# 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%)

Jun 22, 2016

$\text{47.923 u}$

#### Explanation:

When the problem doesn't provide you with the actual atomic mass of an isotope, ${m}_{a}$, you can use its mass number, $A$, as an approximation of its atomic mass.

In this case, you will have

$\text{^46"Ti " -> " "m_a ~~ "46 u}$

$\text{^47"Ti " -> " " m_a ~~ "47 u}$

$\text{^48"Ti " -> " " m_a ~~ "48 u}$

$\text{^49"Ti " -> " " m_a ~~ "49 u}$

$\text{^50"Ti " -> " " m_a ~~ "50 u}$

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 $i$ will contribute to the average atomic mass of the element in proportion to its decimal abundance, which is simply the percent abundance divided by $100$.

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \text{avg. atomic mass" = sum_i m_"a i" xx "abundance of i} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

The decimal abundances for these five isotopes will be

$\text{^46"Ti: } \frac{8.0}{100} = 0.080$

$\text{^47"Ti: } \frac{7.8}{100} = 0.078$

$\text{^48"Ti: } \frac{73.4}{100} = 0.734$

$\text{^49"Ti: } \frac{5.5}{100} = 0.055$

$\text{^50"Ti: } \frac{5.3}{100} = 0.053$

The average atomic mass of titanium will thus be

$\text{avg. atomic mass } =$

$\text{46 u" xx 0.080 + "47 u" xx 0.078 + "48 u" xx 0.734 + "49 u" xx 0.055 + "50 u} \times 0.053$

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