Question

A $0.24g$ sample of compound oxygen and boron analysis to contain $0.096g$ of Boron and $0.144g$ of the percentage composition of the compound by mass. Calculate the percentage composition of the compound by weight.

Answer 1

We have enough parameters to find the percentage of Boron or Oxygen. Finding either one percentage of the two elements and subtracting it from $\,100\,$ (the total percentage) will give the percentage of the other element.

Complete step by step answer:
The solution is to find the percentage of two elements. The percentage of an element in a compound is given by,
${\text{Percentage of elemen}}{{\text{t}}_1}{\text{ = }}\dfrac{{{\text{Mass of elemen}}{{\text{t}}_1}}}{{{\text{Mass of compound }}}} \times 100$
${\text{Percentage of elemen}}{{\text{t}}_2} = {\text{ 100 - Percentage of elemen}}{{\text{t}}_1}$
Complete step by step solution:
Let us list the given parameters from the question.
${\text{Mass of Oxygen (O) = 0}}{\text{.144g}}$
${\text{Mass of Boron(B) = 0}}{\text{.096g}}$
${\text{Mass of the compound = 0}}{\text{.24g}}$
From these parameters, we can find any one percentage of Boron or Oxygen and will subtract it from $\,100\,$, which will give the percentage of the other compound.
Let us find the percentage of Boron. We can substitute the values of mass of Boron and the compound in the following equation.
${\text{Percentage of Boron = }}\dfrac{{{\text{Mass of Boron}}}}{{{\text{Mass of compound }}}} \times 100$
$= > {\text{ }}\dfrac{{0.96}}{{0.24}} \times 100$
${\text{Therefore, percentage of Boron}}$ {\text{ = 40% }}
Now, subtracting the percentage of Boron from $\,100\,$, we get the percentage of Oxygen as $60\%$.

Additional information:
The question can be solved in another way. That is a little longer, which is not necessary when a fixed compound is given. The way is solving the percentage of both the elements by the given formula. The advantages of this method of solving is, if the given compound is not a fixed compound (like in the question, Boron and Oxygen are the only constituents of the compound), we can detect the presence of other elements from the total percentage. If the total percentage is not $\,100\% \,$ , then another element should be present in the compound. This method is used to detect the presence of new elements in a compound.

Note:
If the mass of one element is not given, subtract the mass of another element from the mass of the compound. If the mass of the compound is not given, add the masses of the two elements. Similarly, masses of elements can be found from percentage of the elements by the formula,
${\text{Mass of elemen}}{{\text{t}}_1} = \dfrac{{{\text{Percentage of elemen}}{{\text{t}}_1}{\text{ }} \times {\text{ Mass of compound}}}}{{100}}$