### Molecular Weight

There are a number of terms you need to know, at the same time, in order to know what the term "molecular weight" means.

Definition #1:

The molecular weight of a substance is the weight in atomic mass units of all the atoms in a given formula.

Definition #2:

An atomic mass unit is defined as 1/12 the weight of the carbon-12 isotope.

The most complete definition is a bit more technical (1/12 of the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state and at rest), but the above definition is sufficient for the introductory level.

The old symbol for atomic mass unit was amu, while the most correct symbol is u (a lower case letter u) which comes from the term 'unified atomic mass unit.' Unified comes from a 1961 agreement between the chemistry and physics communities to use the same definition for the atomic mass unit. The ChemTeam will use both u and amu in problem solutions. You need to be able to recognize and use both.

Definition #3:

The carbon-12 isotope is defined as weighing exactly 12 amu.

This is the starting point for how much an atom weighs. For example, if you weigh 1/2 as much as C-12, you weigh 6. If you weigh twice as much, you weigh 24.

The molecular weight of a substance is needed to tell us how many grams are in one mole of that substance.

The mole is the standard method in chemistry for communicating how much of a substance is present.

You should have a periodic table for looking up atomic weights and a calculator. There are many Internet sites that allow you to input a formula and get the molecular weight.

Point #1: You need to know how many atoms of each element are in a substance in order to calculate its molecular weight.

For example H2O has two atoms of hydrogen and one atom of oxygen. H2O2 has two atoms each of oxygen and hydrogen. Mg(OH)2 has one atom of magnesiun and two each of oxygen and hydrogen.

If a subscript follows an atom with no parenthesis, that number tells you how many of that atom are present. If parentheses are involved, you must multiply each subscript inside by the one which is outside.

Example #1: How many of each element are in the following examples?

(a) KCl
There's one K and one Cl.

(b) Fe2O3

There are two irons and three oxygens.

(c) Al(NO3)3

One Al, three nitrogen, and nine oxygens. Note the parentheses.

(d) NH4NO3

Two nitrogen, four H and three O. Note how nitrogen is in two different places in the formula.

(e) Al2(SO4)3

Two aluminum, three sulfur, and 12 oxygen. Note use of parentheses.

(f) CuSO4 5H2O

One copper, one sulfur, 10 hydrogen, nine oxygen. Note that this is a hydrate. See below for more.

Point #2: You need to know the atomic weight of each element in order to calculate the molecular weight of the substance.

The atomic weight of each element is found by examining the periodic table. Here are some typical element tiles, as they might appear in a periodic table: The important number to use is at the bottom, just below the element symbol. For hydrogen the number is 1.0079. For carbon, it is 12.011 and for oxygen it is 15.9994. These numbers are the atomic weight for each element.

The placement of the atomic weights may be sligtly different in the periodic table you are using. Also, the atomic weights in your periodic table may be slightly different than the ones in the example. This is usually due to rounding off by the publisher. Also, atomic weight values are periodically redetermined and refined and this may contribute to minor differences in the weights used. There are lots of periodic table web sites. This sentence is a link to a Google search for periodic table images.

By the way, the whole number is called the atomic number. If you do not know what the means yet, that's perfectly OK. Concentrate on the other number, the atomic weight.

### How to calculate the molecular weight of a substance

Multiply each element's atomic weight by how many atoms are present in the formula, then add the answers.

Example #2: Calculate the molecular weight of Al2(SO4)3

1) There are:

two atoms of aluminum
three atoms of sulfur
twelve atoms of oxygen

2) Look up atomic weights in a periodic table:

the atomic weight of Al is 26.98 amu
the atomic weight of S is 32.06 amu
the atomic weight of O is 16.00 amu

3) Multiply:

2 x 26.98 = 53.96 total weight of all Al in formula
3 x 32.06 = 96.18 total weight of all S in formula
12 x 16.00 = 192.00 total weight of all O in formula

53.96 + 96.18 + 192.00 = 342.14 amu

This answer, 342.14 amu, is the molecular weight of Al2(SO4)3

You might be asking why I used oxygen at 16.00 and not 15.9994. Actually, you could use the more exact value, but then when rounding off your answer, you would get back to the 342.14 value.

