What is the average atomic mass of Titanium? Titanium has 5 isotopes: Ti-46 (8.0%) Ti-47(7.8%) Ti-48(73.4%) Ti-49(5.5%) Ti-50(5.3%)

1 Answer
Stefan V.
Jun 22, 2016

"47.923 u"47.923 u

Explanation:

When the problem doesn't provide you with the actual atomic mass of an isotope, m_ama, you can use its mass number, AA, as an approximation of its atomic mass.

In this case, you will have

""^46"Ti " -> " "m_a ~~ "46 u"46Ti → ma≈46 u

""^47"Ti " -> " " m_a ~~ "47 u"47Ti → ma≈47 u

""^48"Ti " -> " " m_a ~~ "48 u"48Ti → ma≈48 u

""^49"Ti " -> " " m_a ~~ "49 u"49Ti → ma≈49 u

""^50"Ti " -> " " m_a ~~ "50 u"50Ti → ma≈50 u

Now, the average atomic mass of titanium is calculated by taking the weighted average of the atomic masses of its stable isotopes.

Simply put, each isotope ii will contribute to the average atomic mass of the element in proportion to its decimal abundance, which is simply the percent abundance divided by 100100.

color(blue)(|bar(ul(color(white)(a/a)"avg. atomic mass" = sum_i m_"a i" xx "abundance of i"color(white)(a/a)|)))

The decimal abundances for these five isotopes will be

""^46"Ti: " 8.0/100 = 0.080

""^47"Ti: " 7.8/100 = 0.078

""^48"Ti: " 73.4/100 = 0.734

""^49"Ti: " 5.5/100 = 0.055

""^50"Ti: " 5.3/100 = 0.053

The average atomic mass of titanium will thus be

"avg. atomic mass " =

"46 u" xx 0.080 + "47 u" xx 0.078 + "48 u" xx 0.734 + "49 u" xx 0.055 + "50 u" xx 0.053

"avg. atomic mass " = color(green)(|bar(ul(color(white)(a/a)color(black)("47.923 u")color(white)(a/a)|)))

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