chem_formula

Install

/tools install chem_formula
/tools install chem_formula@1.0.0

In a console session, or let the model find it in normal mode: axlr_catalog describes it and axlr_install_tool asks for the same install card. The card reads catalog axlr · chem_formula 1.0.0 · verified once the index signature, the manifest digest and every file digest check out. Then the model runs it with axlr_run_tool chem_formula; each run is approved as a local_exec.

Arguments

One JSON object on stdin, validated against the schema before the program starts.

name	type	required	default	meaning
`formula`	string	no		Ca(OH)2, K4[Fe(CN)6], CuSO4·5H2O, SO4^2-, NH4+. length ≤ 500
`formulas`	array of string	no		items ≥ 1; items ≤ 100
`decimals`	integer	no	`2`	Digits of molar_mass_rounded and mass_percent. ≥ 0; ≤ 6
`masses`	object of ['number', 'string']	no		Atomic weights for elements without a standard atomic weight (Tc, Pm, Po...) or overrides, by symbol

Input schema (JSON)

{
  "type": "object",
  "additionalProperties": false,
  "properties": {
    "formula": {
      "type": "string",
      "maxLength": 500,
      "description": "Ca(OH)2, K4[Fe(CN)6], CuSO4·5H2O, SO4^2-, NH4+"
    },
    "formulas": {
      "type": "array",
      "items": {
        "type": "string",
        "maxLength": 500
      },
      "minItems": 1,
      "maxItems": 100
    },
    "decimals": {
      "type": "integer",
      "minimum": 0,
      "maximum": 6,
      "default": 2,
      "description": "Digits of molar_mass_rounded and mass_percent"
    },
    "masses": {
      "type": "object",
      "additionalProperties": {
        "type": [
          "number",
          "string"
        ]
      },
      "description": "Atomic weights for elements without a standard atomic weight (Tc, Pm, Po...) or overrides, by symbol"
    }
  }
}

Example

Input

{
  "formula": "CuSO4·5H2O"
}

Output (stdout)

{
  "hill": "CuH10O9S",
  "counts": {
    "Cu": 1,
    "S": 1,
    "O": 9,
    "H": 10
  },
  "molar_mass": "249.6770",
  "molar_mass_rounded": "249.68",
  "unit": "g/mol"
}

Files

The command the install card registers is python3 chem_formula.py, run in the workspace with PATH and HOME as its only environment. Each file's SHA-256 is in the signed index; the console checks them before showing the card and again before writing.

chem_formula.py · sha256 752e6b4030954562f4048a4f3574e3c0628649378fb45fe12fc7cad0d81b23bf

#!/usr/bin/env python3
"""Parse a chemical formula and compute element counts, molar mass and mass percent from the
bundled IUPAC/CIAAW abridged standard atomic weights (elements.json, written by
tools/catalog/data/chem_formula.py).

Input (JSON on stdin):
  formula    "Ca(OH)2", "K4[Fe(CN)6]", "CuSO4·5H2O" (also . * • as the hydrate dot),
             "SO4^2-", "NH4+", "Fe+++", "SO4 2-", "2H2O" (leading coefficient)
  formulas   a list of formulas instead of one (at most 100)
  decimals   digits of molar_mass_rounded and mass_percent, default 2 (0-6)
  masses     {"Tc": 98} atomic weights for elements without a standard atomic weight, or to override one
"""
import json
import pathlib
import re
import sys
from decimal import ROUND_HALF_UP, Decimal, InvalidOperation

TABLE = pathlib.Path(__file__).resolve().parent / "elements.json"
DOTS = "·•∙⋅.*"
SUB = str.maketrans("₀₁₂₃₄₅₆₇₈₉", "0123456789")
SUP = str.maketrans("⁰¹²³⁴⁵⁶⁷⁸⁹⁺⁻", "0123456789+-")
SUP_CHARS = "⁰¹²³⁴⁵⁶⁷⁸⁹"
CLOSE = {"(": ")", "[": "]", "{": "}"}


class FormulaError(Exception):
    pass


def fail(message):
    print(json.dumps({"error": message}, ensure_ascii=False))
    sys.exit(2)


