use pKb or Kb, not both.	—	input / output
`Kb`	Base dissociation constant. Use pKb or Kb, not both.	—	input / output
`pH`	pH	—	output
`pOH`	pOH	—	output
`h`	hydrogen-ion concentration	—	output
`oh`	hydroxide-ion concentration	—	output
`B`	—	—	output
`BH`	—	—	output
`fraction_ionized`	—	—	output
`Kw`	—	—	output
`pKw`	—	—	output
`T`	temperature	°C	output
`model`	—	—	output
`include_water`	—	—	output
`solver`	—	—	output

Assumptions / Validity

Declared scope for this capability. Do not use it outside this domain.

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

Not supported

weak-acid ICE
Henderson–Hasselbalch
pH=−log10[H+] identities
polyprotic
activity coefficients
titration

Example

One numerical check. The calculator page holds worked steps and FAQ.

C=0.1 Kb=1.8e-5 mode=ice_no_water → x=(−Kb+√(Kb²+4 Kb C))/2

Open this example in the calculator

Trust

Review-policy: engine tested — automated tests, sources, version lock, and evidence published. Supplemental to CVP; not Domain Expert Review. See CVP and Review policy.

Tier: Engine tested — catalog token engine_tested
Calculation version: 1.0.0
Evidence tests: 13/13 calculation tests · golden 2/2 · boundary 6/6 · property 5/5
Engine tested: Yes
Source checked: Yes
Supplemental domain review: Not performed
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.0.0 (workspace artifacts agree)

Production attestation: 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
Evidence attested at: 2026-09-17T06:27:56.176Z
Last production check: 2026-09-17T06:27:56.176Z
Public / cache: PASS
Origin: PASS

Call this capability

Human page, REST, and MCP share the same engine and calculation_version. Build verified hashes workspace artifacts only. After deploy, attest:production GETs canonical URLs twice — the public/cached view an Agent actually hits, and origin — including every /capabilities/{id} HTML page. Public Capability HTML version must match catalog before production attestation passes. Live Trust rows above fetch /.well-known/calculatorx-production-attestation.json and the output schema const. Build hashes: release integrity. That proves currently published page / engine / schema / evidence / MCP agree — not that a historical version is independently immutable. Reference Calculation Standard — Production surface contract 4/4.

Tool id: weak-base-equilibrium
Engine: weak-base-equilibrium
REST: POST /api/v1/calc/weak-base-equilibrium
MCP: execute_calculation with capability_id: "chemistry.equilibrium.weak_base"
Agent input schema: Canonical (MCP / Agent)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.0.0)
Versioned output schema: Immutable pin (1.0.0)

References

Human-readable sources plus CVP reference evidence classes.

Sources

Try with an agent

Inspect this capability via same-origin MCP, then call execute_calculation.

curl -sS -X POST 'https://www.calculatorx.com/mcp' \
  -H 'Content-Type: application/json' \
  -H 'MCP-Protocol-Version: 2026-07-28' \
  -H 'Mcp-Method: tools/call' \
  -H 'Mcp-Name: inspect_capability' \
  -d '{"jsonrpc":"2.0","id":1,"method":"tools/call","params":{"name":"inspect_capability","arguments":{"capability_id":"chemistry.equilibrium.weak_base"}}}'

Inspect the trust tier and required assurance level before execution. Pin calculation_version (1.0.0) when reproducibility matters. Full protocol notes: MCP docs.