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Determining the empirical formula from percent composition

Determining the empirical formula from percent composition

The formula of a compound tells us the number of atoms of each element in that compound. Given the percent composition for a given compound, it is possible to determine that compounds empirical formula. The empirical formula for a chemical compound is the simplest positive integer ratio of atoms present in a compound. A good example is sulfur monoxide, SO and disulfur dioxide, S2O2 both have the same emphirical formula, SO.

Heres a good example, ethanol is a volatile, flammable, colorless liquid with the chemical formula C2H6O. Its single greatest use is as motor fuel and a fuel additive. It’s also an oxygenate, which means it can be added to gasoline to increase the octane number. Ethanol is composed of 52.14% carbon, 34.72% oxygen and 13.13% hydrogen by mass. From this information determine ethanol’s empirical formula.

Recall that in a chemical formula the subscripts represent the ratio of the number of moles of each element to 1 mole of the compound formed. So, we need to figure out a way to convert from mass to moles. To make the math simple, let’s assume we have a 100 grams of ethanol. Can we convert from grams to moles?

If we assume we have a 100 grams of ethanol, by mass composition we have 52.14 grams of carbon, 34.72 grams oxygen and 13.13 grams hydrogen. Since the subscripts in our chemical formula represent the number of moles of each element relative to one mole of our compound, we need to convert our masses to moles.

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This gives us the formula C4.34H13.03O2.17, which gives the ratio of the moles of each element present in in the compound. However, compounds are written in whole numbers, so we can convert to whole numbers by dividing all of the subscripts by the smallest subscript, in this case 2.17.

C = 4.34/2.17 about 2
H = 13.03/2.17 about 6
O = 2.17/2.17 = 1

In this cases dividing by the subscript with the smallest whole number gives us all integers (without fraction or decimal component). Thus we can assume our chemical formula is equal to C2H6O.

Here is a Khan lecture on the topic:

https://www.khanacademy.org/science/chemistry/chemical-reactions-stoichiome/empirical-molecular-formula/v/formula-mass-composition

Percent composition of compounds

Percent composition of compounds

The percent composition is the percent of the total mass of each element in the compound. We determine percent composition by comparing the molar mass contributed by each element to the molar mass of the compound.

Mathematically our expression looks like this:

Image

Where n, is the number of moles of the element in 1 mole of the given compound compound. For instance, H2O, has two moles of hydrogen and one mole of oxygen.

Consider that there are 18 moles of hydrogen and 8 moles of carbon in an octane, C8H18 compound. The molar mass of octane is 114.2 grams/mole, thus the percent composition of carbon and hydrogen can be calculated as follows:

%H = (18×1.008g/114.2g)x100 = 15.89%

%C = (8×12.01g/114.2g)x100 = 84.13%

The sum of these percentages is 100.0%; thus we performed our calculation correctly. Note that in cases of rounding off of the molar mass of elements you may have a small discrepancy and your percentages may not add up to exactly 100%, but don’t sweat it, as long as your close.

Molecular mass

Molecular Mass

From the periodic table we can determine the mass of individual atoms.

http://www.ptable.com/

Thus we can calculate the mass of a molecule. The sum of the mass of individual atoms that make up a compound is called the molecular mass. Consider the molecule H2O. It’s composed of hydrogen and oxygen in a 2 to 1 ratio, thus its molecular mass is the sum of its parts:

2(atomic mass of H) + (atomic mass of O) =

2*(1.008 amu)+(16.00amu) = 18.02 amu

It’s not a difficult thing to do; we simply multiply the atomic mass of each element by the number of atoms that are present in the molecule. Thus the sum of mass of all atoms present is equal to the molecular mass of the compound.

Avogadro’s number

Avogadro’s number

Atomic mass units provide us with a relative scale for the masses of elements.  However, atoms have such a small mass that no scale exists to weigh them.  Measurements involving a minute amount of chemical substance, contain an inconceivably large number of atoms.  We use units to measure things like length, time, etc.  Well, chemists measure atoms and molecules in moles.

In the SI system the mole, mol, is the unit which expresses the amount of a chemical substance that contains as many elementary entities (atoms, molecules, ions, electrons etc.) as there are in 12 grams of pure carbon-12, the isotope with a relative mass of 12.  The number of atoms in a carbon 12 isotope has been determined experimentally.  This number corresponds to Avogadro’s constant:

NA = 6.0221415 X 10 23

Often reported as 6.022 X 1023

Think of Avogadro’s number like this, a dozen eggs are equal to 12, 1 mole of hydrogen atoms contains 6.022 X 1023 hydrogen atoms.

