Question

What is the percentage of lithium in lithium carbonate $\left( \text{L}{{\text{i}}_{2}}\text{C}{{\text{O}}_{\text{3}}} \right)$ ?

Answer 1

Hint: Mass percentage is used to determine the percentage of an element in a compound or mixture. It can be calculated by dividing the mass of the element by the total mass of the compound and then multiplied by 100. Its formula can be written as
\[\text{Mass percent}=\dfrac{\text{Mass of element in 1 mole of compound}}{\text{Molar mass of 1 mole of compound}}\times 100%\]

Complete answer:

A compound is a pure substance that is composed of different elements. It is made by the specific combination of atoms of different elements. The difference between elements and compounds is that elements are made up of all the same types of atoms while compounds are not. For example, water ($H_2O$) is a compound made up of hydrogen and oxygen atoms.

Each element in a compound is always present in a fixed composition. The composition of elements can be calculated if we know the molar mass of each element and the molecular formula of the compound.

One of the most common methods to find the composition is to calculate the percentage composition or mass percent of elements. It is the percentage of the element by mass present in the compound and can be calculated by using the below given formula:

\[\text{Mass percent}=\dfrac{\text{Mass of element in 1 mole of compound}}{\text{Molar mass of 1 mole of compound}}\times 100%\]

Now, for lithium carbonate, let us first find its molar mass:

\[ {{\text{M}}_{\text{L}{{\text{i}}_{2}}\text{C}{{\text{O}}_{3}}}}=2{{\text{M}}_{\text{Li}}}+{{\text{M}}_{\text{C}}}+3{{\text{M}}_{\text{O}}} \]

\[ \Rightarrow {{\text{M}}_{\text{L}{{\text{i}}_{2}}\text{C}{{\text{O}}_{3}}}}=\left( 2\times 6.94 \right)+\left( 1\times 12.01 \right)+\left( 3\times \text{16} \right) \]

\[ {{\text{M}}_{\text{L}{{\text{i}}_{2}}\text{C}{{\text{O}}_{3}}}}=73.89\text{ g mo}{{\text{l}}^{-1}} \]

The mass percent of lithium in \[\text{L}{{\text{i}}_{\text{2}}}\text{C}{{\text{O}}_{\text{3}}}\] is calculated as follows:

\[ \text{Mass percent}=\dfrac{\text{2}{{\text{M}}_{\text{Li}}}}{{{\text{M}}_{\text{L}{{\text{i}}_{\text{2}}}\text{C}{{\text{O}}_{\text{3}}}}}}\times 100\% \]

\[ \therefore \text{Mass percent}=\dfrac{13.88}{73.89}\times 100\%=18.78\% \]

Hence, the mass percent of lithium in lithium carbonate is 18.78%.

Note:

The total sum of percentage composition of each element present in a compound is always equal to 100%. We can also determine the molecular formula of a compound if we know the mass percent or the percentage composition of elements present.