{
  "id": "molarity",
  "version": "d27f4c92ac3f",
  "status": "published",
  "name": "Molarity Calculator",
  "question": "What is the molarity?",
  "summary": "Computes the molar concentration (mol/L) of a solution from the mass of solute, its molar mass and the solution volume, or the mass, volume or molar mass from the other three.",
  "category": "chemistry",
  "subcategory": "solutions",
  "url": "https://www.acalculator.org/chemistry/molarity-calculator",
  "markdown": "https://www.acalculator.org/chemistry/molarity-calculator.md",
  "kind": "formulas",
  "method": "c = n ÷ V and n = m ÷ M, so c = m ÷ (M × V), with c in mol/L, m in g, M in g/mol and V in L (IUPAC Gold Book).",
  "assumptions": [
    "The volume is the final volume of the solution, measured after the solute dissolves.",
    "The molar mass is for the form you weigh, including any water of crystallization (for example CuSO₄·5H₂O, not CuSO₄).",
    "The molar mass is from 1 to 10,000,000 g/mol and the molarity is at most 100 mol/L (pure water is about 55.5 mol/L). A solved value outside that range has no answer.",
    "The solute is fully dissolved, and the concentration is of the formula unit as weighed (not of the separate ions)."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "m": {
        "title": "Mass of solute",
        "description": "The mass of the substance dissolved.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "mass",
        "exclusiveMinimum": 0
      },
      "mw": {
        "title": "Molar mass (g/mol)",
        "description": "The molar mass of the solute, in grams per mole: the sum of the atomic weights in its formula.",
        "type": "number",
        "minimum": 1,
        "maximum": 10000000
      },
      "v": {
        "title": "Volume of solution",
        "description": "The final volume of the solution, not the volume of solvent added.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "volume",
        "exclusiveMinimum": 0
      },
      "c": {
        "title": "Molarity (mol/L)",
        "description": "The amount of solute per liter of solution, in moles per liter (M).",
        "type": "number",
        "exclusiveMinimum": 0,
        "maximum": 100
      }
    }
  },
  "solve": {
    "fillAny": 3,
    "variables": [
      "m",
      "mw",
      "v",
      "c"
    ],
    "inputsOnly": []
  },
  "outputs": {
    "mass": {
      "label": "Mass of solute",
      "description": "The mass of the substance dissolved.",
      "format": "quantity"
    },
    "molarMass": {
      "label": "Molar mass (g/mol)",
      "description": "The molar mass of the solute, in grams per mole: the sum of the atomic weights in its formula.",
      "format": "number"
    },
    "volume": {
      "label": "Volume of solution",
      "description": "The final volume of the solution, not the volume of solvent added.",
      "format": "quantity"
    },
    "molarity": {
      "label": "Molarity (mol/L)",
      "description": "The amount of solute per liter of solution, in moles per liter (M).",
      "format": "number"
    },
    "millimolar": {
      "label": "Molarity (mmol/L)",
      "description": "The same molarity in millimoles per liter (mM): mol/L × 1,000.",
      "format": "number"
    },
    "moles": {
      "label": "Amount of solute (mol)",
      "description": "The amount of solute in moles: mass in grams ÷ molar mass.",
      "format": "number"
    },
    "massConcentration": {
      "label": "Mass concentration",
      "description": "The mass of solute per volume of solution: mass ÷ volume.",
      "format": "quantity",
      "unit": "g-L"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "m": 0.05844,
      "mw": 58.44,
      "v": 0.001
    },
    "outputs": {
      "molarity": 1,
      "millimolar": 1000,
      "moles": 1,
      "massConcentration": 58.44
    },
    "text": "Dissolving 58.44 g of a solute with molar mass 58.44 g/mol to make 1 L of solution gives 1 mol/L."
  },
  "examples": [
    {
      "given": {
        "m": 0.05844,
        "mw": 58.44,
        "v": 0.001
      },
      "expect": {
        "c": 1,
        "moles": 1,
        "massConcentration": 58.44
      },
      "source": "hand calculation in content.mdx: M(NaCl) = 22.990 + 35.45 = 58.44 g/mol (CIAAW 2021 abridged atomic weights); n = 58.44 ÷ 58.44 = 1 mol; c = 1 mol ÷ 1 L = 1 M",
      "tolerance": 1e-12
    },
    {
      "given": {
        "c": 0.1,
        "mw": 180.156,
        "v": 0.00025
      },
      "expect": {
        "m": 0.004503900000000001,
        "moles": 0.025
      },
      "source": "hand calculation in content.mdx: M(C₆H₁₂O₆) = 6 × 12.011 + 12 × 1.008 + 6 × 15.999 = 180.156 g/mol (CIAAW 2021); m = 0.1 × 0.25 × 180.156 = 4.5039 g",
      "tolerance": 1e-12
    },
    {
      "given": {
        "m": 0.0106,
        "mw": 105.988,
        "v": 0.0005
      },
      "expect": {
        "c": 0.20002264407291392
      },
      "source": "hand calculation in content.mdx: M(Na₂CO₃) = 2 × 22.990 + 12.011 + 3 × 15.999 = 105.988 g/mol; c = 10.6 ÷ (105.988 × 0.5) = 0.20002 M"
    },
    {
      "given": {
        "m": 0.002,
        "mw": 39.997,
        "c": 0.5
      },
      "expect": {
        "v": 0.00010000750056254219
      },
      "source": "hand calculation in content.mdx: V = 2 ÷ (39.997 × 0.5) = 0.10001 L = 100.01 mL"
    }
  ],
  "sources": [
    "IUPAC Compendium of Chemical Terminology (the Gold Book), amount concentration: c = n ÷ V, also called molarity. https://doi.org/10.1351/goldbook.A00295",
    "IUPAC Commission on Isotopic Abundances and Atomic Weights (CIAAW), Abridged standard atomic weights (2021): H 1.008, C 12.011, O 15.999, Na 22.990, Cl 35.45. https://ciaaw.org/abridged-atomic-weights.htm",
    "NIST Special Publication 811 (2008), section 8.6.6: amount-of-substance concentration, mol/m³ and mol/L. https://www.nist.gov/pml/special-publication-811"
  ],
  "related": [
    "dilution",
    "density"
  ],
  "changelog": []
}