Question

A \[{\text{0}}{\text{.24 g}}\] sample of compound of oxygen and boron was found by analysis to contain \[{\text{0}}{\text{.096 g}}\] of boron and \[{\text{0}}{\text{.144 g}}\] of oxygen. Calculate the percentage composition of the compound by weight.

Answer 1

Hint:The mass percent of an element in a compound gives the mass of an element present in one hundred grams of compound. You can use the following formula to calculate the mass percent of an element in a compound.
\[{\text{Mass percent of element = }}\dfrac{{{\text{Mass of element}}}}{{{\text{Mass of compound}}}} \times {\text{100}}\]

Complete step-by-step solution:
When you divide the mass of an element present in a sample of compound with the mass of that sample of compound and multiply the answer with one hundred, you get the mass percent of that element in the compound. You can also call the mass percent as the percentage by mass.

For example, the molecular weight (in grams per mole) of water is 18, whereas the atomic weights (in grams per mole) of hydrogen and oxygen is 1 and 16 respectively.

Thus, one mole of water weighs eighteen grams of water and contains two grams of hydrogen and sixteen grams of oxygen. The mass percent of hydrogen and oxygen in water are 11.11 and 88.89 respectively. Thus, \[{\text{100 grams}}\] of water contains \[{\text{11}}{\text{.11 grams}}\] of hydrogen and \[{\text{88}}{\text{.89 grams}}\] of oxygen.

\[
  {\text{Mass percent of boron = }}\dfrac{{{\text{Mass of boron}}}}{{{\text{Mass of compound}}}} \times {\text{100 }} \\
  {\text{Mass percent of boron = }}\dfrac{{0.096}}{{0.24}} \times {\text{100 }} \\
  {\text{Mass percent of boron = 40\% }} \\
 \]
Hence, the mass percent of boron in the compound is \[{\text{40\% }}\] .
\[
  {\text{Mass percent of oxygen = }}\dfrac{{{\text{Mass of oxygen}}}}{{{\text{Mass of compound}}}} \times {\text{100 }} \\
  {\text{Mass percent of oxygen = }}\dfrac{{0.144}}{{0.24}} \times {\text{100 }} \\
  {\text{Mass percent of oxygen = 60\% }} \\
 \]

Hence, the mass percent of oxygen in the compound is \[{\text{60\% }}\].

Note:When a compound contains two elements boron and oxygen, the sum of the mass percent of boron and the mass percent of oxygen is equal to one hundred.
\[
  {\text{Mass percent of boron + Mass percent of oxygen = }}40{\text{\% }} + 60{\text{\% }} \\
  {\text{Mass percent of boron + Mass percent of oxygen = 100\% }} \\
 \]