DEFINING and CALCULATING RELATIVE ATOMIC MASS
Doc Brown's Chemistry - GCSE/IGCSE/GCE (basic A level) O Level Online Chemical Calculations
1. Explaining and calculating relative atomic mass RAM or Ar*
and relative isotopic mass
Quantitative Chemistry calculations online Help for problem solving in relative atomic mass calculations. Definitions of relative atomic mass and relative isotopic mass (A level students only) Practice revision questions on working out relative atomic mass from isotopic composition (% isotopes, A level students will learn about very accurate mass spectrometer data). What is relative atomic mass? How do you calculate the relative atomic mass of an element. Relative atomic mass is explained below, with reference to the carbon-12 atomic mass scale and the relevance of isotopes. Detailed examples of the method of how to calculate relative atomic mass from the isotopic composition are fully explained with reference to the definition of the relative atomic mass of a compound. For A level students, how to define and use relative isotopic masses to calculate relative atomic mass. These notes on defining, explaining and calculating relative atomic mass and defining relative isotopic mass are designed to meet the highest standards of knowledge and understanding required for students/pupils doing GCSE chemistry, IGCSE chemistry, O Level chemistry, KS4 science courses and A Level chemistry courses.
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1. Explaining and how to calculate the relative atomic mass RAM or Ar of an element
How to calculate relative atomic mass
How do I calculate relative atomic mass?
Examples for Advanced Level Chemistry students only
How to calculate relative atomic mass with accurate relative isotopic masses
Using data from modern very accurate mass spectrometers
(a) Accurate calculation of relative atomic mass (need to know and define what relative isotopic mass is)
Relative isotopic mass is defined as the accurate mass of a single isotope of an element compared to 1/12th the mass of a carbon-12 atom e.g. the accurate relative isotopic mass of the cobalt-5 is 58.9332
If we were to redo the calculation of the relative atomic mass of chlorine (example 1.1 above), which is quite adequate for GCSE purposes (and maybe A level too), but more accurately at A level, we might do ....
chlorine is 75.77% 35Cl of isotopic mass 34.9689 and 24.23% 37Cl of isotopic mass 36.9658
so Ar(Cl) = [(75.77 x 34.9689) + (24.23 x 36.9658)] / 100 = 35.4527 (but 35.5 is usually ok in calculations pre-university!)
See also Mass Spectrometer and isotope analysis on the GCSE-AS(basic) Atomic Structure Notes, with further RAM calculations.
(b) Calculations of % composition of isotopes
It is possible to do the reverse of a relative atomic mass calculation if you know the Ar and which isotopes are present.
It involves a little bit of arithmetical algebra.
The Ar of boron is 10.81 and consists of only two isotopes, boron-10 and boron-11
The relative atomic mass of boron was obtained accurately in the past from chemical analysis of reacting masses but now mass spectrometers can sort out all of the isotopes present and their relative abundance.
If you let X = % of boron 10, then 100-X is equal to % of boron-11
Therefore Ar(B) = (X x 10) + [(100-X) x 11)] / 100 = 10.81
so, 10X -11X +1100 =100 x 10.81
-X + 1100 = 1081, 1100 - 1081 = X (change sides change sign!)
therefore X = 19
so naturally occurring boron consists of 19% 10B and 81% 11B (the data books actually quote 18.7 and 81.3, but we didn't use the very accurate relative isotopic masses)
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