Download The Mole

The Mole
A look at Avogadro's Number
6.02 x 10^23
Molecular Weight
 The
mole is the standard method in
chemistry for communicating how much
of a substance is present.
 What
is Molecular Weight?
 The weight in atomic mass units (amu)
of all the atoms in a given formula
 The molecular weight of a substance is
needed to tell us how many grams are in
one mole of that substance.
Practice Problems
 Calculate
the following
molecular formulas
 1) (NH4)2S
 2) Fe2O3
 3) KClO4
 4) SF6
 5) (NH4)2SO4
The Mole & Molar Mass
In
one mole, there are
6.022
x 1023 atoms, or
molecules, or compounds, or
doughnuts, or cups of
coffee.
So
one mole of ANYTHING
contains 6.022 x 1023
entities.
Just How Big is a Mole?

Enough soft drink cans to cover the
surface of the earth to a depth of
over 200 miles.

If you had Avogadro's number of
unpopped popcorn kernels, and
spread them across the United States
of America, the country would be
covered in popcorn to a depth of
over 9 miles.

If we were able to count atoms at the
rate of 10 million per second, it
would take about 2 billion years to
count the atoms in one mole.
The mole and molecular
weight cont.
 The
symbol for mole is "mol”
 6.02
x 1023 is called Avogadro's
Number
 When
we weigh one mole of a
substance on a balance, this is
called a "molar mass" and has the
units g/mol
The mole and molecular
weight practice problems
 calculate
the mass of one
mole of these substances
 1) (NH4)2S
 2) Fe2O3
 3) KClO4
 4) SF6
 5) (NH4)2SO4
The mole and molecular
weight practice problems

calculate the mass of one mole of
these substances
1.
Lithium Hydride
2.
Calcium Hydroxide
3.
Copper (II) Bromide
Molar Ratios

Molar Ratios

1) N2 + 3 H2 ---> 2 NH3

Write the molar ratios for N2 to H2 and
NH3 to H2.

2) 4 NH3 + 3 O2 ---> 2 N2 + 6 H2O

Write the molar ratios for NH3 to N2 and
H2O to O2.

3) Fe2O3 + 3 CO ---> 2 Fe + 3 CO2

Write the molar ratios for CO to CO2 and
Fe to CO.
Mole Conversions
Given Moles, Convert to Grams
In chemistry, the mole is the standard
measurement of amount. When
substances react, they do so in simple
ratios of moles.
 There are three steps to converting
moles of a substance to grams:
1. Determine how many moles are given
in the problem.
2. Calculate the molar mass of the
substance.
3. Multiply step one by step two.

mole to gram cont.

The three steps above can be
expressed in the following equation:

# of Moles X Molecular weight of
substance= Grams of substance
Mole to gram practice
problems

Convert the following into grams

1) 0.200 moles of H2S

2) 0.100 moles of KI

3) 1.500 moles of KClO

4) 0.750 moles of NaOH

5) 3.40 x 10^5 moles of Na2CO3
Mole Conversions
Given Grams, Convert to Moles

There are three steps to converting grams of a
substance to moles.

Determine how many grams are given in the problem.

Calculate the molar mass of the substance.

Divide step one by step two.
Gram to mole cont

The three steps above can be expressed in the following
equation:

Given Grams x (1 mole/molecular weight)
Gram to mole practice
problem

Convert the following into moles

1) 2.00 grams of H2O

2) 75.57 grams of KBr

3) 100. grams of KClO4

4) 8.76 grams of NaOH

5) 0.750 grams of Na2CO3
Avogadro Number Calculations
How Many Atoms or Molecules?

The value for Avogadro's Number is 6.022 x 10^23 mol

Types of problems you might be asked look something
like these:
1. 0.450 mole (or grams) of Fe contains how many atoms?
2. 0.200 mole (or grams) of H2O contains how many
molecules?
Atoms or molecules cont.

When the word grams replaces mole,
you have a related set of problems
which requires one more step.

Here is a graphic of the procedure
steps:
:
Atoms or molecules

Example : 0.450 mole of Fe contains how many atoms?

Solution: start from the box labeled "mole" and move (to
the right) to the box labeled "atoms." What do you have to
do to get there?

0.450 mol x 6.022 x 10^23 mol
Atoms or molecules practice
problems
Complete the following problems


Calculate the number of molecules in1.058 mole of H2O

Calculate the number of atoms in 0.750 mole of Fe

Calculate the number of molecules in1.058 gram of H2O

Calculate the number of atoms in 0.750 gram of Fe
Molarity

Molarity is the concentration of a solution in moles per
liter

The symbol for molarity is M

A 4.90M solution of NaCl means that there are 4.90
moles on NaCl in 1 liter of the solution

Molarity = mol/L
Stoichiometry

What is Stoichiometry?

