Doc Brown's Chemistry - GCSE/IGCSE/GCE (basic A level) O Level  Online 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 GCE A level AS/A2/IB courses * EMAIL query?comment or request for type of GCSE/IGCSE/AS 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 and oxygen O = 16 amu in the past.
• 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 other words the relative atomic mass of an element is now based on the arbitrary value of the carbon-12 isotope being assigned a mass of 12.0000 by international agreement!
  • Examples are shown in the Periodic Table diagram above.
  • Note that because of the presence of neutrons in the nucleus, the relative atomic mass is usually at least double the atomic/proton number because there usually at the number of neutrons as protons in the nucleus (mass proton = 1, neutron = 1).
  • Also note, that for many calculations purposes, relative atomic masses are usually quoted and used at this academic level to one decimal place eg.
  • hydrogen H = 1.0 or 1, calcium Ca= 40.0 or 40, chlorine Cl = 35.5, copper Cu = 63.6, silver Ag 108 or 107.9 at A level etc.
  • Sometimes at A level, values of relative atomic masses to two decimal places may be quoted.
• 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/IGCSE/AS 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.
  • Therefore you need to know the percentage (%) of each isotope of an element in order to accurately calculate the element's relative atomic mass.

Examples of relative atomic mass calculations for GCSE/IGCSE/AS level students

• and
• 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.
• and
• 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 GCE 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 an integer i.e. 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.

(b) Calculations of % composition of isotopes

It is possible to do the reverse of a relative atomic mass calculation if you know the A_r and which isotopes are present.

It involves a little bit of arithmetical algebra.

The A_r 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 and mass spectrometers can sort out the isotopes present.

If you let X = % of boron 10, then 100-X is equal to % of boron-11

Therefore A_r(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 quote 18.7 and 81.3)

Self-assessment Quizzes

[ram] type in answer Honly  or  multiple choice Honly 

OTHER CALCULATION PAGES

1. What is relative atomic mass?, relative isotopic mass & calculating relative atomic mass (this page)

2. Calculating relative formula/molecular mass of a compound or element molecule

3. Law of Conservation of Mass and simple reacting mass calculations

4. Composition by percentage mass of elements in a compound

5. Empirical formula and formula mass of a compound from reacting masses (easy start, not using moles)

6. Reacting mass ratio calculations of reactants and products from equations (NOT using moles) and brief mention of actual percent % yield and theoretical yield, atom economy and formula mass determination

   • Reacting masses, concentration of solution and volumetric titration calculations (NOT using moles)

7. Introducing moles: The connection between moles, mass and formula mass - the basis of reacting mole ratio calculations (relating reacting masses and formula mass)

8. Using moles to calculate empirical formula and deduce molecular formula of a compound/molecule (starting with reacting masses or % composition)

9. Moles and the molar volume of a gas, Avogadro's Law

10. Reacting gas volume ratios, Avogadro's Law and Gay-Lussac's Law (ratio of gaseous reactants-products)

11. Molarity, volumes and solution concentrations (and diagrams of apparatus)

12. How to do volumetric titration calculations e.g. acid-alkali titrations (and diagrams of apparatus)

13. Electrolysis products calculations (negative cathode and positive anode products)

14. Other calculations e.g. % purity, % percentage & theoretical yield, volumetric titration apparatus, dilution of solutions (and diagrams of apparatus), water of crystallisation, quantity of reactants required, atom economy

15. Energy transfers in physical/chemical changes, exothermic/endothermic reactions

16. Gas calculations involving PVT relationships, Boyle's and Charles Laws

17. Radioactivity & half-life calculations including dating materials

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