Here is a khan lecture on Avogadro’s number:

https://www.khanacademy.org/science/healthcare-and-medicine/lab-values/v/the-mole-and-avogadro-s-number

One mole of a carbon 12 atoms has a mass of exactly 12 g and contains 6.022 X1023 atoms.  12 grams is the molar mass of carbon.  The molar mass is defined as the mass of one mole of a substance.  An important concept is that the molar mass of an element is equal to its atomic mass.  The molar mass of carbon-12 is equal to its atomic mass.  Likewise for other elements on the periodic table.  Oxygen has an atomic mass of 16.00 amu thus its molar mass is also equal to 16.00g.  Calcium has an atomic mass of 40.09 amu, its corresponding molar mass is equal to 40.09g.  If we know the atomic mass of an element, we also know its molar mass.  The atomic mass of a given element can be found on the periodic table:

http://www.ptable.com/

If we know a given elements atomic mass, this can be used to calculate the mass of a single atom in grams.  The atomic mass of an element is equal to its molar mass and Avogadro’s number tells us that there are 6.022 x 1023 atoms in one mole of a substance.  Therefore, the mass of a single carbon 12 atom must be equal to:

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Avogadro’s number allows us to convert between mass and moles of atoms and between moles and the number of atoms.  When doing these calculations we use the following conversion factors:

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X, represents the symbol of an element (C is the symbol for carbon); these conversion factors allow us to convert one quantity to another.

Atomic mass

Atomic mass

The mass of an atom is dependent on the number of electrons, protons and neutrons present with an emphasis on the protons and neutrons because they account for nearly all of the associated mass of an element.  Electrons are nearly 1800 times smaller than protons and neutrons.

Atoms are extremely small particles. The minutest speck of dust, not visible to the human eye, can contain up to a million atoms.  We have no real means of weighing atoms but we can compare one atom’s mass relative to another atom.  In order to do this we chose an element as a standard.

Dalton obtained his atomic weights through experimentation.  Consider that 1 gram of hydrogen reacts with about 7.9 grams of oxygen.  The product of this reaction is the H2 O, or water.  To obtain the atomic weight of hydrogen relative to oxygen you need to know the relative numbers of hydrogen atoms and oxygen atoms in water.  We know water contains two atoms of hydrogen for every atom of oxygen; therefore, the atomic weight of oxygen is 2×7.9 which is 16 times that of the mass of the average hydrogen atom.  Therefore the atomic mass of oxygen is about 16 atomic mass units (amu).

By international agreement, the mass of an atom is measured in atomic mass units (amu).  An amu is defined as being one twelfth of the mass of a carbon 12 atom.  The carbon 12 isotope has 6 protons and 6 neutrons; by setting the atomic mass of carbon-12 at 12, this provides us with a standard that can be used to measure the mass of other elements.  Consider that hydrogen’s mass is about 8.400 percent the mass of carbon.  If the mass of one carbon atom is exactly 12 amu, the mass of hydrogen must be 1.008 amu (12*8.4% = 1.008).

Average Atomic Mass

Elements are a mixture of isotopes with each isotope having its own characteristic mass.  This means that when we measure the atomic mass of a given element we are actually measuring the average mass of a mixture of isotopes.

Carbon 12 is the more abundant of two stable isotopes of carbon. It accounts for 98.98% of carbon.  Carbon 13 is the other stable isotope of carbon and makes up the remaining 1.02% of naturally occurring carbon.  Thus carbons average atomic mass is calculated as follows:

= (.9898×12) + (.0102×13)

= 12.01 amu

Mathematical reasoning deduces that there is a much larger occurrence of carbon 12 just by looking at its atomic mass number.  It is important to understand that when we refer to the atomic mass number or an element we are actually referring to the average value as calculated above.

Naming acids and bases

Acids and Anions
Acids are a big part of chemistry, let’s look at how we name acids and how they relate to the anions we encountered in some ionic compounds.  Acids are molecular compounds that dissociate in water, forming hydrogen ions, H+ and an anion for each molecule that dissolves in water.  For example H 2SO4 dissolves in water to yield 2H+ ions and a SO 4 anion. 
Oxoacids are acids that contain oxygen.  To be more specific, they are acids that :
1. Contains at least one oxygen 
2. Contains one other element
3. Has at least one hydrogen atom bound to an oxygen
4. Forms an ion by the loss of one or more protons (when we say proton we mean H+, since hydrogen’s atomic number is 1 a hydrogen ion has no electrons and corresponds to a bare nucleus consisting of only a proton) 
Naming oxoacids
Sulfuric acid is an example of an oxoacid and oxoacids are simply polyatomic ions with a positively polarized hydrogen.  In water oxoacids yield hydrogen ions (protons) and an oxoanion.  Naming them is simple, if you know the name of the oxoanion you can determine the name by replacing the suffix as follows:
Anion suffix, -ite, -ate       
Acid suffix, -ous, -ic
Sulfuric acid corresponds to a sulfate ion, SO4 2-
Sulfurous acid corresponds to the sulfite ion SO3 2-

