Table of Contents

## Definition of Percentage Composition

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 the chemical analysis of the given compound.

- The percentage composition of any given compound is nothing but the ratio of each element present in the compound to the total amount of individual elements present in the compound multiplied by 100. Here, we measure the quantity in terms of grams of the elements present in the solution.

## Types of Percentage Composition

There are two types of percentage composition :

### 1. Mass Percentage Composition

We use the concept of mass percentage composition to denote the concentration of an element in a compound or a component in a mixture. We use this term to signify the total per cent by mass of each element present in a compound.

It is important to note that we can calculate the mass percentage composition by dividing the mass of a component by the total mass of the mixture. Then this ratio multiplied by 100. We also call it the mass percent(w/w) %.

This is a worked example problem showing how to calculate mass percent composition. Percent composition indicates the relative amounts of each element in a compound.

For each element, the mass percent formula is:

% mass = (mass of element in 1 mole of the compound) / (molar mass of the compound) x 100%

or

mass percent = (mass of solute/mass of solution) x 100%

The units of mass are typically grams. Mass percent is also known as percent by weight or w/w%. The molar mass is the sum of the masses of all the atoms in one mole of the compound.

The sum of all the mass percentages should add up to 100%. Watch for rounding errors in the last significant figure to make sure all the percentages add up.

#### Calculating Mass Percent

- You won’t always be given the total mass of a mixture or solution. Often, you’ll need to add up the masses. This might not be obvious. You may be given mole fractions or moles and then need to convert to a mass unit.
- Watch your significant figures.
- Always make sure the sum of the mass percentages of all components adds up to 100%. If it doesn’t, you need to go back and find your mistake.

#### Importance of Mass Percentage

For many scientific and practical reasons, we ought to know what quantity of an element is present in a given compound. This is indispensable for chemists to get to the empirical formula of many compounds.

This formula helps in showing the lowest whole number of moles and the relative number of atoms of each element in a compound. With the help of the empirical formula, chemists can also calculate the actual molecular formula. This formula shows the exact number of atoms in the compound.

#### Determining the Mass Percent from a Chemical Formula

We will explain this section with the help of an example. It will clear your fundamentals on how to calculate the mass percent.

Let us consider glucose. The formula for glucose is C_{6}H_{12}O_{6}. Let us calculate the mass percent of each of the elements in glucose. From the formula, we can see the number of moles of each of the elements. Glucose has 6 carbon atoms, 12 hydrogen atoms and also 6 oxygen atoms.

Let us now multiply each of the atoms by its molar mass. Thus, we arrive at the mass of each of the elements in glucose. We now divide each mass by mass of 1 mole of glucose to arrive at the mass fraction of each element. Multiplying this value by 100 gives the mass percentage of the elements.

**Example in Detail : **Each mole of Carbon has a mass of 12.01g/mol of Carbon. This, we know, from the periodic table.

So, 6 moles of Carbon will have 12.01g/mol x 6 = 72.06g of Carbon. Similarly, 1 mole of Hydrogen has a mass of 1.008g/mol of Hydrogen.

Therefore, 12 moles of Hydrogen will have a mass of 12 x 1.008 = 12.096g of Hydrogen. Going by the same logic for Oxygen, 1 mole of Oxygen has a mass of 16.00g/mol.

Therefore, 6 moles of Oxygen will have 16.00 x 6 = 96 g of Oxygen. Thus, 1 mole of glucose (C6 H12 O6) has a total mass of 72.06 +12.096 + 96 = 180.16 g/mol.

### 2. Mole Percentage Composition

Mole percentage composition is a mole percentage of each element in a compound. We only need the molecular formula of a compound to determine it.

%mole = Total moles of an element per mole of the compound/Total mole of an element in the compound x100

## The Formula of Percentage Composition

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

%CE = gE /gT × 100.

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.
- gT represents all the elements present in the compound.

The ratio is multiplied by 100 to represent it in terms of percentage.

## Applications of Percentage Composition

Here are two applications of percentage composition

## 1. To Identify Unknown Chemicals

By knowing the mass percentage of each element in a compound, we can determine the molecular formula (or empirical formula if the molar mass of the compound is unknown). Consider an example below

**Example:** To Determine Molecular Formula from Mass Percentages It is known that a chemical compound contains 52.14 % carbon, 13.13 % hydrogen, and 34.73 % oxygen. The molar mass of the chemical is also known; it is 46.069 g mol^{-1}.

**Step 1:**

First, we need to convert the mass percentages into moles. Consider 100g of the compound. So, it has 52.14g of carbon, 13.13g of hydrogen, and 34.73g of oxygen. To now, the respective moles are

n_{C} = 52.14 ÷ 12.011 = 4.341 mol,

n_{H} = 13.13 ÷ 1.008 = 13.026 mol,

and

n_{O} = 34.73 ÷ 15.999 = 2.170 mol.

**Step 2:**

Now, we have to take the mole to mole ratio of each element such that the divisor is the smallest number.

N_{C}/n_{O} = 4.341/2.170 App.2

**Step 3:**

We can determine the empirical formula from the mole ratios. So, the empirical formula is C_{2}H_{6}O. And the molar mass of the empirical mass is as follows:

MC_{2}H_{6}O =2 X 12.011+ 6 X 1.008 + 15.999 =46.069 g mol^{-1 }

Now, the empirical mass and the molar mass are the same; hence, the empirical and molecular formula must be the same, which is C_{2}H_{6}O. The compound can be ethanol, CH_{3}CH_{2}OH or dimethyl ether, CH_{3}OCH_{3}.

## 2. Labelling

The Ingredients of a product are often labelled in mass percentage composition by manufacturers. It is easier to understand the amount of an ingredient in the mass percentage than the mole percentage. Products include food, chemicals, medicine etc.

## Significance of Percentage Composition

The per cent composition of any compound is an expression of its composition in terms of all the elements present. The significance of this composition calculation is found in the chemical analysis.

### Examples

The examples of significance of percentage composition are:

#### Example-1

Consider H_{2}O molecule. The molar mass of Hydrogen (H) = 2g, and the Molar mass of Oxygen (O) = 16g.

Consider 18g of H_{2}O it contains 2g of H and 16g of O.

Mass % of H = (2×1.008×100)/(18.02) = 11.18%

Mass % of O = (16.00×100)/(18.02)= 88.79%

By using information from percentage composition we can calculate empirical formula.

#### Example-2

An example of H_{2}O, i.e. Water.

Water has 2 molecules of hydrogen, and one mole of Water is 18.0152 grams. And one mole of a hydrogen atom is 1.008 grams. So, 2 hydrogen moles weighs 2.016 grams.

Hence, one mole of Water has 2.016 grams of hydrogen mole. Therefore, the percentage composition of hydrogen would be 2.016/18.0152 = 11.19%.

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