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Naturally occurring zirconium exists are five isotopes. axe with a mass of 89.905 u(51.45%); Zr with a mass of 90.906 u (11.22%); Zr with a mass of 91.905 u (17.15%); Zr with a mass of 93.906 u (17.38%) and Zr with a mass of 95.908 u (2.80%). Calculate the average mass of zirconium.

Verified Answer :

Moly42

Isotope 1: 89.905 51.45 = 4625.61225 / 100 = 46.2561225
Isotope 2: 90.906 11.22 = 1019.96532 / 100 = 10.1996532
Isotope 3: 91.905 17.15 = 1576.17175 / 100 = 15.7617075
Isotope 4: 93.906 17.38 = 1632.08628 / 100 = 16.3208628
Isotope 5: 95.908 * 2.08 = 268.5424 / 100 = 2.685424

46.2561225 + 10.1996532 +  15.7617075 + 16.3208628 + 2.685424 = 91.22377
actual mass Zr = about 91.22

adioabiola

Here, we are required to determine the average mass of zirconium based on the respective abundance of the 5 isotopes.

The average mass of Zirconium is 90.2238

To find the average mass of Zr., the relative abundance is taken for each isotope and the algebraic sum of all is taken.

Relative abundance of;

  • Isotope 1 : 89.905 × (51.45/100) = 45.2561

  • Isotope 2 : 90.906 × (11.22/100) = 10.1997

  • Isotope 3 : 91.905 × (17.15/100) = 15.7617

  • Isotope 4 : 93.906 × (17.38/100) = 16.3209

  • Isotope 5 : 95.908 × (2.80/100) = 2.6854

The average mass of Zirconium is the algebraic sum of the relative abundance of all of the isotopes; i.e ;

Average mass of Zirconium =

45.2561 + 10.1997 + 15.7617 + 16.3209 + 2.6854

Therefore, average mass of Zirconium is 90.2238

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