Doc Brown's Chemistry Clinic - Chemical Calculations

On-line Quantitative Chemistry Calculations

Online practice exam chemistry CALCULATIONS and solved problems for KS4 Science GCSE/IGCSE CHEMISTRY and basic starter chemical calculations for A level AS/A2/IB courses

EMAIL query?comment or request for type of GCSE calculation?

Every atom has its own unique atomic mass based on a standard comparison or relative scale e.g. it has been based on hydrogen H = 1, oxygen O = 16. The relative atomic mass scale is now based on an isotope of carbon, carbon-12, , which is given the value of 12.0000 amu. (* The letter A on its own usually means the mass number of a particular isotope)

However there are complications due to isotopes and so very accurate atomic masses are not whole numbers. Isotopes are atoms of the same element with different masses due to different numbers of neutrons. The very accurate atomic mass scale is based on a specific isotope of carbon, carbon-12, ¹²C = 12.0000 units exactly, for most purposes C = 12 is used for simplicity.

For example , and are the three isotopes of hydrogen, though the vast majority of hydrogen atoms have a mass of 1. When their accurate isotopic masses, and their % abundance are taken into account the average accurate relative mass for hydrogen = 1.008, but for most purposes H = 1 is good enough! See also GCSE Atomic Structure Notes

The strict definition of relative atomic mass (A_r) is that it equals average mass of all the isotopic atoms present in the element compared to ¹/₁₂th the mass of a carbon-12 atom.

Examples of relative atomic mass calculations

• Example 1.1: bromine consists of 50% ⁷⁹Br and 50% ⁸¹Br, calculate the Ar of bromine.
  • A_r = [ (50 x 79) + (50 x 81) ] /100 = 80
  • So the relative atomic mass of bromine is 80 or A_r(Br) = 80
  • Note the full working shown. Yes, ok, you can do it in your head BUT many students ignore the %'s and just average all the isotopic masses (mass numbers) given.
• Example 1.2: chlorine consists of 75% chlorine-35 and 25% chlorine-37.
  • Think of the data based on 100 atoms, so 75 have a mass of 35 and 25 atoms have a mass of 37.
  • The average mass = [ (75 x 35) + (25 x 37) ] / 100 = 35.5
  • So the relative atomic mass of chlorine is 35.5 or A_r(Cl) = 35.5
• Example 1.3: 

The mass number for any isotope is the sum of the protons and neutrons in the nucleus, and is always a whole number.

(AS/A2 students only) Relative isotopic mass = 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 mass of is 58.9332!

If we were to redo the chlorine example 1.1 above, which is quite adequate for GCSE purposes, more accurately at A level, we would do ....

chlorine is 75.77% ³⁵Cl of isotopic mass 34.9689 and 24.23% ³⁷Cl of isotopic mass 36.9658

so A_r(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.

• Self-assessment Quizzes
  • [ram] type in answer Honly
  • or multiple choice Honly