# 3.2 Determining empirical and molecular formulas

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By the end of this section, you will be able to:
• Compute the percent composition of a compound
• Determine the empirical formula of a compound
• Determine the molecular formula of a compound

In the previous section, we discussed the relationship between the bulk mass of a substance and the number of atoms or molecules it contains (moles). Given the chemical formula of the substance, we were able to determine the amount of the substance (moles) from its mass, and vice versa. But what if the chemical formula of a substance is unknown? In this section, we will explore how to apply these very same principles in order to derive the chemical formulas of unknown substances from experimental mass measurements.

## Percent composition

The elemental makeup of a compound defines its chemical identity, and chemical formulas are the most succinct way of representing this elemental makeup. When a compound’s formula is unknown, measuring the mass of each of its constituent elements is often the first step in the process of determining the formula experimentally. The results of these measurements permit the calculation of the compound’s percent composition    , defined as the percentage by mass of each element in the compound. For example, consider a gaseous compound composed solely of carbon and hydrogen. The percent composition of this compound could be represented as follows:

$%\phantom{\rule{0.2em}{0ex}}\text{H}=\phantom{\rule{0.2em}{0ex}}\frac{\text{mass H}}{\text{mass compound}}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}100%$
$%\phantom{\rule{0.2em}{0ex}}\text{C}=\phantom{\rule{0.2em}{0ex}}\frac{\text{mass C}}{\text{mass compound}}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}100%$

If analysis of a 10.0-g sample of this gas showed it to contain 2.5 g H and 7.5 g C, the percent composition would be calculated to be 25% H and 75% C:

$%\phantom{\rule{0.2em}{0ex}}\text{H}=\phantom{\rule{0.2em}{0ex}}\frac{2.5\phantom{\rule{0.2em}{0ex}}\text{g H}}{10.0\phantom{\rule{0.2em}{0ex}}\text{g compound}}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}100%=25%$
$%\phantom{\rule{0.2em}{0ex}}\text{C}=\phantom{\rule{0.2em}{0ex}}\frac{7.5\phantom{\rule{0.2em}{0ex}}\text{g C}}{10.0\phantom{\rule{0.2em}{0ex}}\text{g compound}}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}100%=75%$

## Calculation of percent composition

Analysis of a 12.04-g sample of a liquid compound composed of carbon, hydrogen, and nitrogen showed it to contain 7.34 g C, 1.85 g H, and 2.85 g N. What is the percent composition of this compound?

## Solution

To calculate percent composition, we divide the experimentally derived mass of each element by the overall mass of the compound, and then convert to a percentage:

$\begin{array}{c}\\ %\phantom{\rule{0.2em}{0ex}}\text{C}=\phantom{\rule{0.2em}{0ex}}\frac{7.34\phantom{\rule{0.2em}{0ex}}\text{g C}}{12.04\phantom{\rule{0.2em}{0ex}}\text{g compound}}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}100%=61.0%\\ %\phantom{\rule{0.2em}{0ex}}\text{H}=\phantom{\rule{0.2em}{0ex}}\frac{1.85\phantom{\rule{0.2em}{0ex}}\text{g H}}{12.04\phantom{\rule{0.2em}{0ex}}\text{g compound}}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}100%=15.4%\\ %\phantom{\rule{0.2em}{0ex}}\text{N}=\phantom{\rule{0.2em}{0ex}}\frac{2.85\phantom{\rule{0.2em}{0ex}}\text{g N}}{12.04\phantom{\rule{0.2em}{0ex}}\text{g compound}}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}100%=23.7%\end{array}$

The analysis results indicate that the compound is 61.0% C, 15.4% H, and 23.7% N by mass.

A 24.81-g sample of a gaseous compound containing only carbon, oxygen, and chlorine is determined to contain 3.01 g C, 4.00 g O, and 17.81 g Cl. What is this compound’s percent composition?

12.1% C, 16.1% O, 71.8% Cl

## Determining percent composition from formula mass

Percent composition is also useful for evaluating the relative abundance of a given element in different compounds of known formulas. As one example, consider the common nitrogen-containing fertilizers ammonia (NH 3 ), ammonium nitrate (NH 4 NO 3 ), and urea (CH 4 N 2 O). The element nitrogen is the active ingredient for agricultural purposes, so the mass percentage of nitrogen in the compound is a practical and economic concern for consumers choosing among these fertilizers. For these sorts of applications, the percent composition of a compound is easily derived from its formula mass and the atomic masses of its constituent elements. A molecule of NH 3 contains one N atom weighing 14.01 amu and three H atoms weighing a total of (3 $×$ 1.008 amu) = 3.024 amu. The formula mass of ammonia is therefore (14.01 amu + 3.024 amu) = 17.03 amu, and its percent composition is:

who are the alchemist?
alchemy science of transmutation. typically it is aim at tranforming lead to or other base metals to gold and the creation of the philosophers stone which in reality isn't a stone it's something priceless something we all need for coming times. don't be fooled
Kendrick
read Corinthians 5 verses 50 to the end of the chapter then read revelations chapter 2 verse 17
Kendrick
The word "Alchemy" comes from the forgotten name for Ancient Egypt, Khemmet. Khem was the name for the Egyptian Empire, but the actual land of Egypt was called Khemmet because the "T" on the end of a word denoted a physical location on Earth and not just an idea.
Michael
Wow!
mendie
What's the mass number of carbon
Akinbola
mass number of carbon is 12.
Nnenna
wat d atomic number of oxygen
safiya
atomic number of oxygen is 8
Nnenna
which quantum number divides shell into orbitals?
azimuthal
Emmanuel
hi
Charlie
azimuthal
reinhard
azimuthal
Charlie
what is atom
an atom is a smallest indivisible part of an element
Henry
an atom is the smallest part of an element that takes part in a chemical reaction
Nana
wat is neutralization
when any acid reacts with base to decrease it's acidity or vice-versa to form salt and solvent.. which is called neutralization
Santosh
explain buffer
Organic
buffer is a solution which resists changes in pH when acid or alkali added to it..
Santosh
hello, who is online
UTHMAN
buffer is the solution which resist the change in pH by addition of small amount of acid or alkali to it
KAUSIK
neutralisation is the process of mixing of a acid and a base to form water and corresponding salt
KAUSIK
how to solve equation on this
what are the elent of ionic and covalent bonding
Princewill
what is gases
Its one of the fundamental sate of matter alone side with liquid, solid and plasma
John
What is chemical bonding
John
To my own definitions. It's a unit of measurement to express the amount of a chemical substance.
What is mole
It's the unit of measurements used to express the amount of chemical substance.
Ozoaniehe
What is pressure
force over area
Jake
force applied per unit area
john
force applied per unit area
Prajapati
Why does carbonic acid don't react with metals
Why does carbonic acid don't react with metal
Some metals will react depending on their Standard Electrode Potential. Carbonic acid is a very weak acid (i.e. a low hydrogen ion concentration) so the rate of reaction is very low.
Paul
sample of carbon-12 has a mass of 6.00g. How many atoms of carbon-12 are in the sample
a sample of carbon-12 has a mass of 6.00g. How many atoms of carbon-12 are in the sample
an object of weight 10N immersed in a liquid displaces a quantity of d liquid.if d liquid displaced weights 6N.determine d up thrust of the object
how human discover earth is not flat
We don't fall off. If set off in any direction in a straight line and keep going. You'll end up back where you started.
earth is spherical
Unique
Also, every other planet is spherical as that is the most energy efficient shape. gravity pulls equally on all areas. Sphere.