Mass-Mass Stoichiometry

In a mass-mass calculation you are given information in grams and asked for information in grams.  To complete stoichiometry problems you must know the ratio of particles.  The only way to determine this is by writing a balanced reaction.  The coefficients will provide you with the MOLE RATIO.

Remember that a reaction tells you the ratio of particles or moles, NOT MASS!  A gram of one substance will not have the same number of particles as a gram of another substance. That means you will need to convert grams to moles using molar mass.

We approach this type of problem using the same problem solving steps that we've been using all semester.

1. What are we given?
2. What are we looking for?
3. What additional information is needed?

Let's walk through an example problem:

     Example 1:  An excess amount of sodium chloride reacts with 25.0 grams of lead (II) nitrate in water.  How many grams of precipitate will be formed?

1. What are we given?
   excess NaCl, 25.0 g Pb(NO3)2
2. What are we looking for?
   grams of solid (?)
3. What additional information is needed?
   reacts means a reaction, so you need a balanced reaction
   grams means at some point molar mass will be needed
   solid, means you need to know what precipitates, so you need states

Example 2: How many grams of NaCl are actually needed to react all 25.0 g of lead (II) nitrate?

Empirical Formulas from Percent Composition

One way of determining the identity of an unknown in a lab is by analyzing its mass to determine its empirical formula (lowest whole number ratio of each element in a compound).  There are several types of problems, but all of them use the same concepts to start.

Example 1:  An unknown substance is composed of 24.7% potassium, 34.7% manganese and 40.5% oxygen.  Determine the empirical formula for this compound.

Problem!  You can't compare percentage by mass to determine the ratio of ATOMS!

1. The first step is to convert the percentages to MOLES using the MOLAR MASS for each element.
2. Once you have all the substances in moles, you can compare them to find the mole ratio.  There are several ways of doing this.  The easiest is to divide by the smallest value.  This usually works, but remember that an empirical formula is written in the LOWEST WHOLE NUMBER ratio, so if you a left with a fraction, you must multiply the entire ratio by a factor that will convert the fractions into WHOLE NUMBERS.
   
3. Therefore the ratio of K:Mn:O is 1:1:4, so the empirical formula is KMnO4.

Mole Conversions

While we tend to measure amounts in grams, the only way to compare amounts of atoms, molecules or ions is by using moles.  Unit analysis allows us convert one set of units to another.

To convert grams to moles, or visa-versa, we use molar mass that has the units grams/1 mole.

To convert number of particles to moles, or visa-versa, we use Avogadro's number (6.02 x 10^23) that has the units particles/1 mole.

Example: How many chlorine atoms are in 75.0 grams of sodium chloride?

Percent Composition

Percent always allows us to compare a part of something to the whole.
In general

% = part x 100

total

For percent composition

% = total mass of particles requested x 100

molar mass

Example: Determine the % oxygen in sulfuric acid.

% O =       4 oxygen          x 100

(2 H + 1 S + 4 O)

%O =               4(16.0) ___  _  x 100 = 48.9% O

                                                                     2(1.0) + 32.1 + 4(16.0)

Example: Determine the % sulfate in sulfuric acid.

%SO4 =               32.1 + 4 (16.0)___  _  x 100 = 97.9% O

                                                                    2(1.0) + 32.1 + 4(16.0)

Hydrates

Hydrates are ionic salts that trap water molecules in their crystal lattice.  This added mass must be used when making calculations therefore the ration between molecules of ionic salt and water is given in the name.

For instance, calcium sulfate hexahydrate states that for every molecule of calcium sulfate there are 6 water molecules surround it.  We represent a hydrate with a large dot then the number of water molecules.  This dot is NOT a multiplication sign, it is actually a ratio.

To determine the molar mass of hydrate, determine the mass of the salt then add the mass of however many water molecules are attached to it.

1 Ca + 1 S + 4 O + 6(2 H + 1 O)

40.1 + 32.1 + 4(16.0) + 6(18.0)

244.2 g/mole

The Mole

Mole is a term used in chemistry to represent the number 6.02 x 10^23.  Just as we use the word "dozen" to mean 12 objects, "mole" represents 6.02 x 10^23.

Amedeo Avogadro studied molecular theory in the early 19th century and built on the ideas of Dalton and Guy Lussac.  The number of particles in a mole was actually discovered later in the century and named in his honor.

Atoms and molecules are VERY small. Remember we measure their mass in atomic mass units, amu.  An amu is equal to 1/12th the mass of a carbon-12 atom or approximately the mass of a proton or neutron. The wonderful thing about the very odd number is it allows to work with measurable quantities.

One mole of atoms of any element is equal to its atomic mass (average mass number) in grams.  This is called molar mass.

The molar mass of a compound is simply the sum of the masses of each of its atoms.

water is H20
there are 2 Hydrogen and 1 Oxygen
therefore its molar mass is 2(1.0) + 1(16.0) or 18.0 grams/mole

This means that if you have 18.0 grams of water, you will also have 6.02 x 10^23 molecules of water.

Driving Forces

The driving force for a reaction is the reason the reaction moves forward.  It is the reason the reactants become the products.  To truly analyze the driving force, you must write the ionic reaction.  At this point in the semester, we will use the following reasons.

• a solid is produced from an aqueous solution
• a gas is produced
• water is produced
• a more active metal replaces a less reactive metal in a single replacement reaction
• a more reactive nonmetal replaces a less reactive nonmetal in a single replacement reaction
• neutral elements combine to form an ionic compound in a synthesis reaction

The last 3 reasons are types of redox reactions where electrons are transfered.  We will discuss redox reaction in the future.