# Using Percentages in Chemical Weight Problems

Instructor: Matthew Bergstresser
Percentages are very useful when determining the fraction of a total. In this lesson, we will use percentages in chemistry problems involving the weight of compounds.

## Pizza Percentages

Do you love pizza? A medium pizza can be cut into eight equal slices. If your friend takes one slice, we can determine the percent he ate, which is the fraction of the total relative to 100.

Let's say that one perfect slice is separated from the rest of the pie and eaten. What percentage has been eaten? We set up the ratio of the number of slices eaten divided by the original number of slices. This gives us 1/8. To turn it into a percentage, we multiply that fraction by 100 giving us 12.5%. The same process is done with percent by weight calculations for chemical compounds. Let's switch gears from pizza to chemical compounds.

## The Chemical Formula

Formulas for chemical compounds include the symbols for the elements and subscripts representing how many atoms of each are in them. For example, the gaseous compound we all exhale is carbon dioxide, which has the chemical formula CO2. This means there is one atom of carbon and two atoms of oxygen in every molecule of carbon dioxide. To get the percent of each element by weight, we need the relative weights of each element in the compound. This information is on everyone's favorite table - the periodic table!

## Molar Mass

In chemistry, weight and mass are sometimes used interchangeably. Technically, mass is correct because the values under the elements' symbols on the periodic table are in grams, which is a unit of mass. This number is in the box on the periodic table with the chemical symbol and atomic number. It is the number that is not a whole number (in other words it's a decimal).

To get the total mass of carbon dioxide, we have to add the masses of each element in the compound.

 Element Molar Mass (g/mole) Quantity Total Molar Mass of Element in Compound (g/mole) Carbon 12.01 1 12.01 Oxygen 16.00 2 32.00

Total Molar Mass in Compound = 12.01 + 32.00 = 44.01 g/mole

## Percent by Mass

Let's calculate the percent by mass of each element in carbon dioxide. To do this, we need the amount of the individual components divided by the total amount. Since we are dealing with masses, we need the molar mass of the carbon in the compound divided by the total molar mass of the compound. The same goes for the oxygen. First, let's calculate the percent by mass of carbon in carbon dioxide.

Percent of oxygen by mass:

When we add the two percentages together it equals 100%, which is a good way to check if we made any mistakes. Sometimes, though, due to rounding, the sum may not equal 100 exactly.

## Percent by Mass of Elements in Sugar

Common table sugar, or sucrose, has a chemical formula of C12 H22 O11. Let's find the percent by mass of carbon, hydrogen, and oxygen in sugar.

The first step is to get the molar masses for each element from the periodic table. Then we will determine the total molar mass of each element in the compound, followed by adding all of those molar masses together. Finally, we will divide the individual molar masses of each element by the total molar mass and multiply by 100.

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