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Chapter 10 - How does a chemist measure? How does the chemist count?
2H2(g) + O2 → 2H2O(g)
This reaction requires two molecules of hydrogen and one molecule of oxygen. To carry out this chemical reaction a chemist must mix hydrogen and oxygen together in the correct ratio (2:1). How does the chemist know when the correct ratio is present? These molecules are too small to see so we cannot count them directly. The chemist must use an indirect method of counting.
Example: Your job is to put pennies into rolls. How can you do this?
1. You can physically count out fifty pennies.
2. You could find the average mass of a penny and set the balance to mass the 50 pennies.
3. You could use the plastic rolls with the set volume for fifty pennies.
For a chemist, counting directly is not an option because the particles are too small. The chemist uses mass (grams) or volume (liters) to count particles indirectly.
Because molecules, atoms and ions are so small the chemist cannot count them directly. The chemist counts them using the Mole, a word that represents a definite number. The mole is like another word that represents a number, a dozen, which represent 12. The role of the mole in chemistry is that of counting ions, atoms or molecules. The chemist can "count" ions, atoms or molecules by weighing very large numbers of them to get a significant mass. One mole contains as many atoms as there are in 12 grams of carbon-12. There are 6.02 x 1023 atoms of carbon in 12.0 grams of carbon-12. In one mole, there are 6.02 x 1023 particles; the mole can be treated like a very large dozen. The number 6.02 x 1023 is called Avogadro’s number, named in honor of Amedeo Avogadro, an Italian chemist who first suggested it use. The chemist views the Mole as a collection of 6.02 x 1023 representative particles (symbol - N). Representative particles are the smallest pieces of a substance;
For a molecular compound the representative particle is a molecule.
For an ionic compound the representative particle is a formula unit.
For an element the representative particle is an atom (except for elements that are diatomic molecules).
Molar Mass for Elements
The u (atomic mass unit) is a very small unit of mass and is of no use in the lab, so the chemist uses the mole, 6.02x1023 atoms. The mass of 1 mole of atoms of an element in grams is called the molar mass, which is numerically the same as the u (atomic mass unit). The mass in grams of one mole of a substance is called molar mass. Each element has its own unique molar mass. For example, carbon’s molar mass is 12.011 g/mol, and hydrogen’s molar mass is 1.0079g/mol, 1 mole of Fe has a mass of 55.847g. 1 mole of carbon has the same number of atoms as 1.0079 grams of hydrogen and 55.847 grams of iron. We can write this as 12.011 g C = 1 mole C; we count by mass. The mass that describes one mole is the molar mass:
Element Molar Mass
C = 12.01g
mole
H = 1.0079g
mole
Fe = 55.847g
mole
To see why these elements have different molar masses, we need to remember that the atoms of different elements contain different numbers of protons, neutrons, and electrons, so they have different masses. The atomic masses given in the periodic table represent the different weighted average masses of the naturally occurring atoms (isotopes) of each element. Different atomic masses lead to different molar masses. (Compare the mass of 50 pennies, 50 nickels and 50 dimes.)
For example, the atomic mass of hydrogen (1.0079u) shows us that the average mass of hydrogen atoms is about one twelfth the average mass of carbon atoms (12.011u), so the mass of 6.02 x 1023 hydrogen atoms (the number of atoms in 1 mole of hydrogen) is about one twelfth the mass of 6.02 x 1023 carbon atoms (the number of atoms in 1 mole of carbon). Thus, the molar mass of hydrogen is 1.0079g/mol, compared to carbon’s molar mass of 12.011g/mol.
The number of grams in the molar mass of an element is the same as the atomic mass. Translating atomic masses into molar masses, you take the atomic mass of an element and change the unit to grams, which is the mass of one mole of the element. The importance of the molar mass is its use as a conversion factor. In a conversion factor the top term equals the bottom term, the value of the ratio is 1.