The word stoichiometry derives from two Greek words: stoicheion
(meaning "element") and metron (meaning "measure").

Stoichiometry deals with calculations about the masses (sometimes
volumes) of reactants and products involved in a chemical reaction.
Stoichiometry Cont.
What You Should Expect
 The most common stoichiometric problem
will present you with a certain amount of
a reactant and then ask how much of a
product can be formed. Here is a generic
chemical equation:



2 A + 2B ---> 3C
Here is a typically-worded problem: Given
20.0 grams of A and sufficient B, how
many grams of C can be produced?
Stoichiometry Cont.

Keys to solving the problem.

You will need to use molar ratios, molar masses, balancing and
interpreting equations, and conversions between grams and moles.
Stoichiometry Cont.
This type of problem is often called "mass-mass.“
 The Steps Involved in Solving Mass-Mass
Stoichiometry Problems
 Make sure the chemical equation is correctly
balanced.
 Using the molar mass of the given substance, convert
the mass given in the problem to moles.
 Construct a molar proportion (two molar ratios set
equal to each other) following the guidelines set out
in other files. Use it to convert to moles of the
unknown.
 Using the molar mass of the unknown substance,
convert the moles just calculated to mass.

Stoichiometry Cont.

Molar Ratios:

The sources for these ratios are the coefficients of a balanced equation.

sample equation:

2 H2 + O2 ---> 2 H2O

What is the molar ratio between H2 and O2?

Answer: two to one. So this ratio in fractional form is: 2/1
Molar ratio cont.

2 H2 + O2 ---> 2 H2O

What is the molar ratio between O2 and H2O?

Answer: one to two. As a fraction, it is: 1/2
Mole ratio practice problems.






1) N2 + 3 H2 ---> 2 NH3
Write the molar ratios for N2 to H2 and
NH3 to H2.
2) 2 SO2 + O2 ---> 2 SO3
Write the molar ratios for O2 to SO3
and O2 to SO2.
3) PCl3 + Cl2 ---> PCl5
Write the molar ratios for PCl3 to Cl2
and PCl3 to PCl5.
Mole to mole problems
The solution procedure used involves making
two ratios and setting them equal to each
other.
 This is called a proportion.
 One ratio will come from the coefficients of
the balanced equation
 The other will be constructed from the
problem.
 The ratio set up from data will almost always
have one unknown in it.

Mole to mole cont.

Equation: N2 + 3 H2 ---> 2 NH3

Problem: if we have 2.00 mol of N2 reacting with
sufficient H2, how many moles of NH3 will be produced?

Remember “sufficient” means there is more than enough
to react with the other reactant.
Equation: if we have 2.00 mol of N2 reacting with
sufficient H2, how many moles of NH3 will be produced?
How to solve this problem:
 Use the ratio to set up the proportion:


That means the ratio from the equation is:

The ratio from the data in the problem will be:

The proportion (setting the two ratios equal) is:

Solving by cross-multiplying gives x = 4.00 mol of
NH3 produced
Mole to mole practice
problems:




Complete the following mole to mole
conversions.
N2 + 3 H2 ---> 2 NH3 (use this equation
for both problems)
Suppose 6.00 mol of H2 reacted with
sufficient nitrogen. How many moles
of ammonia would be produced?
We want to produce 2.75 mol of NH3.
How many moles of nitrogen would be
required?
Mole to mass



Problem: 1.50 mol of KClO3
decomposes. How many grams of O2
will be produced?
Chemical equation:
2 KClO3 ---> 2 KCl + 3 O2
Use the same steps for solving mole to
mole problems.
Problem: 1.50 mol of KClO3 decomposes. How
many grams of O2 will be produced?
Let's use this ratio to set up the proportion:
 That means the ratio from the
equation is:
 The ratio from the data in the
problem will be:
 The proportion (setting the two
ratios equal) is:
 Cross-multiplying and dividing gives x = 2.25 mol of O2 produced.
 2.25 mol x 32.0 g/mol = 72.0 grams. The 32.0 g/mol is the molar
mass of O2.

Mole to mass practice
problems:




Here's the equation to use for all three
problems:
2 H2 + O2 ---> 2 H2O
1) How many grams of H2O are produced
when 2.50 moles of oxygen are used?
2) If 3.00 moles of H2O are produced, how
many grams of oxygen must be consumed?
3) How many grams of hydrogen gas must
be used, given the data in problem two?
Mass to Mass problems

1.
2.
3.
4.
There are four steps involved in solving
these problems:
Make sure you are working with a
properly balanced equation.
Convert grams of the substance given in
the problem to moles.
Construct two ratios - one from the
problem and one from the equation and
set them equal. Solve for "x," which is
usually found in the ratio from the
problem.
Convert moles of the substance just
solved for into grams.
Mass to mass cont.




