Question

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

Answer 1

Hint: We know that the mole is widely used in chemistry as a convenient way to express amounts of reactants and products of chemical reactions. It is a fundamental unit which helps to calculate a big number. The mole is essentially a count of particles. The formula we will use here is \[avg.\text{ }atomic\text{ }mass\text{ = }\sum\limits_{i}^{{}}{{{m}_{ai}}}\text{ }abundance\text{ }of\text{ }i\]

Complete answer:
Titanium is the \[7\]th most abundant metallic element and \[9\]th most abundant element in the Earth’s crust. It is mostly found as oxides in igneous rocks. It is also found in the lithosphere. Titanium is present in almost all living things, water bodies, rocks and soil. Whenever the problem doesn't provide us with the actual atomic mass of an isotope, ma, we can use its mass number, A, as an approximation of its atomic mass. In this case, we will have
\[{}^{46}Ti\text{ }\to \text{ }ma\approx 46\text{ }u\]
\[{}^{47}Ti\text{ }\to \text{ }ma\approx 47\text{ }u\]
\[{}^{48}Ti\text{ }\to \text{ }ma\approx 48\text{ }u\]
\[{}^{49}Ti\text{ }\to \text{ }ma\approx 49\text{ }u\]
\[{}^{50}Ti\text{ }\to \text{ }ma\approx 50\text{ }u\]
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 \[~100.\] \[avg.\text{ }atomic\text{ }mass\text{ = }\sum\limits_{i}^{{}}{{{m}_{ai}}}\text{ }abudance\text{ }of\text{ }i\]
The decimal abundances for these five isotopes will be
\[{}^{46}Ti:\text{ }\dfrac{8.0}{100}=0.080\]
\[{}^{47}Ti:\text{ }\dfrac{7.80}{100}=0.078\]
\[{}^{48}Ti:\text{ }\dfrac{73.4}{100}=0.734\]
\[{}^{49}Ti:\text{ }\dfrac{5.5}{100}=0.055\]
\[{}^{50}Ti:\text{ }\dfrac{5.3}{100}=0.053\]
The average atomic mass of titanium will thus be
avg. atomic mass \[=\left( 46\text{ }u\times 0.080 \right)+\left( 47\text{ }u\times 0.078 \right)+\left( 48\text{ }u\times 0.734 \right)+\left( 49\text{ }u\times 0.055 \right)+\left( 50\text{ }u\times 0.053 \right)\]
Therefore, average atomic mass is $47.923u$

Note:
Remember that Titanium is very useful in various fields mainly due to its properties such as highest strength to density ratio and corrosion resistance etc. Titanium tetrachloride is used in smoke screens. It is also used as a catalyst. Titanium alloys are strong, durable, and lightweight so they are generally used in missiles, jet engines and spacecraft. It is also used in the military, automotive industry, paper and pulp industry and agriculture.