Molar mass of an element = element atomic mass in grams (periodic table)
1 mole element
For example, the atomic mass of the element sodium on the periodic table is 22.98977u, giving a molar mass of 22.98977g/mol. This molar mass provides two conversion factors for converting between grams and moles of sodium. Conversion factors merely change the unit not the value of the number. Example:
75 cm x 1m = 0.75m
100cm
22.98977g Na or 1 mole Na Example: 11.4949g Na x 1 mole Na = 0.50000 mole Na
1 mole Na 22.98977g Na 22.9898g Na
Molar Mass for Molecular Compounds
The first step in the determination of the molar mass of a molecular compound is to determine the molecular mass of the compound, which is the sum of the atomic masses of each atom in the molecule. This is found by adding the atomic masses of all of the atoms in the molecule.
The chemist studies the composition of matter and knows that water is made up of hydrogen and oxygen as shown in the formula H2O. This formula shows that one molecule of water contains two atoms of hydrogen bonded to one oxygen atom. The mass of the water molecule consists of the mass of these three atoms. The molecular mass of a substance is the total mass of all the atoms given in a formula. The average atomic mass of atoms, found on the Periodic Table, is given in atomic mass units.
For hydrogen the atomic mass is 1.0079 and for oxygen it is 15.9994. To find the molecular mass of water:
2 x H = 2 atoms x 1.0079 amu/atom = 2.0158amu
1 x O = 1 atom x 15.9994amu/atom = 15.9994amu
H2O = 18.0152amu (molecular mass)
The number of grams in one mole of a molecular compound is the same number as its molecular mass. The molar mass has gram as a unit instead of u (atomic mass unit) for the molecular mass.
Molar mass of a molecular compound = molecular mass in grams
1 mole
For water molar mass = 18.0152g Example: 1.50mole H2O x 18.0152g = 27.0g H2O
1 mole 1 mole
Chemical composition
To find the number of atoms of each element in a compound use:
Subscript x coefficient = number of atoms
2H2SO4: H = 2 x 2 = 4 atoms; S = 1 x 2 = 2 atoms; O = 4 x 2 = 8 atoms (total for 2 molecules).
If there are parentheses:
Subscript (outside) x subscript (inside) x coefficient = number of atoms
Ca(NO3)2: Ca = 1 x 1 = 1Ca; 2 x 1 x 1 = 2N; O 2 x 3 x 1 = 6O (total for 1 formula unit).
Find the number of atoms or ions in each of these:
Al(NO3)3
(NH4)2CO3
3H2O2
Molar Mass for Ionic Compounds
For an ionic compound the representative particle is the formula unit Al2(SO4)3. The first step in the determination of the molar mass of an ionic compound is to find the formula mass. To find the formula mass multiply each element's atomic mass by how many atoms are present in the formula:
2 x Al = 2 atoms x 26.98amu/atom = 53.96amu
3 x S = 3 atoms x 32.06amu/atom = 96.18amu
12 x O = 12 atoms x 16.00amu/atom = 192.00amu
Al2(SO4)3 = 342.14amu (formula mass)
So formula mass = the sum of the atomic masses of each atom in a formula unit
The number of grams in the molar mass of any ionic compound is the same number as the formula mass.
Molar mass of an ionic formula = formula mass expressed in grams
1 mole
The molar mass for Al2(SO4)3 is 342.14 g.
mole
The formula mass of sodium chloride is equal to the sum of the atomic masses of sodium and chlorine, which can be found on the periodic table.
Formula mass NaCl = 22.9898u + 35.4527u = 58.4425u
The molar mass for NaCl = 58.4425g
1 mole
Practice:
What is the molar mass of Fe2O3?
2 x Fe x 55.85u = 111.70u
3 x O x 16.00u = 48.00u
Total formula mass = 111.70u + 48.00u = 159.70u.
the molar mass of Fe2O3 = 159.70g
mole
Examples:
Calculate the molar mass of the following.
Na2S
N2O4
Ca(NO3)2
C6H12O6
(NH4)3PO4
Using Molar Mass
1. We can make a conversion factor using the Molar Mass to change grams of a compound to moles of a compound.
How many moles is 5.69 g of NaOH?
5.69g NaOH x 1 mole = 0.142mole NaOH.
40.0g
How many moles is 4.56 g of CO2?
4.56g CO2 x 1 mole = 0.104 mole CO2.
44.0g
Now you try:
How many moles of H2O in 29.87g?
