Molar mass, equation balancing, pH and the gas laws on all 118 elements of the IUPAC 2021 table, with every interval mass and every approximation named.
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Twelve kinds of physics problem with every constant named as defined, measured or conventional, results printed to the figures those constants justify, and an independent check on each answer.
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You need the pH of a very dilute hydrochloric acid, 10⁻⁸ mol/L, and you want it to be right.
pH mode
concentration 0.00000001 mol/L · strong acid · 25 °C
Results
pH 6.9783 pOH 7.0217 ACIDIC -log₁₀(c) would give 8.0000, which is alkaline pH + pOH = 14.000000 = pKᵥᵥ
Water contributes its own ions, and below about 10⁻⁶ mol/L they are comparable with the ones the acid adds. So the usual -log₁₀(c) is not an approximation there, it is the wrong answer: it calls a bottle of hydrochloric acid alkaline. The charge balance gives [H⁺] = (C + √(C² + 4Kᵥᵥ))/2, and the page checks pH + pOH against pKᵥᵥ on the two numbers it just printed.
Molar mass and percent composition from a formula, chemical equations balanced exactly, pH and pOH from the charge balance at a temperature you choose, molarity, dilution and the ideal gas law. All 118 elements are here, on the IUPAC 2021 standard atomic weights, with each mass labelled as an interval, a measurement or a mass number.
The accuracy question for a chemistry calculator is a PUBLISHED TABLE, and the shipped version of this one carried 43 of the 118 elements with lithium given as 6.941, the value IUPAC withdrew in 2009, and argon as 39.948, withdrawn in 2017. Both are now intervals rather than numbers, because their isotopic composition varies with where the material came from: lithium's standard atomic weight is [6.938, 6.997] and argon's is [39.792, 39.963]. Fourteen elements are like that, and when a compound contains one this tool gives the molar mass as a range as well as a conventional value. Thirty-four more have no stable isotope at all, so IUPAC gives a mass number in brackets rather than an atomic weight, and the page says so. The formula parser reads nesting, hydrates and charges (Mg3(PO4)2, K4[Fe(CN)6], CuSO4.5H2O, SO4^2-) and is case sensitive, because CO is carbon monoxide and Co is cobalt. Equations are balanced by finding the null space of the element-count matrix over exact fractions, and then every element is counted again on the answer and both counts are shown, which is the check that needs nothing external. And pH comes from the charge balance rather than from -log10(c): below about 10^-6 mol/L that formula is not an approximation but the wrong answer, and at 10^-8 M it calls a bottle of hydrochloric acid alkaline at pH 8 where the answer is 6.9783. The temperature is part of the answer too: pKw is 14.00 at 25 degrees only, and at body temperature neutral water is pH 6.81.
Molar mass, molarity and dilution with the arithmetic checked on its own output.
Any equation up to twelve substances, with the element counts shown so the answer can be verified rather than trusted.
Fourteen elements have intervals rather than numbers, and the table says which and why.
Below 10^-6 mol/L the usual pH formula breaks down, and this one keeps working because it starts from the charge balance.
PV = nRT in atmospheres, kilopascals, bar or millimetres of mercury, with R exact in each.
Because 6.941 was withdrawn by IUPAC in 2009. Lithium's standard atomic weight is now the interval [6.938, 6.997], because commercially available lithium has been isotopically depleted and its composition varies with the source. 6.94 is the conventional value to use when the source is unknown, and this tool shows the interval alongside it.
Because the compound contains at least one element whose standard atomic weight is an interval. The range is the molar mass at each end of those intervals, and it says how precisely the answer can be known without measuring the sample.
Each element gives one linear equation saying its count is the same on both sides, and a balanced equation is a vector in the null space of that matrix. It is solved over exact fractions, so there is no tolerance and no search. Then every element is counted again on the ANSWER and both counts are shown.
Because water contributes its own ions. Below about 10^-6 mol/L those are comparable with the ones the acid adds, so -log10(c) stops being the answer, and at 10^-8 M it gives 8, which is alkaline, for an acid. The charge balance gives [H+] = (C + sqrt(C^2 + 4Kw))/2 and a pH of 6.9783.
Because Kw does. pKw is 14.00 at 25 degrees Celsius only; it is 14.95 at 0 and 12.26 at 100. Neutral water is pH pKw/2, so at body temperature it is 6.81 rather than 7, and pure water is still neutral there.
No. CO is carbon monoxide at 28.010 g/mol and Co is cobalt at 58.933. Element symbols are case sensitive and this tool treats them that way rather than guessing.
Because that is its exact value. R is the product of the Avogadro and Boltzmann constants, and both have been exact by definition since the 2019 revision of the SI, so R is too. Writing 8.314 is a rounding of an exact number, and it moves the molar volume at standard conditions from 22.413970 to 22.414689 L.
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