def split_charge(text):
    """Return (formula without charge, charge as int)."""
    patterns = [
        (r"\^\{?(\d*)([+-])\}?$", lambda m: (m.group(1), m.group(2))),
        (r"\^\{?([+-])(\d*)\}?$", lambda m: (m.group(2), m.group(1))),
        (r"\s+(\d*)([+-])$", lambda m: (m.group(1), m.group(2))),
    ]
    for pattern, parts in patterns:
        m = re.search(pattern, text)
        if m:
            digits, sign = parts(m)
            size = int(digits) if digits else 1
            return text[:m.start()], size if sign == "+" else -size
    m = re.search(f"([{SUP_CHARS}]*)([⁺⁻])$", text)
    if m:
        digits = m.group(1).translate(SUP)
        size = int(digits) if digits else 1
        return text[:m.start()], size if m.group(2) == "⁺" else -size
    m = re.search(r"(\++|-+)$", text)
    if m:
        size = len(m.group(1))
        return text[:m.start()], size if m.group(1)[0] == "+" else -size
    return text, 0


class Parser:
    def __init__(self, text, known):
        self.text, self.pos, self.known = text, 0, known

    def peek(self):
        return self.text[self.pos] if self.pos < len(self.text) else ""

    def number(self):
        start = self.pos
        while self.peek().isdigit():
            self.pos += 1
        return int(self.text[start:self.pos]) if self.pos > start else None

    def group(self, closing=None):
        counts = {}
        while True:
            ch = self.peek()
            if ch == "":
                if closing:
                    raise FormulaError(f"missing '{closing}'")
                break
            if ch == closing:
                break
            if ch in CLOSE:
                self.pos += 1
                inner = self.group(CLOSE[ch])
                if self.peek() != CLOSE[ch]:
                    raise FormulaError(f"missing '{CLOSE[ch]}'")
                self.pos += 1
                n = self.number()
                if n == 0:
                    raise FormulaError(f"zero count after '{CLOSE[ch]}' at position {self.pos}")
                for symbol, c in inner.items():
                    counts[symbol] = counts.get(symbol, 0) + c * (n or 1)
            elif ch.isupper():
                start = self.pos
                self.pos += 1
                if self.peek().islower():
                    self.pos += 1
                symbol = self.text[start:self.pos]
                if symbol not in self.known:
                    raise FormulaError(f"unknown element '{symbol}' at position {start + 1}")
                n = self.number()
                if n == 0:
                    raise FormulaError(f"zero count after {symbol}")
                counts[symbol] = counts.get(symbol, 0) + (n or 1)
            elif ch in ")]}":
                raise FormulaError(f"unexpected '{ch}' at position {self.pos + 1}")
            elif ch.islower():
                raise FormulaError(f"element symbols start with a capital letter: '{ch}' at position {self.pos + 1}")
            elif ch.isdigit():
                raise FormulaError(f"a count must follow an element or a bracket (position {self.pos + 1})")
            else:
                raise FormulaError(f"unexpected character '{ch}' at position {self.pos + 1}")
        return counts


def parse(formula, known):
    text = formula.strip().translate(SUB)
    if not text:
        raise FormulaError("empty formula")
    text, charge = split_charge(text)
    text = text.replace(" ", "")
    pieces = re.split(f"[{re.escape(DOTS)}]", text)
    total, parts = {}, []
    for piece in pieces:
        if not piece:
            raise FormulaError("empty part around a hydrate dot")
        m = re.match(r"\d+", piece)
        coefficient = int(m.group()) if m else 1
        body = piece[m.end():] if m else piece
        if coefficient == 0 or not body:
            raise FormulaError(f"bad part '{piece}'")
        parser = Parser(body, known)
        counts = parser.group()
        if parser.pos != len(body):
            raise FormulaError(f"unexpected '{body[parser.pos]}'")
        parts.append({"part": piece, "coefficient": coefficient})
        for symbol, c in counts.items():
            total[symbol] = total.get(symbol, 0) + c * coefficient
    return total, charge, parts


