Question

The commonly used pain reliever, aspirin, has the molecular formula ${C_9}{H_8}{O_4}$ . If a sample of aspirin contains 0.968 g of carbon, what is the mass of hydrogen in the sample?
A. 0.717 g
B. 0.0717 g
C. 8.000 g
D. 0.645 g

Answer 1

Hint: The formula of aspirin gives us moles of each component present, the number of atoms in 1 molecule of aspirin also gives us moles of substance in 1 mole of aspirin.
We find first the moles of Carbon according to given weight, and then from that moles of aspirin. From Aspirin moles, we can find moles of hydrogen, then from moles of hydrogen, we can get mass of hydrogen. Most of these calculations involve a simple cross multiplication method.

Complete step by step answer:
Now, we know that aspirin is commonly used pain reliever medicine, with formula of ${C_9}{H_8}{O_4}$
So from the formula, we can say that 1 mole aspirin contains 9 moles of carbon, 8 moles of hydrogen and 4 moles of Oxygen.
Mass of 1 mole of aspirin = molar mass of aspirin.
\[
  Molar{\text{ }}mass{\text{ }}of{\text{ }}aspirin{\text{ }} = 9 \times gram{\text{ }}atomic{\text{ }}mass{\text{ }}of{\text{ }}Carbon \\
   + 8 \times gram{\text{ }}atomic{\text{ }}mass{\text{ }}of{\text{ }}Hydrogen \\
   + 4 \times atomic{\text{ }}mass{\text{ }}of{\text{ }}oxygen \\
 \]
We know atomic masses of all the above elements, so we substitute them.
\[
  {\text{Molar mass of aspirin = }}(9 \times 12) + (8 \times 1) + (4 \times 16) \\
   = 108 + 8 + 64 \\
   = 180g \\
 \]
Thus, on simplification, we get molar mass of aspirin as 180 g.
\[
  {\text{mass of 9 moles of carbon = }}9 \times 12 \\
   = 108g \\
 \]
Thus, 180 g aspirin contains 108 g carbon.
So, let us assume x gm of aspirin, in 0.968 gm carbon (given weight).
So, apply unitary method and we get:
$\dfrac{{108}}{{0.968}} = \dfrac{{180}}{x}$
Taking x on one side, and other numerical values on other side, we get
\[x = \dfrac{{180 \times 0.968}}{{108}}\]
\[\therefore x = 1.613\]
Thus, 1.613 gm of aspirin is present.
Applying same unitary method,
From formula of aspirin,
We know, 180 gm aspirin has 8 gm hydrogen.
Assume mass of hydrogen to be y gm in 1.613 gm aspirin
So, 1.613 gm aspirin has y gm hydrogen.
We can write,
\[\dfrac{{180}}{{1.613}} = \dfrac{8}{y}\]
Taking y on one side, and numerical values on other side,
\[y = \dfrac{{8 \times 1.613}}{{180}}\]
\[\therefore y = 0.0717\]
Thus the mass of hydrogen is 0.0717 g.

Hence the correct option is B.

Note: We must know the value of atomic masses of the elements, and that can be approximated to the nearest whole number or may be 1 decimal point. Example: for hydrogen the mass is 1.008 g, but we can take the whole number as 1 g. We might observe very small differences in answer, maybe up to $3^{rd}$ decimal to be different, but we may choose from options accordingly.