Doc Brown's Chemistry - Chemical Calculations

Online 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?

Introduction

• 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 amu, oxygen O = 16 amu.
• The relative atomic mass scale is now based on an isotope of carbon, carbon-12, , which is given the value of 12.0000 amu.
• In using the symbol A_r for RAM you should bear in mind that the letter A on its own usually means the mass number of a particular isotope and amu is the acronym shorthand for atomic mass units)
• 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.
  • So, you are taking into account the different isotopic masses of the same elements, but also their % abundance in the element.

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 RAM 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, in this case bromine-79 and bromine-81.
• 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 RAM or A_r(Cl) = 35.5
  • Note: ³⁵Cl and ³⁷Cl are the most common isotopes of chlorine, but, there are tiny percentages of other chlorine isotopes which are usually ignored at GCSE/IGCSE and Advanced AS/A2 A level.
• 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.

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, with further RAM calculations.

Self-assessment Quizzes

[ram] type in answer Honly  or  multiple choice Honly