def hill(counts, charge):
    symbols = sorted(counts)
    if "C" in counts:
        symbols = ["C"] + (["H"] if "H" in counts else []) + [s for s in symbols if s not in ("C", "H")]
    text = "".join(s + (str(counts[s]) if counts[s] > 1 else "") for s in symbols)
    if charge:
        text += f"^{abs(charge) if abs(charge) > 1 else ''}{'+' if charge > 0 else '-'}"
    return text, symbols


def compute(formula, table, overrides, decimals):
    known = {e["symbol"]: e for e in table}
    counts, charge, parts = parse(formula, known)
    text, order = hill(counts, charge)
    q = Decimal(1).scaleb(-decimals)
    total, unc, rows = Decimal(0), Decimal(0), []
    for symbol in order:
        e = known[symbol]
        if symbol in overrides:
            weight, u, origin = overrides[symbol], None, "input"
        elif e["weight"] is None:
            raise FormulaError(f"{e['name']} ({symbol}) has no standard atomic weight; give it in masses")
        else:
            weight, u, origin = Decimal(e["weight"]), Decimal(e["uncertainty"]), "CIAAW 2024"
        mass = weight * counts[symbol]
        total += mass
        if u is not None:
            unc += u * counts[symbol]
        rows.append({"symbol": symbol, "name": e["name"], "count": counts[symbol], "atomic_weight": str(weight),
                     "weight_source": origin, "mass": str(mass)})
    for row in rows:
        row["mass_percent"] = str((Decimal(row["mass"]) * 100 / total).quantize(q, ROUND_HALF_UP))
    out = {"formula": formula, "hill": text, "charge": charge, "parts": parts,
           "counts": counts, "atoms": sum(counts.values()), "elements": rows,
           "molar_mass": str(total), "molar_mass_rounded": str(total.quantize(q, ROUND_HALF_UP)), "unit": "g/mol",
           "abridged_uncertainty_sum": str(unc)}
    if charge:
        out["note"] = "molar mass of the ion ignores the mass of the electrons gained or lost"
    return out


def main():
    try:
        request = json.load(sys.stdin)
    except ValueError as error:
        fail(f"stdin is not JSON: {error}")
    if not isinstance(request, dict):
        fail("input must be a JSON object")
    extra = set(request) - {"formula", "formulas", "decimals", "masses"}
    if extra:
        fail(f"unknown field(s): {', '.join(sorted(extra))}")
    try:
        data = json.loads(TABLE.read_text(encoding="utf-8"))
    except (OSError, ValueError) as error:
        fail(f"cannot read the bundled table: {error}")
    table = data["elements"]
    decimals = request.get("decimals", 2)
    if isinstance(decimals, bool) or not isinstance(decimals, int) or not 0 <= decimals <= 6:
        fail("decimals must be an integer from 0 to 6")
    overrides = {}
    masses = request.get("masses", {})
    if not isinstance(masses, dict):
        fail("masses must be an object of element symbol to atomic weight")
    symbols = {e["symbol"] for e in table}
    for symbol, value in masses.items():
        if symbol not in symbols:
            fail(f"masses: unknown element '{symbol}'")
        if isinstance(value, bool) or not isinstance(value, (int, float, str)):
            fail(f"masses.{symbol} must be a number")
        try:
            weight = Decimal(str(value).strip())
        except InvalidOperation:
            fail(f"masses.{symbol} must be a number")
        if not weight.is_finite() or weight <= 0:
            fail(f"masses.{symbol} must be positive")
        overrides[symbol] = weight
    source = {"table": data["title"], "basis": data["basis"], "url": data["source_url"], "fetched": data["fetched"]}
    if ("formula" in request) == ("formulas" in request):
        fail("give formula or formulas")
    if "formula" in request:
        formula = request["formula"]
        if not isinstance(formula, str) or len(formula) > 500:
            fail("formula must be a string of at most 500 characters")
        try:
            result = compute(formula, table, overrides, decimals)
        except FormulaError as error:
            fail(f"formula {formula!r}: {error}")
        result["source"] = source
        print(json.dumps(result, ensure_ascii=False))
        return
    formulas = request["formulas"]
    if not isinstance(formulas, list) or not 1 <= len(formulas) <= 100:
        fail("formulas must be a list of 1 to 100 strings")
    results = []
    for i, formula in enumerate(formulas):
        if not isinstance(formula, str) or len(formula) > 500:
            fail(f"formulas[{i}] must be a string of at most 500 characters")
        try:
            results.append(compute(formula, table, overrides, decimals))
        except FormulaError as error:
            results.append({"formula": formula, "error": str(error)})
    print(json.dumps({"results": results, "source": source}, ensure_ascii=False))


