What is the average atomic mass of titanium on that planet?

Question

On another planet, the isotopes of titanium have the given natural abundances.

Isotope Abundance Mass(u)

46Ti	78.600%	45.95263
48Ti	19.700%	47.94795
50Ti	1.700%	49.94479

What is the average atomic mass of titanium on that planet?

average atomic mass:?

Answer 1

It's a weighted average calculation

m_avg = (a×m₁ + b×m₂ + c×m₃)/(a + b + c) where a, b and c are fractional amount.

In the question a = 78.6% = 0.786, b = 19.7% = 0.197 and c = 1.7% = 0.017

Since a + b + c = 1, we can just add up a×m₁ + b×m₂ + c×m₃ to get our answer.

0.786(45.95263) + 0.197(47.94795) + 0.017(49.94479) = 46.41357

Answer 2

You need to multiply the abundance, expressed as a decimal, by the mass of each isotope and add them together.

0.78600 x 45.95263 + 0.19700 x 47.94795 + 0.01700 x 49.94479

36.11877 + 9.44575 + 0.84906 = 46.41358

The underlined numbers are the sig figs from each multiplication. The final result can have no more decimal places than 3 according to the rules for adding numbers to obtain a result with the correct number of sig figs. The final result should then be written as 46.414.