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.

Download the handout by clicking on the link underneath the description for this

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.