if __name__ == "__main__":
    try:
        main()
    except SystemExit:
        raise
    except Exception as error:  # never a traceback
        fail(f"{type(error).__name__}: {error}")

elements.json · sha256 c1ac4b63fb2f6a9131930e23fbd6a11b5217a23b49106ec4483e1984ffb58cb9

{
 "title": "IUPAC/CIAAW Abridged Standard Atomic Weights 2024",
 "basis": "Atomic Weights 2021 report (Prohaska et al., Pure Appl. Chem. 94 (2022) 573-600) with the 2024 revisions of Gd, Lu and Zr",
 "source_url": "https://www.ciaaw.org/abridged-atomic-weights.htm",
 "licence": "official table of the IUPAC commission (page (c) CIAAW); numerical values reproduced as facts, with attribution",
 "fetched": "2026-10-18",
 "generator": "tools/catalog/data/chem_formula.py",
 "notes_legend": {
  "g": "geological materials with an isotopic composition outside normal limits are known",
  "m": "modified isotopic compositions may be found in commercial material",
  "r": "range in isotopic composition of normal terrestrial material limits precision"
 },
 "elements": [
  {
   "z": 1,
   "symbol": "H",
   "name": "hydrogen",
   "weight": "1.0080",
   "uncertainty": "0.0002",
   "notes": [
    "m"
   ]
  },
  {
   "z": 2,
   "symbol": "He",
   "name": "helium",
   "weight": "4.0026",
   "uncertainty": "0.0001",
   "notes": [
    "g",
    "r"
   ]
  },
  {
   "z": 3,
   "symbol": "Li",
   "name": "lithium",
   "weight": "6.94",
   "uncertainty": "0.06",
   "notes": [
    "m"
   ]
  },
  {
   "z": 4,
   "symbol": "Be",
   "name": "beryllium",
   "weight": "9.0122",
   "uncertainty": "0.0001",
   "notes": []
  },
  {
   "z": 5,
   "symbol": "B",
   "name": "boron",
   "weight": "10.81",
   "uncertainty": "0.02",
   "notes": [
    "m"
   ]
  },
  {
   "z": 6,
   "symbol": "C",
   "name": "carbon",
   "weight": "12.011",
   "uncertainty": "0.002",
   "notes": []
  },
  {
   "z": 7,
   "symbol": "N",
   "name": "nitrogen",
   "weight": "14.007",
   "uncertainty": "0.001",
   "notes": [
    "m"
   ]
  },
  {
   "z": 8,
   "symbol": "O",
   "name": "oxygen",
   "weight": "15.999",
   "uncertainty": "0.001",
   "notes": [
    "m"
   ]
  },
  {
   "z": 9,
   "symbol": "F",
   "name": "fluorine",
   "weight": "18.998",
   "uncertainty": "0.001",
   "notes": []
  },
  {
   "z": 10,
   "symbol": "Ne",
   "name": "neon",
   "weight": "20.180",
   "uncertainty": "0.001",
   "notes": [
    "g",
    "m"
   ]
  },
  {
   "z": 11,
   "symbol": "Na",
   "name": "sodium",
   "weight": "22.990",
   "uncertainty": "0.001",
   "notes": []
  },
  {
   "z": 12,
   "symbol": "Mg",
   "name": "magnesium",
   "weight": "24.305",
   "uncertainty": "0.002",
   "notes": []
  },
  {
   "z": 13,
   "symbol": "Al",
   "name": "aluminium",
   "weight": "26.982",
   "uncertainty": "0.001",
   "notes": []
  },
  {
   "z": 14,
   "symbol": "Si",
   "name": "silicon",
   "weight": "28.085",
   "uncertainty": "0.001",
   "notes": []
  },
  {
   "z": 15,
   "symbol": "P",
   "name": "phosphorus",
   "weight": "30.974",
   "uncertainty": "0.001",
   "notes": []
  },
  {
   "z": 16,
   "symbol": "S",
   "name": "sulfur",
   "weight": "32.06",
   "uncertainty": "0.02",
   "notes": []
  },
  {
   "z": 17,
   "symbol": "Cl",
   "name": "chlorine",
   "weight": "35.45",
   "uncertainty": "0.01",
   "notes": [
    "m"
   ]
  },
  {
   "z": 18,
   "symbol": "Ar",
   "name": "argon",
   "weight": "39.95",
   "uncertainty": "0.16",
   "notes": []
  },
  {
   "z": 19,
   "symbol": "K",
