Molarity

Molarity is a method of representing concentration.  In this case, it is the ratio of the moles of solute to the liter of solution. The abbreviation for molarity is a capital M (MUST be capitalized, "m" means molality).

Reminder- Solute is the substance that is dissolved or dispersed in a solution. Solvent is the substance that actively separates or disperses the solute. Water is the most common solvent.

There are 3 possible unknowns for simple problems dealing with molarity- M, g of solute, L of solution.

Example 1- What is the molarity of a solution made from completely dissolving 5.25 g of NaCl in 435 mL of water?

Example 2- How many grams of NaCl are needed to make 200.0 mL of 0.0150 M solution?

Example 3- How many mL of water are needed to make a 0.250 M solution using 10.00 g of NaCl?

Limiting Reactants

To put it in simplest terms, the limiting reactant is whatever runs out first. Once one of the essential components runs out, you can't make anymore of the final product.

Basic Example 1- A company builds little red wagons.  Each wagon must have a body, 4 wheels and 2 axels. If the company has 125 bodies, 400 wheels and 300 axels in stock, how many complete wagons can they produce?

While there are several ways of approaching this, we'll solve for the maximum number of complete wagons that can be made from the number of each component given.

While there are sufficient bodies and axels to make more wagons, once the company makes 100 wagons, it will run out of wheels. The wheels are the limiting reactant and therefore all other amounts are dependent on them.


Basic Example 1 con't- How many axels will the company have left over after all the wheels are used?

300 axels were available - 200 axels used = 100 axels left over

Now let's look at chemistry example-

Example 2 - 204.3 g of sodium hydroxide reacts with 79.4 g of aluminum chloride. How many grams of the base will be produced?

After 43.8 g of  aluminum hydroxide is produced, all of the aluminum chloride will be consumed (used up), so the reaction stops. Therefore the aluminum chloride is the limiting reactant (also called the limiting reagent). There will be sodium hydroxide left over- it is in excess.

Example 2 con't - What will be the mass of the excess reactant remaining?

To determine the amount remaining, we must know how much we started with (204.3 g NaOH) and how much will be used. To find how much is needed, we start with the LR (in this case, the 74.9 g of aluminum chloride).

Therefore, 204.3 g initially - 67.3 g needed = 137 g NaOH remaining

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.

Percent Composition by Mass

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)

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?

Hydrates

Hydrates are ionic salts that trap water molecules in their crystal lattice.  This added mass must be used when making calculations therefore the ratio 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