Question

What is the percentage by mass of hydrogen in aspirin, \[{C_9}{H_8}{O_4}\]?

Answer 1

Hint: Percentage by mass is the proportion of the element in a compound. Use the formula of percentage by mass or a mass percentage to calculate the percentage of hydrogen in aspirin.
Formula:
\[Mass{\text{ }}percentage{\text{ }} = {\text{ }}\dfrac{{mass{\text{ }}of{\text{ }}the{\text{ }}element}}{{molar{\text{ }}mass}} \times 100\] mass of the element is the mass of total number of element in a compound.

Complete answer:
Percentage by mass is the percentage of each element in a compound in terms of mass. It is a way to describe what proportions of the different elements are there in a compound. It is calculated by using the formula:
\[Mass{\text{ }}percentage{\text{ }} = {\text{ }}\dfrac{{mass{\text{ }}of{\text{ }}the{\text{ }}element}}{{molar{\text{ }}mass}} \times 100\]\[\]
We need the mass of hydrogen in aspirin. The mass of one hydrogen atom is \[1.00784\;{\text{ }}gmo{l^{ - 1}}\] . In aspirin there are eight hydrogen atoms so we will multiply the mass of one hydrogen atom with eight to get the mass of eight hydrogen atoms.
Thus \[1.00784\;{\text{ }}gmo{l^{ - 1}} \times 8\]
\[ \Rightarrow 8.06272\;{\text{ }}gmo{l^{ - 1}}\]
This is the mass of eight hydrogen atoms in aspirin.
Next, we need the molar mass of aspirin. It is easy to calculate, just multiply the number of elements with their atomic masses and add all the numbers obtained, the final answer you get is the molar mass.
The atomic masses of carbon, hydrogen and oxygen are $C = 12.0107{\text{ }}gmo{l^{ - 1}}$, $H = 1.00784{\text{ }}gmo{l^{ - 1}}$ and $O = 16{\text{ }}gmo{l^{ - 1}}$
Molar mass of aspirin: \[{C_9}{H_8}{O_4}\]
$ \Rightarrow \left( {9 \times 12.0107} \right) + \left( {8 \times 1.00784} \right) + \left( {4 \times 16} \right)$
$ \Rightarrow {\text{108}}{\text{.0963}} + {\text{8}}{\text{.06272}} + 64$
$ \Rightarrow {\text{180}}{\text{.15902 }}gmo{l^{ - 1}}$
Thus molar mass of aspirin is ${\text{180}}{\text{.15902 }}gmo{l^{ - 1}}$
Now we will use the formula of mass percentage to finally calculate the percentage of hydrogen in aspirin.
\[Mass{\text{ }}percentage{\text{ }} = {\text{ }}\dfrac{{mass{\text{ }}of{\text{ }}the{\text{ }}element}}{{molar{\text{ }}mass}} \times 100\]
Now substitute the value of mass of the element (hydrogen) and the molar mass of aspirin.
\[ \Rightarrow Percentage{\text{ }}by{\text{ }}mass{\text{ }} = {\text{ }}\dfrac{{8.06272}}{{180.15902}} \times 100\]
\[ \Rightarrow Percentage{\text{ }}by{\text{ }}mass{\text{ }} = {\text{ 4}}{\text{.4753}}\% \]
Therefore percentage by mass of hydrogen in aspirin is \[{\text{4}}{\text{.4753}}\% \]

Note:
To solve this problem you need to know the mass of the hydrogen because we have to find the percentage by mass of hydrogen. If it was carbon or oxygen we would be finding their masses. It is also known as the percentage composition of the element in a compound. Sometimes when there is a solution instead of a compound then the formula changes slightly. It becomes:
\[Mass{\text{ }}percentage{\text{ }} = {\text{ }}\left( {\dfrac{{mass{\text{ }}of{\text{ }}the{\text{ }}solute}}{{mass{\text{ }}of{\text{ }}the{\text{ }}solution}}} \right) \times 100\]