# 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:

what is lattice energy
why is CO a neutral oxide and CO2 an acidic oxide
Because when CO2 dissolves in water forming a weak acid. CO does not dissolve in water as it has strong triple bond.
Abdelkarim
What is acid
which donate H+ or accept lone pair of electron
Kajal
kinetic theory of matter and gas law
hi
Victoria
pls explain
Victoria
what is clay
material containing clay minerals. Clays develop plasticity when wet, due to a molecular film of water surrounding the clay particles, but become hard, brittle and non–plastic upon drying or firing. Most pure clay minerals are white or light-coloured, but natural clays show a variety of colours
Abdelkarim
due iron oxide. The four types of clay are Earthenware clay, Stoneware clay, Ball clay, and Porcelain. All of them can be used to make pottery, but the end result would differ a lot thanks to their different textures, colors, and flexibilities.
Abdelkarim
And do you know that god has created human from clay (وَلَقَدۡ خَلَقۡنَا ٱلۡإِنسَـٰنَ مِن صَلۡصَـٰلࣲ مِّنۡ حَمَإࣲ مَّسۡنُونࣲ) [سورة الحجر 26] And We did certainly create man out of clay from an altered black mud. You can install Quran from paly store for free with translations.
Abdelkarim
darw a periodic table
draw a periodic table
Hazard
You will arrange the elements into row and coloumns according to increasing proton number. You may want to use symbols or their names. Hydrogen, Helium, etc. God has created all these elements from nothing, in Islam we know God is the creator.
Abdelkarim
why are you drawing a periodic table? why not just print one from the internet and use as a reference
Jakhari
Great thought
Bright
how are you?
Marina
am fine
Agbo
Marina
my name is amel
Farid
l use the email of my husband
Farid
Define organic chemistry
It is the chemistry concerning molecules that have Carbon skeletons and hydrogen atoms. We find organic molecules like in plants, living derivatives, etc.
Abdelkarim
what's matter
Anything that can be to cutting from all dimensions to halve. So you end up with 4 cubes of 5 cm side. Repeat with one of the cubes. 10, 5, 2.5, .., 0 1st 2nd 3rd Nth Un= a(r) ^ n-1
Abdelkarim
Anything that has mass and can reflect or absorb waves. GOD created everything from nothing only he can destroy it as prooved.
Abdelkarim
Suppose you have a cube of side 10 cm. Then you start cutting from all dimensions to halve. So you end up with 4 cubes of 5 cm side. Repeat with one of the cubes. 10, 5, 2.5, .., 0 1st 2nd 3rd Nth Un= a(r) ^ n-1 0= 10 (1/2)^n-1 0= (1/2) ^ n-1 Log0= (n-1) Log(1/2) - infinity =( n-1)
Abdelkarim
matter is anything that has mass,volume and can occupy space
Getrude
what is electrolysis
good equation
Aliyu
differenciate between fat and oil
what is the meaning of coordinate bond
It is the alternative for dative which is a covalent bond but both electrons of the pair are from shared from the same (one) atom.
Abdelkarim
can someone please tell me what does an Entropy means
what is chemistry?
what is chemistry
Afiwape
chemistry is a brach of science which deal with the study of the nature, composition structure and with the force that hold the structure together and the change matter will undergo undedifferent conditions
Afiwape
And god has created everything from nothing
Abdelkarim
forms of biotechnology