TABLE I. A few oxoanions and their corresponding oxoacids

Oxoanion
 
Oxoacid
 
CO 32-
carbonate
H 2CO3
Carbonic acid
NO 2
nitrite
HNO 2
Nitrous acid
NO 3
nitrate
HNO 3
Nitric acid
PO 43-
phosphate
H 3PO4
Phosphoric acid
SO 32-
sulfite
H 2SO3
Sulfurous acid
SO 42-
sulfate
H 2 SO4
Sulfuric acid
ClO
hypochlorite
HClO
Hypochlorous acid
ClO 2
chlorite
HClO 2
Chlorous acid
ClO 3
chlorate
HClO 3
Chloric acid
ClO 4
perchlorate
HClO 4
Perchloric acid
Binary acids are molecular compounds in which hydrogen is combined with a second nonmetallic element.  Naming them is a breeze!  Add the prefix hydro- and the suffix –ic followed by the word acid.
HF (hydrogen and fluoride) is hydrofluoric acid
HCl (hydrogen and chloride) is hydrochloric acid
HBr (hydrogen and bromide) is hydrobromic acid
HI (hydrogen and iodide) is hydroiodic acid
Naming Bases
A base is a substance that yields hydroxide ions (OH ) when dissociated in water.  Hydroxides tend to form with the alkali and alkaline earth metals, a few examples are
NaOH – Sodium hydroxide
KOH – Potassium hydroxide
Ca(OH)2 – Calcium hydroxide
Ammonia is a molecular compound of nitrogen and hydrogen with the chemical formula NH 3.  At first glance this compound may seem like an exception to the definition of the base; however, this substance yields hydroxide ions when dissolved in water.  Ammonia reacts with water to yield NH4+ and OH ions.

Naming molecular compounds

A molecule is an electrically neutral compound consisting of two or more atoms covalently bonded together.  Molecular substances are substances that are composed us molecules.  Molecules in substances are extremely small.  Even a minute sample of a molecular substance contains many trillions of molecules (think Avogadro’s number, 10^23).
A Binary compounds is composed of two or more elements.  A binary ionic compound is composed of a metal from the left hand side of the periodic table and nonmetal from the right hand side of the periodic table, However, a binary molecular compound (or molecule) is composed of two nonmetals or metalloids and its bonds are covalent in nature.  For instance:

CO2 – Carbon Dioxide

CO – Carbon monoxide
Rules for naming binary molecular compounds or molecules
1) The name of the compound, generally, has the elements in the order given in the formula
2) The first element is given its exact name
3) The second element is given the suffix –ide
4) Prefixes, derived from the Greek language are used to denote how many atoms of each element are present in the compound
Greek prefixes for naming binary molecular compounds
1
mono
2
di
3
tri
4
tetra
5
penta
6
hexa
7
hepta
8
ocata
9
nona
10
deca
Let’s consider a nitrogen oxide compound with the chemical formula N2O3.  This compound requires the Greek prefix di and the prefix tri in order to properly name the compound.  Thus, we name the compound dinitrogen trioxide. Recall the first element is given its exact name and the second compound is given an –ide ending.  
There are two compounds involving carbon and oxygen, CO and CO2.  We name these compounds carbon monoxide and carbon dioxide in order to distinguish one from the other.
Some other examples of covalent compounds:
SO2 – sulfur dioxide
SF6 – sulfur hexafluoride
CCl4 – carbon tetrachloride
ClO2 – chlorine dioxide
Cl2O7 – dichloride heptoxide
The final vowel in a prefix is often dropped for ease of pronunciation.  In the case of tetraoxide, it becomes tetroxide. 
There are some compounds that have well established names, thus are not generally named according to the rules above:  

