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Stoichiometry
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"Stoichiometry" is a word used in chemistry to describe the relationships between reactants and products in a chemical reaction.  It comes from the Greek word stoikheion, which means element, and the suffix -metry. 
 
In this Topic, we will explore the mathematical relationships that are used in chemistry to make specific products.  Here we dive into what professional chemists do everyday in order to make our always expanding variety of consumer goods. 
 
We start by first defining some basic concepts...
 
Formula Mass
 
Remember that compounds are represented by formulas that show the type and number of atoms present in the compound.  Because compounds are represented by formulas, the mass of the smallest unit of the compound is called the
 
Formula Mass - is the sum of the atomic masses of all the atoms present in a compound.  This term is used for ionic compounds and covalent network solids.
 
Molecular Mass - is also the sum of the atomic masses of all the present  atoms present in a compound.  This term is used for molecular compounds becuase they form discrete molecules.
 
We can measure mass in two ways:
 
1. In Atomic Mass Units (amu); the mass of an atom is a relative value based on the mass of the carbon-12 atom.  All atoms are compared to this standard.  So, when we are referring to 1 atom of a substance, we note its mass in atomic mass units.  We find this number in the upper left-hand corner of the elements box on the Periodic Table.
 
2. In grams (g); We call the the GRAM FORMULA MASS and is simply the formula mass expressed in grams.  We use the same number as in atomic mass units, but we change the unit to grams.  If the mass is a molecular compound, we would use the label GRAM MOLECULAR MASS.    
 
 
EXAMPLE PROBLEMS #1
 
What is the formula mass of K2CO3?
 
1. Find each element of the Periodic Table and its corresponding mass (round to tenths)
 
2. Multiply by the number of atoms of each element present
 
3. Add!
 
Element and Mass:     # of atoms:
     K  (39.1 amu)                         2
     C  (12.0 amu)                         1
     O  (16.0 amu)                          3
 
Total Formulas Mass = 138.2 amu
 
Practice Problems

Determine the molecular/formula mass of the following compounds

  1. copper (I) chloride
  2. ammonium sulfide
  3. water
  4. hydrochloric acid
  5. dinitrogen pentoxide

CLICK FOR ANSWERS

Percent Composition
 
Since formulas represent the composition of a substance, we can use this information to find the percentage of each element in the formula.  There is a very simple equation and it is even listed on the back of your reference tables! 
 
For Example
 
What is the percentage of carbon in CO2?
 
1. Find the formula mass
2. Divide the total mass of Carbon by the formula mass and multiply by 100%
 
Element and Mass:           # of atoms:
    
     C  (12.0 amu)            1  =  12.0 amu
     O  (16.0 amu)            2  =  32.0 amu
 
Formula Mass = 44.0 amu
 
12.0 amu / 44.0 amu  x  100%  =  27.3 %
 

Moles

If asked you to give me a dozen paper clips, what would you do?

Assuming you had them, you would reach into your desk drawer and hand me twelve paper clips. Because you know that:

1 dozen paperclips = 12 paper clips

paperclips.jpeg

Just like a dozen of anything means that I have twelve anythings, one mole of anything means that I have
602,200,000,000,000,000,000,000 of these anythings.

So if I asked you for a mole of paper clips, what would you do? You would reach into your desk drawer and hand me 602,200,000,000,000,000,000,000 paper clips! This is because:
1 mole paper clips = 602,200,000,000,000,000,000,000 paper clips

That's a lot of paper clips, isn't it?

This big number is called "Avogadro's number". We could say:
Avogrado's number = 602,200,000,000,000,000,000,000 items/mole
But to make it easier to read, write and remember, we refer to it this way:
NA = 6.022 x 1023 items/mole

6.022 x 1023 means 6.022 * 1023.

 

So, if we were to discuss bicycles:

1 mole of bicycles = 6.022 x 1023 bicycles
2 moles of bicycles = 2 * (6.022 x 1023 bicycles) = 1.204 x 1024 bicycles.

Now, this may seem like a lot of bicycles, but in Chemistry, we usually discuss much smaller objects, like atoms. Atoms are very small. You probably don't have enough space in your driveway for a mole of bicycles, but you certainly have space for many moles of atoms!


