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Molarity (M) is the amount of solute, in moles, dissolved per liter of solution. It is the most common concentration unit in analytical and inorganic chemistry: 1 M = 1 mol/L.

Molarity divides moles of solute by the total volume of the solution in liters. Molality (m) divides moles of solute by the mass of the solvent in kilograms. Molality does not change with temperature; molarity does, because solution volume expands with temperature.

Convert mass to moles by dividing by the molecular weight, then divide moles by the volume of the solution in liters: M = m / (MW × V). For 5.85 g NaCl (MW 58.44 g/mol) dissolved to make 0.500 L of solution, M = 5.85 / (58.44 × 0.500) = 0.200 M.

The calculator accepts mass in g, mg, µg, or kg; volume in L, mL, or µL; and concentration in M, mM, µM, or nM. Internally every value is converted to grams, liters, and mol/L before the arithmetic, so any mixed unit input works as long as MW is entered in g/mol.

The dilution equation. C₁ is the concentration of a stock, V₁ is the volume of stock you pipette, and C₂ and V₂ are the concentration and volume of the diluted (working) solution. The identity says the number of moles of solute you take from the stock equals the number of moles that end up in the diluted solution.

When V₁ is smaller than the smallest volume you can accurately pipette (usually ≤ 1 µL on a P2). A serial dilution splits a large dilution factor into several small ones, each in a range your pipette can handle. Use the serial dilution calculator for a step plan.

Yes — the identity is unit-agnostic as long as C₁ and C₂ are in the same unit and V₁ and V₂ are in the same unit. This calculator only accepts M/mM/µM/nM; for %(w/v) or mg/mL, do the algebra with those units directly (e.g., 30 % H₂O₂ diluted 1:10 gives 3 %).

For most dilutions the order is not chemically important — but for concentrated acids, always add acid to water, never water to acid. Diluting concentrated H₂SO₄ or HCl releases a large amount of heat; adding water on top of the acid can boil it and splash it. The calculator does not enforce this; treat it as a lab safety rule.

In practice they're used interchangeably. Molar mass is the mass of one mole of a substance in g/mol; molecular weight (MW) is the dimensionless sum of atomic weights. For any real-world calculation the numeric values are identical, so this tool labels the output g/mol.

Use ·, *, or . as the separator between the anhydrous formula and the water group, and prefix the water with the number of waters. Examples: CuSO4·5H2O, MgSO4*7H2O, Na2CO3.10H2O. Every one parses to the same result.

Chemistry symbols are Capitalized: 'Co' is cobalt but 'CO' is carbon monoxide (C + O). If you type 'co' the parser can't tell what you meant, so it errors instead of guessing wrong. Same reason organic shorthand like 'Me' (methyl), 'Et' (ethyl), 'Ph' (phenyl) isn't supported — expand to the full formula.

No. Charge is dropped in formula-mass calculations (an ion has the same molar mass as its neutral form, within a fraction of an electron mass we can ignore). Isotope notation like ^13C is rejected; the calculator uses the IUPAC conventional atomic weight for the natural-abundance mixture.

pH = pKa + log10([A⁻] / [HA]). It tells you the pH of a buffered solution given the ratio of the conjugate base to the weak acid form and the acid's pKa. A ratio of 1 (equimolar) gives pH = pKa — the point of maximum buffering capacity.

The rule is: choose a buffer whose pKa is within ±1 unit of your target pH. At pH = pKa the buffer has maximum capacity; beyond ±1 unit the ratio becomes extreme (>10:1) and small acid or base additions swing the pH more. This calculator warns you when your target lies outside the pKa ± 1 window.

For most buffers, no — the ΔpKa/°C is small enough that a value measured at 25 °C is fine anywhere from 4 °C to 37 °C. The big exception is Tris, whose ΔpKa/°C ≈ -0.028, meaning a pH-8.0 Tris buffer prepared at 25 °C is actually pH 7.75 at 37 °C or pH 8.3 at 4 °C. Adjust the pH at the temperature you'll actually use the buffer at.

Henderson-Hasselbalch uses concentration in place of activity. For low ionic strength buffers (< 0.1 M) the error is under 0.1 pH unit; for high-salt buffers or biological media the actual pH can differ by 0.2 pH or more. For precise work (enzyme assays, protein crystallography) measure pH at working conditions with a calibrated meter.

When a single-step C₁V₁ = C₂V₂ dilution would need a stock volume below your pipette's accurate range (typically ~1 µL on a P2, ~10 µL on a P200). Splitting the total dilution into N smaller steps of the same factor D keeps every transfer in the pipette's linear range.

Match D to the smallest pipette you have and the working volume you can afford. For 1 mL working volumes and a P200: D = 10 means 100 µL transfers (easy, accurate); D = 2 means 500 µL transfers (also easy). At D = 50 you'd need 20 µL transfers on 1 mL, still fine. Below that, either raise V_step or add another step.

It's a convention — with V_step constant, D and the transfer volume are constant across the ladder (V_transfer = V_step / D), which makes pipetting a repetitive rhythm and reduces mistakes. It also gives every tube the same amount of test solution, useful for parallel assays like MIC panels or ELISA titrations.

N × V_transfer, where N is the number of steps. The calculator reports this as 'Total stock consumed' on the summary. Add a small overhead if you'll be pipetting into other assays from the same tubes.

The ideal gas law is PV = nRT, connecting pressure (P), volume (V), amount of substance (n, in moles), and absolute temperature (T, in kelvin) through the molar gas constant R. It is the combined form of Boyle's, Charles's, and Avogadro's laws, and it describes the behavior of gases whose particles have negligible volume and no intermolecular forces.

Real gases deviate from PV = nRT at high pressure (where molecular volume matters) and low temperature near condensation (where intermolecular attractions matter). Below about 2 atm and above about 200 K the ideal-gas approximation is usually within a few percent for common gases; outside that window, use a real-gas equation of state such as van der Waals or the virial expansion.

The molar gas constant R = 8.314 462 618 J/(mol·K) is exact by the 2019 SI redefinition (R = N_A × k_B, both defining constants). In other unit systems it is 0.082 057 L·atm/(mol·K), 62.363 L·torr/(mol·K), or 8.314 L·kPa/(mol·K). This calculator does the arithmetic in SI (Pa, m³, mol, K) and converts your inputs internally, so you can mix units freely.

STP (standard temperature and pressure) has two competing definitions. IUPAC's post-1982 STP is 273.15 K and 100 kPa (1 bar), giving a molar volume of 22.711 L/mol. The older IUPAC (pre-1982) and much of the textbook literature use 273.15 K and 1 atm (101.325 kPa), giving 22.414 L/mol. NTP (normal temperature and pressure) usually means 20 °C and 1 atm (24.06 L/mol). Always confirm which STP a problem or table intends.