I. CHANGING MASS TO NUMBER OF MOLES
We know that we can find the molar mass
of a substance from the periodic table. We also know that we can find the mass of a
sample by using a balance in the laboratory. By dividing the mass of a sample by its
molar mass, we get the number of moles of the substance.
mass of the sample
# of moles of the substance = ---------------------------
Molar mass of substance
Example 1. If you find the mass of a sample of glucose (C6H12O6)
to be 90.0 g, how many moles of glucose do you have?
Solution - We find the Molar mass of glucose the same way as we
would find its molecular mass. We look up the masses of each atom on the periodic
table, multiply by the number of atoms present and add the total.
Molar mass of C6H12O6 is:
Carbon = 12.0 g x 6 atoms = 72.0 g
Hydrogen = 1.01 g x 12 atoms = 12.1 g
Oxygen = 16.0 x 6 atoms = 96.0 g
---------
180.1 g or 180 g (1.80 x 102 g)
Now use the formula:
mass of the sample
# of moles of the substance = ---------------------------
Molar mass of substance
Given: The mass of the sample is 90.0 g
The Molar mass of the
substance is 180 g/mol
90.0 g
# of moles of glucose = ------------------- = 0.500 mol
180 g/mol
Answer - 0.500 moles of glucose.
II. CHANGING NUMBER OF MOLES TO MASS
If we are given the number of moles of a
substance, we can convert that into a mass, based on our knowledge of Molar mass. We
can use the formula from the section above, and adjust it for the new unknown, which will
be mass of the sample:
mass of the sample
# of moles of the substance =
---------------------------
Molar mass of substance
To isolate the mass of the sample, we must multiply both sides by
Molar mass of a substance:
mass of the sample x Molar mass of substance
# of moles of the substance x Molar mass of substance =
---------------------------
Molar mass of substance
So we are left with the formula:
mass of the sample = # of moles of the
substance x Molar mass of the substance.
Example 1. A certain laboratory procedure requires the use
of 0.100 moles of magnesium. How many grams of magnesium would you mass out on
the balance?
Solution, from the period table we get the Molar mass of
magnesium as 24.3 g. We then place that information in the formula below:
mass of the sample = # of moles of the substance x Molar mass of
the substance.
Given: The # of moles of the substance = 0.100 mol
The Molar mass of the
substance = 24.3 g/mol
mass of the sample = 0.100 mol of magnesium x
24.3 g/mol
Answer =
2.43 g of magnesium
III. CHANGING NUMBER OF MOLES TO NUMBER OF
PARTICLES
This is like asking you to change 3
dozen doughnuts into total number of doughnuts. A very simple calculation that you
can do in your head. We know that a dozen is always 12, so 3 x 12 = 36.
Changing number of moles to number of particles should not be much harder. We know
that one mole is always Avogadro's number (6.02 x 1023). So, we just need
to multiply the number of moles by Avogadro's number.
Total number of particles = number of moles x 6.02
x 1023
Example 1. How many molecules of carbon dioxide are found
in 2.50 moles of carbon dioxide?
Solution: We use the formula:
Total number of particles = number of moles x 6.02 x 1023
Given: Number of moles = 2.50 mol
Total number of molecules of CO2 = 2.50 mol
x 6.02 x 1023 molecules/mol
Answer
= 1.51 x 1024 molecules of CO2
IV. CHANGING NUMBER OF PARTICLES TO NUMBER OF
MOLES
This calculation is obviously the
opposite of the calculation shown in the section above. If I told you I had 30
doughnuts and I asked you how many doughnuts there are, you could divide 30 by 12 and get
2.5 dozen. The logic is the same for determining number of moles.
# of moles = total number of particles
------------------------
6.02 x 1023
Example 1. How many moles of O2 are represented
by 7.45 x 1024 molecules of O2?
Notice that it does not matter what compound the question asks
for. Just as 30 of any item would represent 2.5 dozen, 7.45 x 1024 of any
molecule will represent a set number of moles. There is no need to use the periodic
table for this type of problem
Solution: Use the formula:
# of moles = total number of particles
------------------------
6.02 x 1023
Given: The total number of particles = 7.45 x 1024
molecules
# of moles of O2 = 7.45 x 1024
molecules
-----------------------------
6.02 x 1023 molecules/mol
Answer = 12.4 moles of O2
V. CHANGING NUMBER OF PARTICLES TO MASS
This is an example of what might
be called a "two-step problem". The first step is to change the
number of particles to number of moles, as shown in section IV of this page. Then
change the number of moles into mass, as shown in section II of this page.
Example 1. What would be the mass of 3.75 x 1021
atoms of iron?
Solution: First change number of atoms to moles with the
formula:
# of moles = total number of particles
------------------------
6.02 x 1023
Given: The total number of particles = 3.75 x 1021
atoms
# of moles of iron = 3.75 x 1021 atoms
---------------------------
6.02 x 1023 atoms/mol
Answer to step one = 0.00623 moles of iron.
Now, change number of moles to mass using the equation:
mass of the sample = # of moles of the substance x Molar mass of
the substance.
Given: The number of moles of the substance = 0.00623 mol
The Molar mass of iron
(from periodic table) = 55.8 g/mol
mass of the Fe sample = 0.00623 mol x 55.8 g/mol
Final Answer: Mass of the iron = 0.348 g
VI. CHANGING MASS TO A NUMBER OF PARTICLES
We can, of course, do the opposite of
the procedure described in step V, in order to change a given mass into the number of
particles. This would also be a two-step operation. First we would change the
mass to number of moles, as described in step I. Then we would change number of
moles to number of particles as shown in step III.
Example 1. How many water molecules would be found in a
54.0 gram sample of water?
Solution. First we would change the mass of the sample to
number of moles. Find the Molar mass of water:
Molar mass of H2O
H = 1.01g x 2 atoms = 2.02 g
O = 16.0 g x 1 atom = 16.0 g
--------
Molar mass of H2O = 18.0 g
Now we use the formula:
mass of the sample
# of moles of the substance = ---------------------------
Molar mass of substance
Given: The mass of the sample is 54.0 g
The Molar mass of the
substance is 18.0 g/mol
54.0 g
# of moles of water = ---------------
18.0 g/mol
Answer to step one = 3.00 moles of water.
Now, change the number of moles of water to number of particles
using the formula:
Total number of particles = number of moles x 6.02 x 1023
Given: The number of moles of water = 3.00 mol
The Total number of molecules of water = 3.00 mol x 6.02 x 1023
molecules/mol
Final Answer = 1.81 x 1024 molecules of water.
VII. VARIATIONS
Please be aware that the six types of
problems described above are only some of the major types of problems that you might be
asked. You must read each question carefully and determine what the question is
asking for. Changing one or more words in the question can completely change the
answer, as shown in the two examples below:
Example 1. How many molecules would be found in a 36.0 gram
sample of water?
Example 2. How many atoms would be found in a 36.0 gram
sample of water?
Do you see the difference? Example 2 requires you to
have your answer in atoms. Since there are three atoms (two hydrogen and one oxygen)
in one molecule of H2O, the answer would be three times as great as the answer
to example 1.
There are many other possible variations to these types of
questions. This is why I encourage you to solve each problem logically instead of
mechanically. Memorizing formulas is not enough, you need to be able to reason what
the question is actually asking for.
Please forward all questions, comments and criticisms to Gregory L. Curran.
© Copyright 2004 Fordham Preparatory School, All Rights Reserved.
Last Modified March 24, 2004 |
