Question: How do you calculate the percent composition of chromium in \[BaCr{O_4}\]?...

Question

How do you calculate the percent composition of chromium in $BaCr{O_4}$ ?

Answer 1

Solution

The percent composition is the percentage of the weight of a component in a compound. It expresses the amount responsible or the weight contribution of a component in the total weight of the compound.

Complete step by step answer:
The percentage composition of a component present in a compound is termed as the ratio of the amount of each component and the sum of amounts of all the components present in the compound multiplied by $100$ . In general for convenience the amounts are measured in grams of the component.
The significance of percent composition is that it helps in determining the empirical and the molecular formula of a compound. The reverse is also true that if the formula of the compound is known then the percent composition of each component is evaluated.
The percentage composition of a component is expressed by the following mathematical equation as,
$P{C_x} = \dfrac{{{w_x}}}{{MW}} \times 100$ where $P{C_x}$ is the percent composition of the component $x$ , ${w_x}$ is the amount of the component $x$ and $MW$ is the total weight of all the components present in the compound. The factor $100$ is multiplied to express the fraction amount in terms of percentage.
The following steps are employed for determining the percent composition of $BaCr{O_4}$ .
a. At first the molar mass of the compound $BaCr{O_4}$ is evaluated by adding up the atomic masses of each of the atoms present in $BaCr{O_4}$ .
Molar mass = atomic mass of $Ba$ + atomic mass of $Cr$ + $4{\text{ }} \times$ atomic mass of $O$
= $137 + 52 + 4 \times 16 = 253g$
As the compound contains a single chromium atom so the weight of the chromium atom is $52.0g$ . Hence the percent composition of chromium in $BaCr{O_4}$ is
$P{C_{Cr}} = \dfrac{{{w_{Cr}}}}{{MW}} \times 100$
$P{C_{Cr}} = \dfrac{{52}}{{253}} \times 100 = 20.5\%$

Note:
The percent composition should not be confused with the mole fraction of a compound. The mole fraction is also a ratio of the moles of a compound in a mixture of compounds or solutions. But a percent composition is an element percent determination which constitutes a fraction in a compound.