   "name": "potassium",
   "weight": "39.098",
   "uncertainty": "0.001",
   "notes": []
  },
  {
   "z": 20,
   "symbol": "Ca",
   "name": "calcium",
   "weight": "40.078",
   "uncertainty": "0.004",
   "notes": [
    "g"
   ]
  },
  {
   "z": 21,
   "symbol": "Sc",
   "name": "scandium",
   "weight": "44.956",
   "uncertainty": "0.001",
   "notes": []
  },
  {
   "z": 22,
   "symbol": "Ti",
   "name": "titanium",
   "weight": "47.867",
   "uncertainty": "0.001",
   "notes": []
  },
  {
   "z": 23,
   "symbol": "V",
   "name": "vanadium",
   "weight": "50.942",
   "uncertainty": "0.001",
   "notes": []
  },
  {
   "z": 24,
   "symbol": "Cr",
   "name": "chromium",
   "weight": "51.996",
   "uncertainty": "0.001",
   "notes": []
  },
  {
   "z": 25,
   "symbol": "Mn",
   "name": "manganese",
   "weight": "54.938",
   "uncertainty": "0.001",
   "notes": []
  },
  {
   "z": 26,
   "symbol": "Fe",
   "name": "iron",
   "weight": "55.845",
   "uncertainty": "0.002",
   "notes": []
  },
  {
   "z": 27,
   "symbol": "Co",
   "name": "cobalt",
   "weight": "58.933",
   "uncertainty": "0.001",
   "notes": []
  },
  {
   "z": 28,
   "symbol": "Ni",
   "name": "nickel",
   "weight": "58.693",
   "uncertainty": "0.001",
   "notes": [
    "r"
   ]
  },
  {
   "z": 29,
   "symbol": "Cu",
   "name": "copper",
   "weight": "63.546",
   "uncertainty": "0.003",
   "notes": [
    "r"
   ]
  },
  {
   "z": 30,
   "symbol": "Zn",
   "name": "zinc",
   "weight": "65.38",
   "uncertainty": "0.02",
   "notes": [
    "r"
   ]
  },
  {
   "z": 31,
   "symbol": "Ga",
   "name": "gallium",
   "weight": "69.723",
   "uncertainty": "0.001",
   "notes": []
  },
  {
   "z": 32,
   "symbol": "Ge",
   "name": "germanium",
   "weight": "72.630",
   "uncertainty": "0.008",
   "notes": []
  },
  {
   "z": 33,
   "symbol": "As",
   "name": "arsenic",
   "weight": "74.922",
   "uncertainty": "0.001",
   "notes": []
  },
  {
   "z": 34,
   "symbol": "Se",
   "name": "selenium",
   "weight": "78.971",
   "uncertainty": "0.008",
   "notes": [
    "r"
   ]
  },
  {
   "z": 35,
   "symbol": "Br",
   "name": "bromine",
   "weight": "79.904",
   "uncertainty": "0.003",
   "notes": []
  },
  {
   "z": 36,
   "symbol": "Kr",
   "name": "krypton",
   "weight": "83.798",
   "uncertainty": "0.002",
   "notes": [
    "g",
    "m"
   ]
  },
  {
   "z": 37,
   "symbol": "Rb",
   "name": "rubidium",
   "weight": "85.468",
   "uncertainty": "0.001",
   "notes": [
    "g"
   ]
  },
  {
   "z": 38,
   "symbol": "Sr",
   "name": "strontium",
   "weight": "87.62",
   "uncertainty": "0.01",
   "notes": [
    "g",
    "r"
   ]
  },
  {
   "z": 39,
   "symbol": "Y",
   "name": "yttrium",
   "weight": "88.906",
   "uncertainty": "0.001",
   "notes": []
  },
  {
   "z": 40,
   "symbol": "Zr",
   "name": "zirconium",
   "weight": "91.222",
   "uncertainty": "0.003",
   "notes": [
    "g"
   ]
  },
  {
   "z": 41,
   "symbol": "Nb",
   "name": "niobium",
   "weight": "92.906",
   "uncertainty": "0.001",
   "notes": []
  },
  {
   "z": 42,
   "symbol": "Mo",
   "name": "molybdenum",
   "weight": "95.95",
   "uncertainty": "0.01",
   "notes": [
    "g"
   ]
  },
  {
   "z": 43,
   "symbol": "Tc",
   "name": "technetium",
   "weight": null,
   "uncertainty": null,
   "notes": []
  },
  {
   "z": 44,
   "symbol": "Ru",
   "name": "ruthenium",
   "weight": "101.07",
   "uncertainty": "0.02",
   "notes": [
    "g"
   ]
  },
  {
   "z": 45,
   "symbol": "Rh",
