Question

Silicon has 3 stable isotopes: 28Si (92.2%, 27.98 g/mol), 29Si (4.7%, 28.98 g/mol), and 30Si (3.1%, ???? g/mol). Calculate the isotopic mass of 30Si. Show your work.

Answer 1

Molecular weight of Si is 28.055 grams , which is the mass average Molar mass (means that molecular mass is the masses of its isotopes mutiplied by their natural abundance)

Thus , Molecular weight of Silicon = (27.98)$\times$(92.2%) + (28.98)$\times$(4.7%) + (x)$\times$(3.1%) ,
where x is the isotopic mass of 30 Si , and first term referrs to 28 Si (Isotopic weight times the abundance) , second term referrs to 29Si , and third to 30Si.

Thus , 28.055 = $27.98\times\frac{92.2}{100} + 28.98\times\frac{4.7}{100} + x\frac{3.1}{100}$

Solving , 28.055 = 25.797 + 1.362 + 0.031x
We get , x = 28.90 grams .

Thus the Isotopic mass of 30Si is 28.90 grams.