Double check the equation. I have seen lots of
students go right ahead and solve using the
unbalanced equation supplied in the problem (or
test question for that matter).
DON'T use the same molar mass in steps two and
four.
Don't multiply the molar mass of a substance by
the coefficient in the problem BEFORE using it in
one of the steps above. For example, if the
formula says 2 H2O, DON'T use 36.0 g/mol, use
18.0 g/mol.
Don't round off until the very last answer. In other
words, don't clear your calculator after step two
and write down a value of 3 or 4 significant
figures to use in the next step. Round off only
once after all calculations are done.
Mass to mass

This chart is used to help set up mass to mass problems.
Mass to Mass
Each of the example problems below has an
associated image which lays out the solution.
Reading from left to right, the top row gives:
 1. the molar ratio used in the problem's
solution.
2. the conversion of the grams given in the
problem to moles. The second row gives:
 3. the molar proportion used to convert from
moles of the given to moles of the unknown.
4. the conversion of moles of the unknown
back to grams.

Mass to Mass Cont.

How many grams of chlorine can be
liberated from the decomposition of
64.0 g. of AuCl3 by this reaction: 2
AuCl3 ---> 2 Au + 3 Cl2
Practice problems
1.
Calculate the mass of AgCl that can be prepared from 200. g of AlCl3
and sufficient AgNO3, using this equation: 3AgNO3 + AlCl3 --> 3 AgCl
+ Al(NO3)3
2.
Given this equation:
2 KI + Pb(NO3)2 --> PbI2 + 2 KNO3 calculate mass of PbI2 produced
by reacting of 30.0 g KI with excess Pb(NO3)2
Limiting Reagents

You will see the word "excess" used in this section and in the problems.
Three examples of Excess being used:
a) "compound A reacts with an excess of compound B" - In this case,
mentally set compound B aside for the moment. Since it is "in excess,"
this means there is more than enough of it. Some other compound
(maybe A) will run out first.
Limiting reagent Cont

b) "20 grams of A and 20 grams of B react.
Which is in excess?" What we will do below is
find out which substance runs out first (called
the limiting reagent). Obviously (I hope), the
other compound is seen to be in excess.
c) "after 20 gm. of A and 20 gm. of B react,
how much of the excess compound remains?"
To answer this problem, we would subtract
the limiting reagent amount from the excess
amount.
What is the Limiting Reagent?
The substance in a chemical reaction that runs
out first.
 Example:
 Reactant A is a test tube. I have 20 of them.
Reactant B is a stopper. I have 30 of them.
 Product C is a stopper and test tube.
 The reaction is: A + B ---> C
or: test tube plus stopper makes stopper and
test tube combination.
 we run out of one of the "reactants." Which
one?

Limiting Reagents Cont



Practice Problem:
A cup of coffee costs 50 cents.
In your possession, you have 100 grams of
each coin:




You know how much a single coin weighs:




nickels (5-cent pieces)
dimes (10-cent) pieces
quarters (25-cent pieces)
one nickel = 5.00 g
one dime = 2.22 g
one quarter = 5.55 g
How many cups of coffee can you buy?
Limiting reagent cont
How do you figure out HOW MANY coins there
are?
 Divide the total weight by the weight per one
coin.
 Divide the total weight by the weight per one
coin.
 Chemistry does the same thing. Divide total
mass by the weight of one unit. In the
example the unit is a coin, in chemistry it is
the mole.

Limiting Reagent Problems

Consider the reaction:
2 Al + 3 I2 ------> 2 AlI3

Determine the limiting reagent and the theoretical yield of the product
if one starts with:

a) 1.20 mol Al and 2.40 mol iodine.
b) 1.20 g Al and 2.40 g iodine
c) How many grams of Al are left over in part b?
Part A solution

Take the moles of each substance and divide it by the coefficient of the
balanced equation.

For aluminum: 1.20 / 2 = 0.60
For iodine: 2.40 / 3 = 0.80

The lowest number indicates the limiting reagent.

Aluminum will run out first.
Part A solution cont.

"theoretical yield" depends on finding out the
limiting reagent.

Once we do that, it becomes a stoichiometric
calculation.

Al and AlI3 stand in a one-to-one molar
relationship

so 1.20 mol of Al produces 1.20 mol of AlI3

Notice that the amount of I2 does not play a
role, since it is in excess.