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Percent Composition Formula

The percentage composition of a given compound is defined as the ratio of the amount of each element to the total amount of individual elements present in the compound multiplied by 100. Here, the quantity is measured in terms of grams of the elements present.

The percent composition of any compound expresses its composition in terms of all the elements present. Thus, it helps in chemical analysis of the given compound.

The formula for Percentage Composition

The percentage composition of a given element is expressed using the following formula,

\(\begin{array}{l}\%C_{E}=\frac{g^{E}}{g^{T}}\times 100\end{array} \)

Here, %CE is the percentage composition of the element E, that is to be calculated. gE represents the total amount of element E present in the compound and gT represents the total amount of all the elements present in the compound. The ratio is multiplied by 100 so as to represent it in terms of percentage.  

Solved Examples

Example 1: For the compound (Ca(OH)2) or calcium hydroxide, find the per cent composition of the element Calcium(Ca).

Solution:

Given that the chemical formula for calcium hydroxide = (Ca(OH)2)

Using the above formula, we calculate the formula mass of this compound.

For calcium hydroxide, the formula mass can be calculated as,

\(\begin{array}{l}Formula\; mass=one\; calcium\frac{a}{mu}+2\times hydrogen\frac{a}{mu}+2\times oxygen\frac{a}{mu}\end{array} \)


Molar mass (approx) of each element can be given as,

\(\begin{array}{l}1Ca\left ( \frac{a}{mu} =40\right )=40\end{array} \)

\(\begin{array}{l}20\left ( \frac{a}{mu}=16 \right )=2\times 16=32\end{array} \)

\(\begin{array}{l}2H\left ( \frac{a}{mu}=1 \right )2\times 1=2\end{array} \)

Formula mass of Ca(OH)2 

Formula mass = 40 + 32 + 2 = 74

Using this value, we calculate the percentage composition of Calcium in the compound as,

\(\begin{array}{l}\%Ca=\frac{40}{74}\times 100\end{array} \)

\(\begin{array}{l}\%Ca=54.05\%\end{array} \)

 

Question 2: Find the per cent composition of each element in water.

Solution:

The chemical formula for water is H2O.

We now calculate the molar mass of water.

The molar mass of Oxygen = 16.00 × 1 = 16 g/mole

The molar mass of Hydrogen = 1.01 × 2 = 2.02 g/mole

Now, using the molar mass of each of the given elements, we find out the percentage composition of each element in H2O.

\(\begin{array}{l}\%composition = \frac{grams\; of\; element}{grams\; of\; total\; elemnts\; in\; the\; compound}\times 100\end{array} \)

Calculating the percentage composition for Hydrogen,

\(\begin{array}{l}\%H=\frac{g^{H}}{g^{T}}\times 100\end{array} \)

\(\begin{array}{l}\%H=\frac{2.02}{18.02}\times 100\end{array} \)

\(\begin{array}{l}\%H=11.21\end{array} \)

Calculating the percentage composition of Oxygen,

\(\begin{array}{l}\%O=\frac{g^{O}}{g^{T}}\times 100\end{array} \)

\(\begin{array}{l}\%O=\frac{16}{18.02}\times 100\end{array} \)

\(\begin{array}{l}\%O=88.79\end{array} \)

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