Mole-Mass-Particle Conversions
Remember, chemists measure amounts of atoms using the quantity, the
mole, which is 6.02x1023 particles of a substance. This value is known
as Avogardro’s number. Its symbol is NA.
Converting between particles and moles
• If we are given the # of moles of a substance we can determine
the # of particles & vise-versa using Avogardo’s number.
N = n x NA
where n = moles
N = the number of particles
NA = 6.02x1023 particles/mol
Example 1: Find the number of particles in of 0.50 mol of water.
Solution
1. Choose the equation that relates the
three quantities: moles, particles and
Avogadro’s number.
2. Rearrange the equation if necessary .
3. Substitute the known data into the
equation.
4. Perform necessary calculations
5. List final answer to the correct
number of sig figs and proper units.
N = n x NA
N = 0.50 mol x 6.02x1023 particles
mol
N = 3.0x1023 particles
Example 2: How many moles are in 1.43 x 1022 particles of Na2O
Solution
6. Choose the equation that relates the
three quantities: moles, particles and
Avogadro’s number.
7. Rearrange the equation if necessary .
8. Substitute the known data into the
equation.
9. Perform necessary calculations
10. List final answer to the correct
number of sig figs and proper units.
N = n x NA
n=N
NA
n = 1.43x1022 particles
6.02x1023 particles
mol
N = 0.0238 mol
Example 3: How many atoms of sodium are in 1.25 moles of Na2O?
Solution
1. Choose the equation that relates the
three quantities: moles, particles and
Avogadro’s number.
2. Rearrange the equation if necessary .
3. Substitute the known data into the
equation.
4. Perform necessary calculations
5. List final answer to the correct
number of sig figs and proper units.
N = n x NA
N = 1.25 mol x 6.02x1023 molc
mol
N = 7.525 x1023 molecules
# atoms Na=7.525 x1023 molc x
= 1.50x1024
Background: atomic masses
• Look at the “atomic masses” on the periodic table.
• What do these represent?
• e.g. the atomic mass of C is 12.01 u (atomic # is 6)
• Represents the mass of 1 mole of Carbon atoms
• What is the actual mass of a C atom?
(6 x mass of e-) + (6 x mass of protons) + (6x mass of n)
= (6 x 9.1093897.10-28 g ) + (6 x 1.6726430.10-24 g ) +
(6×1.674954.10-24 g)
= 2.0x10-23 g
Two problems
1. Atomic masses do not convert easily to grams
2. They can’t be weighed (they are too small)
• It is useful to associate atomic mass with a mass in grams.
2 atoms Na
1 molc Na2O
• It has been found that
1 g H, 12 g C, or 23 g Na have 6.02 x 1023 atoms
• 6.02 x 1023 is a “mole” or “Avogadro’s number”
Molar mass
• The mass of one mole is called “molar mass”
• E.g. 1 mol Li = 6.94 g Li
• This is expressed as 6.94 g/mol
What are the molar masses of SO2 and Cu3(BO3)2?
SO
Number of Atoms
X
Atomic Mass = Total Mass
Number of Atoms
X
Atomic Mass = Total Mass
S
O
Cu3(BO3)2
Cu
B
O
Converting between grams and moles
• If we are given the # of grams of a compound we can determine
the # of moles, & vise-versa
• In order to convert from one to the other you must first calculate
Molar mass
g=nxM
where g = grams, n = moles and M = molar mass
Example 3: How many grams are in 0.25 mol of HCl?
Solution
1. Choose the equation that relates the three
quantities: moles, mass and molar mass.
2. Rearrange the equation if necessary.
3. Calculate the molar mass of the substance.
4. Substitute the known data into the
equation.
5. Perform necessary calculations.
6. List final answer to the correct number of
sig figs and proper units.
g=nxM
M = 1 g/mol + 35.45 g/mol
= 36.45 g/mol
Substitute
g=nXM
= 0.25 mol x 36.45 g/mol
= 9.1 g
Ex. 4 How many mol are in 53.15 g of H2SO4?
g=nxM
Rearrange to n = g
M
n = 53.15 g
98.09g/mol
= 0.5418 mol
M = (2x1) + 32.09 + (4x16) = 98.09 g/mol