Want to determine the ratios, in moles, of elements in an analysis.

- A compound of mercury, oxygen, and nitrogen gave an analysis of 61.80% mercury and 8.63% nitrogen by weight. What is the empirical formula for this compound? (Note that oxygen is commonly not given in these analyses because it is used to react with other substances in the analysis process, and so is difficult to measure itself.)

First need to find the amount of oxygen: 100% - 61.80% - 8.63% = 29.57%

Next we need to find the number of moles. Easiest to assume 100 g total, and find moles of each:

Hg: (61.80g)/(200.6g/mole) = 3.081 x 10 ^{-1}moles

N: (8.63g)/(14.01g/mol) = 6.16 x 10 ^{-1}moles

O: (29.57g)/(16.00g/mol) = 1.848 moles

therefore: formula = Hg _{0.3081}N_{0.616}O_{1.848}

But we want whole number ratios, so divide each coefficient by the smallest:

Hg _{0.3081/0.3081}N_{0.616/0.3081}O_{1.848/0.3081}to get:

Hg _{1}N_{1.999}O_{5.998}, and rounding off

= HgN_{2}O_{6}

When should you round off?One of the problems in finding the simplest formula is determining how much error is legitimate in rounding off. Ultimately this is a decision determined by the error of the experimental data - how many significant figures do we have. For this course we generally have at least three sig figs, but I promise not to get too subtle, so as a rule of thumbfor this classvalues such as x.2xx, x.33x, x.25x and x.5xx should be assumed to be not due to error, and so must be multiplied to get the correct formula. (e.g. XY_{2.331}gives X_{3}Y_{7})

Notice that for molecular compounds the empirical formula is

notnecessarily the molecular formula! That is the actual molecular formula could be a multiple of the simplest formula. Thus, to find molecular formulae we need two kinds of information, the empirical formula (from percentage composition) and the molecular weight (from physical characterization).

- Example: A molecule is found to have an empirical formula of C
_{3}H_{5}by elemental analysis and a MW of 85 by freezing point depression. What is its molecular formula?

First we need to determine the formula weight = 3 (12.01) + 5 (1.008) = 41.07,

Then we divide the MW by the FW: 85/41 = 2.07.

Now we know the MW is not terribly precise, so we use it as a decision number, that is the MW = FW, or 2 x FW, or 3 x FW etc. Obviously ours is 2 x, so:

Molecular formula = C_{6}H_{10}_{}

Reaction Stoichiometry: Chemical Equations We now want to look at chemical equations. As implied in the name, there is an equality involved in the two sides of any chemical equation - each side

musthave the same numbers of the same kinds of atoms on each side (which also means, of course, that the total masses are identical on both sides). For example, consider the combustion of propane in excess oxygen to give carbon dioxide and water:

C _{3}H_{8}+ O_{2}CO_{2}+ H_{2}OConservation of Mass tells us that we must have the same numbers of atoms on each side, so we need to

Balancethe equation. First look at the carbons (it is generally most effective to look at the atom with the least number of atoms oxygen last). Propane has 3 carbons, so we need 3 carbon dioxides:

C _{3}H_{8}+ O_{2}3 CO_{2}+ H_{2}O

Now balance hydrogen. There are 8 H's in propane so need 8/2 = 4 waters:

C _{3}H_{8}+ O_{2}3 CO_{2}+ 4 H_{2}O

Finally, 3 carbon dioxides and 4 waters requires 3 (2) + 4 = 10 oxygen atoms/2 = 5 oxygen molecules:

C _{3}H_{8}+ 5 O_{2}3 CO_{2}+ 4 H_{2}ONotice that this chemical equation gives both

qualitativeinformation (what things react to give what products) andquantitativeinformation (how much stuff is produced if a particular amount of stuff reacts). This gives rise to various practical applications.

- Example: How many grams of carbon dioxide are produced during the complete combustion of 475.5 g of natural gas (methane, CH
_{4})

First need to find moles of CH _{4}:

MW = 12.01 + 4 (1.008) = 16.04

Moles of CH _{4}= 475.5 g / 16.04 g/mol = 29.64 mole.

Next need balanced equation:

CH _{4}+ 2 O_{2}CO_{2}+ 2 H_{2}O

Note from the equation we have a 1:1 ratio of moles methane to mole carbon dioxide

So we have 29.64 moles CO _{2}

& MW of CO _{2}= 12.01 + 2 (16.00) = 44.01

and (29.64 mol)(44.01 g/mol) = 1.304 kgLet's look at a slightly more complicated reaction.

- Example: How many moles of oxygen will be needed for the complete combustion of 275.5 g of butane (C
_{4}H_{10}).

First we need the MW of butane: MW = 4 (12.01) + 10 (1.008) = 58.12 g/mol

and the number of moles of butane = (275.5 g) / (58.12 g/mol) = 4.740 mole

Then from the balanced equation:

2 C _{4}H_{10}+ 13 O_{2}8 CO_{2}+ 10 H_{2}O

we can find the number of moles of oxygen required

O _{2}= (4.740 moles butane)(13 moles O_{2}/ 2 moles butane) =30.81 moles

Limiting Problems Asking question of what is the maximum amount of something which can be produced from a given mixture of stuff. This is a fairly straight-forward sort of problem in the day-to-day world, but seems to cause a great deal of difficulty for lots of folks in chemistry. Let's start by looking at a non-chemical problem:

Consider you have to make a bunch of sandwichs for a party. The equation for the sandwichs (in slices) is:

2 Bread + 1 Cheese + 1 Meat 1 Sandwich

You have a 32 oz loaf of bread, 22 oz of sliced cheese and 32 oz of sliced meat. If bread slices weigh 1/2 oz, cheese slices 3/4 oz and meat slices 1 oz, how many sandwichs can you make?

Look at how many sandwichs can be made from each ingredient:

- If bread limits: (32 oz bread)(2 slices bread/oz bread)(1 sandwich/2slices bread) = 32 sandwichs
- If cheese limits: (22 oz cheese)(1 slice cheese/3/4 oz cheese)(1 sandwich/slice cheese) = 29.3 sandwiches
- If meat limits: (32 oz meat)(1 slice meat/oz meat)(1 sandwich/slice meat) = 32 sandwiches
Cheese limits and we can make 29 sandwichs.

Syllabus / Schedule |

*© R A Paselk*

*Last modified 4 February 2011*