   "name": "rhodium",
   "weight": "102.91",
   "uncertainty": "0.01",
   "notes": []
  },
  {
   "z": 46,
   "symbol": "Pd",
   "name": "palladium",
   "weight": "106.42",
   "uncertainty": "0.01",
   "notes": [
    "g"
   ]
  },
  {
   "z": 47,
   "symbol": "Ag",
   "name": "silver",
   "weight": "107.87",
   "uncertainty": "0.01",
   "notes": [
    "g"
   ]
  },
  {
   "z": 48,
   "symbol": "Cd",
   "name": "cadmium",
   "weight": "112.41",
   "uncertainty": "0.01",
   "notes": [
    "g"
   ]
  },
  {
   "z": 49,
   "symbol": "In",
   "name": "indium",
   "weight": "114.82",
   "uncertainty": "0.01",
   "notes": []
  },
  {
   "z": 50,
   "symbol": "Sn",
   "name": "tin",
   "weight": "118.71",
   "uncertainty": "0.01",
   "notes": [
    "g"
   ]
  },
  {
   "z": 51,
   "symbol": "Sb",
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  {
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   "name": "lawrencium",
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   "name": "rutherfordium",
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   "notes": []
  },
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   "name": "dubnium",
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   "name": "bohrium",
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   "name": "hassium",
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  {
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   "name": "meitnerium",
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   "notes": []
  },
  {
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   "symbol": "Ds",
   "name": "darmstadtium",
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   "notes": []
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  {
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   "symbol": "Rg",
   "name": "roentgenium",
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   "notes": []
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  {
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   "symbol": "Cn",
   "name": "copernicium",
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   "notes": []
  },
  {
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   "symbol": "Nh",
   "name": "nihonium",
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   "notes": []
  },
  {
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   "symbol": "Fl",
   "name": "flerovium",
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   "notes": []
  },
  {
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   "symbol": "Mc",
   "name": "moscovium",
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   "notes": []
  },
  {
   "z": 116,
   "symbol": "Lv",
   "name": "livermorium",
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   "notes": []
  },
  {
   "z": 117,
   "symbol": "Ts",
   "name": "tennessine",
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  },
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   "symbol": "Og",
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 ]
}

Where it is served

The registry serves only AXLR clients, so a browser gets 403; fetch with a User-Agent that starts with axlr:

curl -A axlr-docs/1.0 -O https://registry.underpassai.com/tools/chem_formula/1.0.0/manifest.json
curl -A axlr-docs/1.0 -O https://registry.underpassai.com/tools/chem_formula/1.0.0/chem_formula.py
curl -A axlr-docs/1.0 -O https://registry.underpassai.com/tools/chem_formula/1.0.0/elements.json