Question
Question: What is the percentage by mass of hydrogen in aspirin, \[{C_9}{H_8}{O_4}\]?...
What is the percentage by mass of hydrogen in aspirin, C9H8O4?
Solution
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 percentage = molar massmass of the element×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$$$$$$
We need the mass of hydrogen in aspirin. The mass of one hydrogen atom is 1.00784;{\text{ }}gmo{l^{ - 1}}.Inaspirinthereareeighthydrogenatomssowewillmultiplythemassofonehydrogenatomwitheighttogetthemassofeighthydrogenatoms.Thus1.00784;{\text{ }}gmo{l^{ - 1}} \times 8 \Rightarrow 8.06272;{\text{ }}gmo{l^{ - 1}}
This is the mass of eight hydrogen atoms in aspirin.
Next, we need the molar mass of aspirin. It is easy to calculate, just multiply the number of elements with their atomic masses and add all the numbers obtained, the final answer you get is the molar mass.
The atomic masses of carbon, hydrogen and oxygen are $C = 12.0107{\text{ }}gmo{l^{ - 1}}$, $H = 1.00784{\text{ }}gmo{l^{ - 1}}$ and $O = 16{\text{ }}gmo{l^{ - 1}}$
Molar mass of aspirin:{C_9}{H_8}{O_4}
$ \Rightarrow \left( {9 \times 12.0107} \right) + \left( {8 \times 1.00784} \right) + \left( {4 \times 16} \right)$
$ \Rightarrow {\text{108}}{\text{.0963}} + {\text{8}}{\text{.06272}} + 64$
$ \Rightarrow {\text{180}}{\text{.15902 }}gmo{l^{ - 1}}$
Thus molar mass of aspirin is ${\text{180}}{\text{.15902 }}gmo{l^{ - 1}}$
Now we will use the formula of mass percentage to finally calculate the percentage of hydrogen in aspirin. Mass{\text{ }}percentage{\text{ }} = {\text{ }}\dfrac{{mass{\text{ }}of{\text{ }}the{\text{ }}element}}{{molar{\text{ }}mass}} \times 100Nowsubstitutethevalueofmassoftheelement(hydrogen)andthemolarmassofaspirin. \Rightarrow Percentage{\text{ }}by{\text{ }}mass{\text{ }} = {\text{ }}\dfrac{{8.06272}}{{180.15902}} \times 100 \Rightarrow Percentage{\text{ }}by{\text{ }}mass{\text{ }} = {\text{ 4}}{\text{.4753}}% Thereforepercentagebymassofhydrogeninaspirinis{\text{4}}{\text{.4753}}% $$
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 percentage = (mass of the solutionmass of the solute)×100