 # The Mole Mantra

So let’s consider the mole in the mole
mantra. First you want to look at some images. “What do these images have in
common?” Write down some commonalities in each
case. We saw that we had a triangle. These triangles are summarized on this handout.
tutorial, and we discovered that these are all ratios. The upper left-hand
corner is our density triangle. Density is a ratio of mass per volume, where mass is
given and grams and volume is given in milliliters (or cubic centimeters). Our focus in this tutorial
is to look at the mole triangle. Molar mass ratio (MM) is the ratio of mass per
amount where mass will be given in grams and amount will be given in moles, and
the mole is a accounting device. So let’s turn to your supplemental packet and let’s
consider physical methods for counting. Here I have a hand with five fingers; one
hand equals five fingers. We can write that as a ratio. The ratio can be written
as one hand for five fingers or five fingers per one hand. Again, these are
counting device ratios. “And if there are 70 fingers in this room, how many
complete hands of five fingers are there?” To answer this question, we can show a
math setup with number and unit to support our answer. “Which counting ratio
do we use in our math setup? One hand for five fingers or five fingers for one
hand?” We will use one hand per five fingers since we’re trying to determine
how many hands there are in this room. If there are 70 fingers, one hand for five
fingers times seventy fingers equals fourteen hands, and we can see that our
units fingers cancel out, and we’re left with the image hand, and certainly
raise your hand if you don’t understand. And a good mantra is to raise
your hand if you don’t understand, and we can simplify our counting ratio by
writing the following: one hand for five fingers times 70 fingers equals 14 hands
removing the hand pictogram. “So how does this apply to the mole?” First, we need to
be familiar with counting devices for physical objects larger than atoms and
we are. One dozen of anything equals twelve units of anything and we could draw a
pictogram of that twelve of anything per one dozen, or we could write the ratio as one
dozen per twelve units as a pictogram which is equal to twelve and we can simplify our
ratio as twelve per one dozen or one dozen per twelve and then we can answer a question
like the following: “A basket has 18 eggs, how many dozen eggs are contained in the
basket well we know there’s twelve per dozen or, one dozen or one dozen per twelve? We know
there’s twelve eggs per one dozen eggs or one dozen eggs four twelve eggs. Thus 18
eggs times one dozen eggs per twelve eggs is equal to 1.5 dozen eggs,
and know that the unit’s eggs cancel out. We could also cross out the units
directly above because anything above itself is equal to one. Thus, eggs cancel
with eggs, eggs cancel with eggs, eggs cancels with eggs and when we multiply
through we multiply by 18 eggs per one dozen.