So if one mole of objects is 6.022 x 1023 objects, then:
    one mole of hydrogen atoms = 6.022 x 1023 hydrogen atoms
    one mole of sodium atoms = 6.022 x 1023 sodium atoms
    one mole of water (H2O) atoms = 6.022 x 1023 H2O atoms

    two moles of hydrogen atoms = 2 * 6.022 x 1023 hydrogen atoms = 12.044 x 1023hydrogen atoms
    two moles of sodium atoms = 2 * 6.022 x 1023 sodium atoms = 12.044 x 1023 sodium atoms
    two moles of water (H2O) atoms = 6.022 x 1023 H2O atoms

and so on.

Molar Mass

If one bicycle weighs 20 pounds, how much would a dozen bicycles weigh?
               20 lbs * 12 bicycles = 240 lbs

I'm just going to rewrite this slightly, using the concept of Dimensional Analysis:
       (20 lbs/bicycle) * (12 bicycles/dozen) = 240 lbs/dozen

So now we know specifically that the weight is 240 lbs per dozen.

How much would a mole of bicycles weigh?
       (20 lbs/bicycle) * (6.022 x 1023 bicycles/mole) = 1.204 x 1025 lbs/mole

So the molar mass (MM) of bicycles is 240 lbs/mole. Wow!


Now let's talk about atoms. Take a look at your Periodic Table. Hydrogen is the first element listed. Its symbol is H, its atomic number is 1 and it has an molar mass of 1.008 grams/mole.

1
H
1.01 grams/mole

This means that the mass of one mole of hydrogen is 1.01 grams.


Question: What is the mass of one mole of carbon?

6
C
12.01 grams/mole
Answer: 12.01 grams


Question: What is the mass of three moles of carbon?
Answer: 3 * 12.01 grams = 36.03 grams


Question: If you were given 24.02 grams of carbon, how many moles would you have?
Answer: 24.02 grams / 12.01 grams per mole = 2 moles

Great! Piece of cake, right?


Next, let's find the mass of table salt. Its chemical formula is NaCl. That means that one mole of sodium (Na) has combined with one mole of chlorine (Cl).

From the periodic table, we see that Na has a molar mass of 22.99 grams/mole. We also see that Cl has a molar mass of 35.45 grams per mole.
    Na: (22.99 grams / 1 mole) x 1 mole Na in NaCl = 22.99 grams
    Cl: (35.43 grams / 1 mole) x 1 mole Cl in NaCl = 35.43 grams

Now just add up the masses:
    22.99 + 35.45 = 58.44 grams NaCl / mole

Finding Molecular Formulas from Empirical Formulas
 
Since we know understand how to find the mass of a substance, we can use the moelcular mass and the empirical formula to find the molecular mass of a substance.
 
What does this mean?  A quick RECAP:
 
Empirical formula is the simplest ratio of elements in a formula
Molecular formula shows the actual number of atoms in the molecule
 
For ex:  CHO  vs. C2H2O2
 
How does this work?  Its easy!
 
For Example:
 
If a compound has a molecular mass of 180 amu and an empirical formula of CH2O, what is its molecular formula?
 
To Solve...think logically
 
Empirical formula = most basic ratios = CH2O = 30.0 amu
 
30.0 amu x  _____  =  180 amu?  The answer is 6!
 
So the Molecular Formula = C6H12O6
 
 
Mole Relations in Balanced Equations
 
Remember, chemical equations include both qualitative and quantitative information about the reaction.
 
Formulas give qualitative info
 
Coefficients and subscripts yield quantitative info
 
In problems involving chemical reactions, the relative amounts of reactants and products are represented by the coefficients.  Coefficients represent both the basic unit and mole ratios in balanced equations.
 
Consider the following equation and mole relationships:
 
F2  +  2NaCl   -->  Cl2  +  2NaF
 
1 mole  +     2 moles        -->       1 mole   +     2 moles
 
Questions:
1.  How many moles of F2 are required to make 1 mole Cl2?
2.  If we double the number of moles of NaCl, how many moles of NaF will be made?
 
These questions are easy to answer..HOW? 
 
ALWAYS REMEMBER..the numbers represent mole ratios..so if you double something, you double everything else also..
 
Same goes for reducing amounts..what ever you reduce a reactant or product by, you must reduce everything else in the equation by the same amount...
 
So to answer the questions...
1. 1 mole of F2 makes 1 mole of Cl2
2. 4 moles of NaCl will make 4 moles of NaF

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