Ciencias
Relative Atomic Mass: Why Chlorine Is 35.5
Relative atomic mass is a weighted average across an element's isotopes. Chlorine is 35.5 because three quarters of its atoms are Cl-35 and one quarter Cl-37.
Relative atomic mass
Relative atomic mass is the mean mass of an element's atoms, weighted by isotope abundance, compared with one twelfth of the mass of a carbon-12 atom.
- También llamado
- Ar, Atomic weight
- Dónde lo encuentra el alumnado
- Grade 9 chemistry, straight after isotopes, and in every mole and formula-mass calculation that follows, where it is read off the periodic table.
La respuesta corta
Relative atomic mass, written Ar, is the average mass of an element's atoms weighted by how common each isotope is, measured against one twelfth of the mass of a carbon-12 atom. Chlorine is 35.5 because about three quarters of chlorine atoms are chlorine-35 and one quarter are chlorine-37. It has no units.
Un ejemplo
Ar of chlorine = [(75 × 35) + (25 × 37)] ÷ 100 = (2625 + 925) ÷ 100 = 35.5
Multiply each isotope's mass number by its percentage abundance, add the results, then divide by 100. Chlorine-35 makes up about 75 per cent of chlorine atoms and chlorine-37 about 25 per cent, so the average is dragged three quarters of the way towards 35 and lands at 35.5. If you divide by 2 instead of by 100 you have taken a plain average and thrown away the abundances, which gives 36 and is wrong.
Why it is not a whole number
A single atom has a whole-number mass number, because protons and neutrons come in whole units. An element, though, is a population of atoms of several isotopes, and the relative atomic mass describes that population rather than any individual member of it.
So there is no chlorine atom weighing 35.5. Every one is either 35 or 37. The number 35.5 is what a very large sample averages out to, and it is useful for exactly that reason: chemists never weigh out one atom, they weigh out billions, and the average is what governs the mass on the balance.
The calculation examiners set
The standard question gives two or three isotopes with their mass numbers and percentage abundances and asks for the Ar. Multiply each mass by its abundance, total the products and divide by 100. Copper is the usual second example: about 69 per cent copper-63 and 31 per cent copper-65 gives (69 × 63 + 31 × 65) ÷ 100 = 63.62, which rounds to the 63.5 printed on the table.
The same question is often asked backwards, giving the Ar and both isotope masses and asking for the abundance. It is the same relationship with a letter in place of one of the percentages, so the arithmetic is worth setting out in full rather than done in your head.
Three numbers that get mixed up
Mass number belongs to one atom and is always a whole number. Relative atomic mass belongs to the element as a mixture and usually is not. Relative formula mass, Mr, belongs to a compound and is found by adding the Ar values of everything in the formula, so water comes to 18 and carbon dioxide to 44.
None of them carries a unit, and that is not an oversight. Each is a ratio against the same reference: one twelfth of the mass of a carbon-12 atom, a quantity fixed by definition. Comparing a mass with a mass leaves a bare number, which is why the answer to an Ar calculation should never be written with grams after it.
- Relative atomic mass of chlorine: about three quarters chlorine-35, one quarter chlorine-37
- 35.5Relative atomic mass of chlorine: about three quarters chlorine-35, one quarter chlorine-37[1]
Preguntas frecuentes
Why is the relative atomic mass of chlorine 35.5?
Because chlorine is a mixture of two isotopes in roughly a three to one ratio: chlorine-35 and chlorine-37. Weighting 35 by three quarters and 37 by one quarter gives 35.5. The measured abundances are near 75.8 and 24.2 per cent, so the true figure is 35.45, and exam questions round to make the arithmetic clean.
Does relative atomic mass have units?
No. It is a comparison between two masses — the average atom against one twelfth of a carbon-12 atom — so the units cancel and a bare number is left. The word relative in the name is the clue. Writing grams or kilograms after an Ar value is treated as an error.
What is the difference between mass number and relative atomic mass?
Mass number counts the protons and neutrons in one particular atom, so it is always a whole number and applies to a single isotope. Relative atomic mass is the weighted average across all the isotopes of an element as it is found naturally, so it usually is not a whole number.
What is relative formula mass, Mr?
The same idea applied to a compound. Add the relative atomic masses of every atom shown in the formula: water, H₂O, gives 1 + 1 + 16 = 18. For an ionic compound the term relative formula mass is used rather than molecular mass, because there is no individual molecule to weigh, only a repeating ratio.
Fuentes
- Atomic Weights and Isotopic Compositions — National Institute of Standards and Technology
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