Calculate the isotopic distribution of a molecular formula: the M, M+1 and M+2 peaks with their masses and relative heights from natural abundances.
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Calculator Functions
The calculator works out the isotope pattern of a molecular formula: the cluster of peaks a mass spectrum shows because some molecules carry heavier isotopes such as carbon-13 or chlorine-37. It lists each peak with its mass, its height relative to the tallest peak and its share of all molecules.
| Function | Use it when | You enter |
|---|---|---|
| Isotope pattern of a formula | You want the M, M+1 and M+2 peaks expected for a compound, or want to check a measured pattern against a formula | The molecular formula, such as C6H12O6 or CH2Cl2 |
M is the peak of molecules made only from the most abundant isotope of each element, M+1 is one mass unit heavier, and so on. Formulas can use brackets, such as Ca(OH)2, and a dot for a hydrate, such as CuSO4.5H2O. Capital letters matter, because Co is cobalt and CO is carbon monoxide. For the exact mass of the M peak alone, or the m/z of an ion, use the Exact Mass Calculator.
Isotopic Distribution Formulas
m = m₁ + m₂ + … + mₙ [1]
| P | Share of molecules with one particular choice of isotope for every atom |
| p | Natural abundance of the isotope chosen for one atom |
| m | Mass of that molecule: the sum of its isotope masses (u) |
| n | Number of atoms in the formula |
The calculator does this for every possible choice of isotopes and adds together the shares that land on the same whole-number mass. That sum is the height of one peak, and the mass shown for the peak is the average of the molecules in it. The abundances and masses come from the NIST table of isotopic compositions [1].
Relative height
S is the share of molecules in a peak and Smax is the share in the tallest peak, so the tallest peak is always 100%. For glucose, 92.26% of molecules are in M and 6.33% in M+1, so M+1 is 6.33 ÷ 92.26 × 100 = 6.9%.
The M+1 peak of a small molecule
0.012% × H + 0.37% × N +
0.038% × O
For a small organic molecule the M+1 peak is close to this sum, where C, H, N and O are the numbers of those atoms and each percentage is the abundance of the heavier isotope divided by that of the lighter one [1]. Glucose gives 6 × 1.08 + 12 × 0.012 + 6 × 0.038 = 6.9%. The calculator does not use this shortcut: it works out every peak in full.
Chlorine and bromine patterns
Chlorine is 75.76% chlorine-35 and 24.24% chlorine-37, so one chlorine atom adds an M+2 peak about 32% as tall as M. Bromine is 50.69% bromine-79 and 49.31% bromine-81, so one bromine atom gives two peaks of almost equal height, and two give a 51 : 100 : 49 triplet [1].
Limits of This Estimate
- Peaks are grouped by whole-number mass. A high-resolution instrument can separate the different molecules inside one peak, which the calculator reports as a single averaged mass.
- The abundances are representative natural values. Real samples vary a little, and labeled or enriched compounds do not follow them [1].
- The pattern is for the formula as entered. For an ion, enter the formula of the ion itself, for example with one more H for a protonated molecule.
- Formulas are limited to 5,000 atoms, peaks below 0.05% of the tallest are left out, and elements with no natural isotopic composition, such as promethium, are not supported.
Sources
- National Institute of Standards and Technology, Atomic Weights and Isotopic Compositions for All Elements: the relative atomic mass and natural isotopic composition of every isotope used