2. We can make a conversion factor using the Molar Mass to change moles of a compound to grams of a compound.
Examples
What is the mass of 2.50 moles of carbon? (start with moles and want grams in the end)
2.50mole x 12.01g = 30.0gC
mole
What is the mass of 0.100 moles of magnesium?
0.100 mole Mg x 24.3g = 2.43g of Mg
1 mole
Now you try:
How many grams are in 9.87 moles of H2O?
3. Avogadro’s number can also be used as a conversion factor to change moles to number of particles. When given the mass of an element convert to moles and then to number.
0.100 mole Mg x 6.02x1023 = 6.02x1022 atoms Mg.
1 mole
How many molecules in 6.8 g of CH4?
6.8g CH4 x 1 mole = 0.425 mole CH4 x 6.02 x 1023 molecules = 2.56 1023 molecules
16.0g 1 mole
What is the mass of 49 molecules of C6H12O6?
49 molecules x 1 mole = 8.14 x 10 –23 mole x 180.0g = 1.47 x 10-20g
6.02 x 1023 molecules 1 mole
Try these questions
1. How many molecules of CO2 are the in 4.56 moles of CO2?
2. How many moles of water is 5.87 x 1022 molecules?
3. How many atoms of carbon are there in 1.23 moles of C6H12O6?
4. How many moles are 7.78 x 1024 formula units of MgCl2?
5. How many atoms of lithium in 1.00 g of Li?
Gases and the Mole
Many of the chemicals we deal with are gases. Gases are difficult to mass. As with solids we need to know how many moles of gas we have. There are three variables that affect the volume of a gas: temperature, pressure and the number of particles. At higher temperature particles move faster, collide harder and spread further apart (become less dense). At lower temperature particles move slower, softer collisions and move closer together (become more dense).
An increase in pressure squeezes the molecules closer together and a reduction in pressure allows the particles to move further apart.
When the number of particles increases the particles will occupy a greater volume.
To make a comparison of volumes of gases fair we need to compare the volumes at the same temperature and pressure. When we have equal volumes at the same pressure and temperature, the equal volumes contain equal numbers of moles (particles) of gas. Because the temperature, pressure and moles of gas affect the volume of a gas the chemist will measure the volume of a gas under controlled conditions. The chemist has set the conditions to measure the volumes of gas to 0ºC and 101kPa, known as standard temperature and pressure (STP). Since temperature and pressure are held constant the volume of the gas depends on the number of particles. The chemist counts by using moles, so if 1 mole of any gas is measured at STP it will have a volume of 22.4L. We an express this as 1 mole of gas = 22.4L at STP or molar volume = 22.4L/mole. Avogadro’s Hypothesis states that at the same temperature and pressure equal volumes of gas have the same number of particles.
As with molar mass, molar volume can be used as a conversion factor.
22.4L or 1 mole
1 mole 22.4L
Examples:
What is the volume of 4.59 mole of CO2 gas at STP?
You must convert mole to L (volume).
4.59 mole x 22.4L = 102.816L = 103L at STP
1 mole
How many moles is 5.67 L of O2 at STP?
You must convert L (volume) to mole.
5.67L x 1 mole = 0.253125 mole = 0.253mole
22.4L
Here is one for you to try.
What is the volume of 8.8g of CH4 gas at STP?
We have learned how to change:
moles to grams; moles to numbers; moles to liters
Stoichiometry
Stoichiometry is Greek for “measuring elements” and involves the calculations of quantities in chemical reactions based on a balanced equation. We can interpret balanced chemical equations several ways.
In terms of Particles
Element - atoms
Molecular compound (nonmetals)- molecules
Ionic Compounds (Metal and nonmetal) - formula units
2H2(g) + O2(g) → 2H2O(l)
Two molecules of hydrogen and one molecule of oxygen form two molecules of water.
2Al2O3(s) → 4Al(s) + 3O2(g)
2 formula units of Al2O3 decompose to yield 4 atoms of solid aluminium metal and 3 molecules of oxygen gas.
2Na(s) + 2H2O(l) → 2NaOH(aq) + H2(g)
2 atoms of solid sodium metal react with 2 molecules of liquid water to yield 2 formula units of aqueous sodium hydroxide and one molecule of hydrogen gas.