Library / Foundations: Chemistry / FCH-19
Foundations: Chemistry
Relative atomic mass from isotopes
Weighted average mass of an element from its isotopes.
- Ref
- FCH-19
- Rev
- v1
- Field
- Foundations: Chemistry
- Result
- Ar
Abundances can be percentages or ratios, as long as both are in the same form. The calculator uses two isotopes, as for chlorine.
Because an element is a mixture of isotopes, its average atomic mass sits between them, closer to the more common one.
Calculator
- Total abundance100 %
- Heavier isotope share25 %
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- Chlorine’s Ar of 35.5 does not match any single atom; it is the average of ³⁵Cl and ³⁷Cl.
- The value lies between the two isotope masses, nearer the more abundant one.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing () | Local step | Change in result |
|---|---|---|---|---|---|---|
| m₁ Mass of isotope 1 | 1 to 240 | 10 | 189.3 | 179.3 | +10% | +7.39 % |
| m₂ Mass of isotope 2 | 1 to 240 | 26.5 | 86.25 | 59.75 | +10% | +2.61 % |
| a₁ Abundance of isotope 1 | 0.1 to 100 % | 35.4 | 36.99 | 1.592 | +10% | −0.0983 % |
| a₂ Abundance of isotope 2 | 0.1 to 100 % | 35 | 36.14 | 1.14 | +10% | +0.103 % |
Sweep of Abundance of isotope 1
| Abundance of isotope 1 (%) | Relative atomic mass |
|---|---|
| 0.1 | 36.99 |
| 12.59 | 36.33 |
| 25.08 | 36 |
| 37.56 | 35.8 |
| 50.05 | 35.67 |
| 62.54 | 35.57 |
| 75.03 | 35.5 |
| 87.51 | 35.44 |
| 100 | 35.4 |
Sweep one variable
Variables and how each one contributes
Relative atomic mass
What the equation gives you. Everything else feeds it.
Mass of isotope 1
Mass number of isotope 1 (³⁵Cl). Pulls the average towards isotope 1.
Abundance of isotope 1
Relative abundance of isotope 1. Weights the average towards isotope 1.
Mass of isotope 2
Mass number of isotope 2 (³⁷Cl). Pulls the average towards isotope 2.
Abundance of isotope 2
Relative abundance of isotope 2. Weights the average towards isotope 2.
Worked example with the values above
- Isotope 1: 35 × 75 = 2,625; isotope 2: 37 × 25 = 925.
- Sum: 3,550; total abundance 100.
- Ar = 35.5.
Assumptions and limits
- Abundances are those of natural samples.
- Isotope masses are close to the mass numbers.
Common mistakes
- Dividing by 2 instead of by the total abundance.
- Not weighting by abundance.
Statistics and uncertainty
Mass spectrometer peak heights typically give abundances to about ±1%, which shifts Ar by tenths of a unit.
Where it is used
- Interpreting mass spectra.
- Verifying isotopic composition.
Maths you need
- Isotopes: same protons, different neutrons
- Weighted mean: abundance-weighted average