H2O – water

O3 – ozone

NH3 – ammonia

NO – nitric oxide

N2O – nitrous oxide

Naming ions

Naming monatomic ions
When naming ions, we are dealing with cations and anions.  Cations are positively charged ions, whereas anions are negatively charge.  The easy way to remember the difference, is the word cation, has the letter t and the letter t looks like a plus symbol, +……at least it does to me anyway.  
With naming monatomic ions we have three general rules. 
1)The newer system of naming Monoatomic cations (positive) are generally named after the element, with the addition of a Roman numeral in parenthesis to indicate the charge if the element forms more than one cation.  Iron can form both Fe2+ and Fe 3+, therefore we’d call them iron (II) and iron (III) respectively. 
2) The older system consists of adding the suffixes ous and ic to the end of the element to differentiate between cations of higher and lower charge.  These endings are added to the latin name of the element.  Fe2+, Iron (II) is named ferrous (not like Ferris Bueller’s Day off) and Fe3+, Iron (III) would be named ferric. 
3) Naming monoatomic anions (negative) is a breeze, you simply add the suffix ide.  For instance, an oxygen anion is called an oxide.
Other examples: H Hydride, F Fluoride, S Sulfide, etc.
Common Transition Element Cations (memorize)
Ion
Ion name
Ion
Ion name
Ion
Ion name
Cr 3+
Chromium (III)
or chromic
Co 2+
Cobalt (II)
or cobaltous
Zn 2+
Zinc
Mn 2+
Manganese (II)
or manganous
Ni 2+
Nickel (II)
or nickel
Ag +
Silver
Fe 2+
Iron (II)
or ferrous
Cu +
Copper (I)
or cuprous
Cd 2+
Cadmium
Fe 3+
Iron (III)
Ferric
Cu 2+
Copper (II)
or cupric
Hg 2+
Mercury (II)
Polyatomic ions are molecular ions that are charged chemical species composed of two or more atoms that are covalently bonded together.  
Most polyatomic ions are oxoanions which means that they contain oxygen.  This is because oxygen is a very electronegative compound, meaning it likes electrons.  Sulfur forms the oxoanions sulfate SO42- and sulfite, SO32-.  The name of an oxoanion stems from the central element, then includes the suffix ate or ite.  These suffix attached to the compound gives us some indication of the amount of oxygen.  The suffix ate indicates the ion with a greater number of oxygen atoms (I like to remember it like the central element ate until it was full of oxygen).  The ite is the opposite, it indicates less oxygen atoms (ite, think tiny).
Common polyatomic ions (memorize)
Name
Formula
Name
Formula
Thiosulfate
S 2O3 2-
Mercury (I) or mercurous
Hg 22+
Hydrogen sulfate
HSO 4
Ammonium
NH 4+
Hydrogen sulfite
HSO 3
Cyanide
CN
Sulfate
SO 42-
Carbonate
CO 32-
Sulfite
SO 32-
Hydrogen carbonate (or        bicarbonate)
HCO 3
Dihydrogen phosphate
H ­2PO 42-
Acetate
C 2H3O 2
Monohydrogen phosphate
HPO 42-
Oxalate
C 2O4 2-
Phosphate
PO­ 43-
Chromate
CrO 42-
Peroxide
O 22-
Dichromate
Cr 2O7 2-
Hydroxide
OH
Permanganate
MnO 4
Nitrate
NO 3
 
 
Nitrite
NO 2
 
 
 
In some cases, however, these prefixes are not enough. Chlorine forms a whole family of compounds with oxygen: ClO, ClO2,ClO3 and ClO­­4.  In these cases two prefixes are used, hypo and per (hyper is how I remember that per indicates the most oxygen), in addition to the two suffixes.  So the naming goes like this:
Family of chlorine oxoanions (memorize)
Hypochlorite
ClO
Chlorite
ClO 2
Chlorate
ClO 3
Perchlorate
ClO 4
The chlorine oxoanion with the least amount of oxygen gets the hypo in addition to the suffex ite, the one with the most gets the prefix per (hyper) and the two in the middle just get ite and ate. 
Some polyatomic ions are bonded to two or more hydrogen atoms.  These compounds are sometimes referred to as acid ions.  In these cases we name the ion, for instance SO4 2- sulfate, hydrogen sulfate.  In cases where ions have more than one hydrogen, we use the Greek prefixs like mono (one) and di (two) to indicate the number of hydrogen atoms present.  For instance, dihydrogen monoxide…..which of course is water, H2O.  Read more about the dihydrogen monoxide hoax here:
https://en.wikipedia.org/wiki/Dihydrogen_monoxide_hoax
Lastly, in naming polyatomic ions we use the prefix thio when an oxygen atom in a compound has been replaced by a sulfur atom.  So, S2O32- would be name thio sulfate (originally SO42- which is sulfate).  

Predicting charges on monatomic ions

Monatomic ions are ions that consists of single atom (hint: mono).  Here are a few common monatomic ions that are in the main group of the periodic table.

Rules for predicting charges on monatomic ions:

charges on main group elements

  1. Most main group metallic elements form one monatomic cation that is equal to that of the group number they belong to in the periodic table.  The first group of elements on the periodic table form cations with 1+ charge, the second group form cations with a 2 + charge.
  2. Some metallic elements can form more than one cation.  These elements tend to have charges equal to the group number minus two in addition to forming a cation with a charge that is equal to their group number.  Lead is a good example it’s in  group IVA and has a charge of 4-2, Pb2+
  3. Elements in the transition area of the periodic table elements tend to form multiple cations.  Iron forms the cations Fe2+ and Fe3+
  4. The charge on a monoatomic anion for nonmetallic main group elements is equal to the group number minus eight.  Fluorine’s charge for instance, is equal to -1.  (the group number is 7; so the charge is 7-8).