## Molecular Weight, Percent Composition, Empirical Formula

The molecular weight of a substance is the sum of the atomic weight of the atoms in a molecule. The atomic weight is the average atomic mass for a naturally occurring element. This means that molecular weight is the average mass of a molecule of a substance. Molecular weight is expressed in atomic mass units. For example, we might want to find the molecular weight of a molecule of water. We have 2 atoms of H, with each hydrogen atom weighing 1 amu. We multiply 2 H atoms by 1 amu a piece to get 2 amu. We add the 16 amu from one O atom to the 2 amu from the oxygen to get a total of 18 amu for one molecule of water.

H2O = 2 atoms of hydrogen and 1 molecule of oxygen

2 H * 1 amu = 2 amu
1 O * 16 amu = 16 amu

2 amu + 16 amu = 18 amu = molecular weight of water

The formula weight of a substance is the sum of the atomic weights of all atoms in a formula unit of the compound. Formula weight doesn't depend on whether or not the substance is a molecule.For example, sodium chloride, which is NaCl, has a formula weight of 58.44 amu. This results from having 22.99 amu from Na and 35.45 amu from Cl. You would use the formula weight for substances which are not molecules, such as ionic compounds.

### Gram Formula Weight Examples:

Find the gram formula weight of H2SO4

1.  2H = 2 x 1 = 2 1S = 1 x 32 = 32 4O = 4 x 16 = 64 98g/mole

Find the gram formula weight of Na2CO3 . 10 H2O

2.  2Na = 2 x 23 = 46 1C = 1 x 12 =12 3O = 3 x 16 = 48 10H2 = 10 x 18 = 180 286g/mole

Sometimes we want to find out what the formula of a compound would be. To figure this out, we analyze the compound into amounts of the elements for a given amount of the compound. This is expressed as the percent composition which is the mass percentages of each different element in a compound. We must know the molecular weight of the compound in order to determine the molecular formula.

Say we have an element X in a compound. This element X is just part of the whole compound. We define the mass percentage of X as the parts of X per hundred parts of the total, by mass. That is:

Mass % X = (mass of X in the whole)/(mass of the whole) * 100%

### Percent Composition Example:

Calculate the percent composition of Mg(NO3)2
 1Mg = 1 x 24 = 24 2N = 2 x 14 = 28 6O = 6 x 16 = 96 148g/mole
 %Mg = 24/148 x 100 = 16.2% %N = 28/148 x 100 = 18.9% %O = 96/148 x 100 = 64.0%

The percentage composition of a compound leads directly to its empirical formula. An empirical formula for a compound is the formula of a substance written with the lowest integer subscripts. For example, hydrogen peroxide has the molecular formula H2O2. The molecular formula tells us the precise number of atoms of different elements in the substance. The empirical number tells us ratio of numbers of atoms in the compound. The empirical formula of hydrogen peroxide is HO, while the molecular formula is H2O2. Compounds with different molecular formulas can have the same empirical formulas and such substances will have the same percentage composition. An example is acetylene, C2H2 and benzene, C6H6. In order to obtain the molecular formula of a substance, you need to know the percent composition and the molecular weight. The molecular weight allows us to choose the correct multiple of the empirical formula for the molecular formula.

### Empirical Formula Example:

Determine the empirical formula for a compound which is 54.09% Ca, 43.18% O, and 2.73% H

Divide each percent by that element's atomic weight. To get the answers to whole numbers, divide through by the smallest one.
 Ca = 54.09/40 = 1.352 1.352/1.352 = 1 O = 43.18/16 = 2.699 2.699/1.352 = 2 H = 2.73/1 = 2.73 2.73/1.352 = 2

CaO2H2 =

Ca(OH)2

Calcium Hydroxide

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## Molecular formula from Empirical Formula

The molecular formula of a compound is a multiple of its empirical formula. The empirical formula is the simplest formula of a substance, written with the smallest integers. For example, the molecular formula of benzene C6H6is equivalent to the empirical formula, (CH)6. This means that the molecular weight is some multiple of the empirical formula weight. The empirical formula weight is obtained by summing the atomic weights from the empirical formula. For any kind of molecular compound, we can write:

Molecular weight = n * empirical formula weight

where n is the number of empirical formula units in a compound. We can get the molecular formula by multiplying the subscripts of the empirical formula by whatever n is. We can calculate this from the equation:

n = (molecular weight)/(empirical formula weight)

Once we determine the empirical formula of a compound, we can calculate is empirical formula weight. If we have an experimental determination of its molecular weight, we can calculate n and then its molecular formula.

### Molecular Formula Example:

A hydrocarbon is 84.25% carbon and 15.75% hydrogen and has a molecular weight of 114. What is its molecular formula?
 C 84.25/12 = 7.021 7.021/7.021 = 1 x 4 = 4 H 15.75/1 = 15.75 15.75/7.021 = 2.25 x 4 = 9
 4 C = 48 9 H = 9 57

114 / 57 = 2

2(C4H9) = C8H18

Octane

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