Example #3: Calculate the molecular weight of H2O2

hydrogen: two atoms
oxygen: two atoms

The atomic weight of hydrogen is 1.0079 amu.
The atomic weight of oxygen is 15.9994 amu.

(2 x 1.0079) + (2 x 15.9994) = 34.0146 amu

### Review: Four steps to calculating a substance's molecular weight

Step One: Determine how many atoms of each different element are in the formula.

Step Two: Look up the atomic weight of each element in a periodic table.

Step Three: Multiply step one times step two for each element.

Step Four: Add the results of step three together and round off as necessary.

By the way, the Internet contains many molecular weight calculators, of all different sizes and shapes. This is the one I use. You can even use Google, if so desired. There is one small problem with Google that I discuss below.

I am sure you'll find one that strikes your fancy.

Example #4: (NH4)2S

Step One: two atoms of nitrogen, eight of hydrogen and one of sulfur

Step Two: N = 14.0067 amu, H = 1.0079 amu, S = 32.06 amu

Step Three: (2 x 14.0067) + (8 x 1.0079) + (1 x 32.06)

Step Four: 28.0134 + 8.0632 + 32.06 = 68.14 amu (when rounded off to the correct number of significant figures)

Please note that the number of atoms does not dictate significant figures. The atomic weights you use dictate sig figs.

Example #5: Fe2O3

One: two atoms of iron and three of oxygen

Two: Fe = 55.847 amu and O = 15.9994 amu

Three: (2 x 55.847) + (3 x 15.9994)

Four: 111.694 + 47.9982 = 159.692 amu (when rounded off to the correct number of significant figures)

If you are unsure how the number of sig figs is determined, please review the rules for addition using sig figs.

Example #6: KClO4

1) one atom of potassium, one of chlorine, and four of oxygen.

2) K = 39.098 amu, Cl = 35.453 amu, O = 15.9994 amu

3) (1 x 39.098) + (1 x 35.453) + (4 x 15.9994)

4) 39.098 + 35.453 + 63.9976 = 138.549 amu (when rounded off to the correct number of significant figures)

Example #7: NH4NO3

two atoms of N, four atoms of H, three atoms of O <--- note that the N are in different places in the formula

(2 x 14.007) + (4 x 1.008) + (3 x 15.999) = 80.043 amu

When I use my online calculator, it returns a value of 80.0426.

Another example of the same atom being shown in different places in the formula is CH3COOH (molec. wt. = 60.0516 amu).

Example #8: (NH4)2SO4

two atoms of nitrogen, eight of hydrogen, one of sulfur, and four of oxygen (note the influence of the parentheses)

When you do the Google, you see that the unit on the answer is not amu but, rather, g/mol (which stands for grams per mole). For the moment, set aside wondering what g/mol stands for. It will be presented to you soon enough.

Example #9: Calculate the molecular weight of CuSO4 ⋅ 5H2O

Remember that the dot DOES NOT mean multiply. However, the five in front of the water does mean multiply. There are 10 hydrogen atoms and five oxygen atoms in five water molecules.

Add the atomic weights of one copper, one sulfur, nine oxygens, and ten hydrogens.

Example #10: Calculate the molecular weight of K2CO3 32H2O

Just the K2CO3: two atoms of potassium, one of carbon and three of oxygen.

Answer: figure out the molecular weight of water (it's 18.015 amu) and multiply it by three-halves to get 27.0225 amu.

(2 x 39.0983) + (1 x 12.011) + (3 x 15.9994) + 27.0225 = 165.228 amu

The name of this compound is potassium carbonate sesquihydrate.

Bonus Example: What is the total amu of 15 atoms of Al?

Look up aluminum on the periodic table to find its atomic weight to be:
26.982 amu

The weight of 15 atoms:

(26.982 amu) (15) = 404.73 amu