Compounds

Chemical Proportions and Percentage Composition

6.1

Compounds That Contain the Same Elements in the Same Proportions

Water on Earth has the same chemical composition as water on the Moon. More than 200 years ago, scientists discovered that compounds contain elements in fixed proportions. Water ALWAYS has 2 hydrogen atoms and 1 oxygen atom. This discovery was accepted into law almost 100 years after it was made

The Law of Definite Proportions

The elements in a chemical compound are always present in the same proportions by mass.

Mass Percent

According to the law, all water molecules have the same chemical composition. Therefore, 1 mol of water has a mass of 18.02g and contains 16.00g of oxygen and 2.02g of hydrogen. However, the law deals with proportions—not mass. As a result, the proportion of each element is often expressed as a percentage of the total mass. This is known as mass percent.

Calculating Mass Percent Using the Chemical Formula

Determine the mass percent of hydrogen in water:

Calculating Mass Percent Using Experimental Data

A 650 mg sample was analyzed and found to contain 51.0 mg of hydrogen. What is the mass percent of the sample?

Compounds that Contain the Same Elements in Different Proportions

All water has the same chemical formula—H₂O. But there are hundreds of compounds that contain the same elements, but in different proportions. For example, H₂O and H₂O₂. Water is a stable compounds, whereas hydrogen peroxide is quite reactive.

NO₂ and N₂O are two very different compounds, despite containing the same elements. Nitrogen dioxide is a product of car exhaust is highly toxic. Dinitrogen monoxide (aka “laughing gas”) is routinely used to calm patients during dental procedures.

Different Proportions = Different Properties

Percentage Composition

When you combine the mass percent for all of the elements in a compound, you have the percentage composition of the compound.

Percentage Composition of NO_2(g) Percentage Composition of N₂O_(g)

Mass percent of N = 30.45% mass percent of N = 63.65%

Mass percent of O = 69.55% mass percent of O = 36.25%

Determining Percentage Composition from Mass Data

A volatile chemical was removed from a crime scene. Analysis of a 35.20 mg sample of the chemical showed that it contained 3.56 mg of carbon and 0.28 mg of hydrogen. Later, investigators learned that the chemical was chloroform, CHCl_3(l). What is the percentage composition of chloroform?

mass of total sample: 35.2 mg

mass of carbon sample: 3.56 mg

mass of hydgrogen sample: 0.28 mg

1. 
   Calculate the mass of the chlorine sample
   

2. 
   Determine the percentage composition of each element
   

Repeat for hydrogen and chlorine:

• 
  Mass percent of hydrogen: 0.80%
  
• 
  Mass percent of chlorine: 89.09%
  

Determining Percentage Composition from a Chemical Formula

Given the chemical formula, any mass for the sample sized could be picked. For convenience, 1 mol of the substance is used as the sample size.

Determine the mass percent of Cu in copper (I) sulfide, Cu₂S.

Empirical and Molecular Formulas

The molecular formula of a compound shows the number of atoms of each element that make up a molecule. For example, H₂O and C₆H₁₂O₆ (glucose).

The empirical formula of a compound shows the smallest whole-number ratio of the elements in a compound. For example, CH₂O (glucose).

The empirical formula gives a very basic glimpse into the composition of a compound—and is therefore a very good starting point.

Determining the Empirical Formula

1. 
   Convert percentage composition data into mass data assuming that the total mass of the sample is 100g.
   
2. 
   Determine the number of moles of each element in the sample by dividing the mass by the molar mass of each element.
   
3. 
   Convert the number of moles of each element into subscripts.
   
4. 
   Convert the number of moles of each element into whole numbers by dividing each subscript by the smallest amount.
   
5. 
   If the subscripts are not yet whole numbers, determine the least common multiple that will make the decimal values into whole numbers. Multiply all subscripts by this common multiple.
   

Example:

Determine the empirical formula for a compound that is found by analysis to contain 27.37% sodium, 1.200% hydrogen, 14.30% carbon and 57.14% oxygen.

Determining the Molecular Formula

Because the molecular formula is so close to the empirical formula, you can determine the molecular formula of a compound by using the empirical formula and the molar mass of the compound.

1. 
   Determine the molar mass of the empirical formula
   
2. 
   Use the given molar mass of the compound (mass spectrometer) to determine the whole number multiplier.
   

Ex. The empirical formula for glucose is CH₂O_(s). The molar mass of glucose is 180.18 g/mol. Determine the molecular formula for glucose.

1. 
   Determine the molar mass of CH₂O_(s)
   

2. 
   Determine the whole number multiplier:
   

3. 
   Multiply all the subscripts of the empirical formula by 6
   

Molecular formula of glucose is C₆H₁₂O₆