These Molar Math examples are from Lynda Jones. They originally were at chemistryiseasy.com, but that website no longer exists. This is an archived copy. ______________________________________________________________________

Problem 2: Find the Number of Moles from Particles You’re given a number of particles, and must convert back to the units of moles.

You have 2.56 x 10^25 particles of substance. Find out how many moles you have.

Begin by placing your units first.

Next, choose a conversion ratio. Set it up so that we get rid of the units that we don’t want, and have left over the units that we do want!

In this case, if you chose possibility "B," you are correct. Particles will cancel and you will end up with moles, which is what we want.

Now put the numbers in, cancel units, do the calculations, determine significant figures, and write the answer in final form.

Review: In doing simple conversions we can use the conversion ratio either "right side up" or "upside down," depending on what we're converting FROM and what we're converting TO. The steps to solving these kinds of problems are: 1. Place the starting and ending units in their correct locations. 2. Choose the correct conversion ratio to make unwanted units cancel. 3. Plug in the numbers and do the calculation. 4. Put the answer in final form. EASY!

Ratio # 2: The Volume of a Mole of Gas at STP Interlude by R.K. - Standard conditions for Temperature and Pressure (STP) are sometimes defined so that one can make comparisons. Sstandard temp = 273.15 K (0 °C, 32 °F), and the standard gas pressure is 1 atmosphere. We use STP only for problems where the particles are in a gaseous state. The molar volume Vm is the volume occupied by one mole of a substance, at a given temperature and pressure. It is defined as 22.4 Liters per mole at STP (Standard Temperature and Pressure). What does that mean? It means that if you have one mole of oxygen gas, it takes up 22.4 liters of volume. If we have one mole of CO2 or N2 gas, or methane gas - it also takes up the same volume? How is that possible? Don’t these gas molecules all have different sizes? Sure! So shouldn’t larger molecules take up more space than smaller molecules? If they were close together, then sure. But in a gas that ain’t so. In a gas, molecules are usually far apart, compared to the size of the molecule themselves. See the following picture. Note that that size of the molecule doesn’t matter much:

STP was arbitrarily set and agreed upon to mean 25 degrees C and 1 atmosphere pressure, the pressure at sea level. At DIFFERENT temperatures and pressures, the volume occupied by one mole of gas is different - and can be calculated using the gas laws.

Nevertheless, for many calculations volume is measured and compared at STP,. The ratio representing the volume of a mole of gas at STP may be written in either of two ways:

Problem 3: Find the Number of Liters from Moles

You have 4.0 moles of pure nitrogen gas at STP. How many Liters of gas do you

have?

Analysis: Start with units of moles and end up with units of Liters.

Now choose the correct conversion ratio to make the unwanted units cancel.

Next, insert the numbers, cancel units, do the calculation, and write the answer.

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Problem 4: Find the Number of Moles from Liters You have 49.7 Liters of oxygen gas at STP. How many moles do you have?

Analysis: Start with units of Liters and end up with units of moles.

Choose the correct conversion factor, plug in the numbers and calculate the final answer.

Using Two Ratios in One Problem Problem 5: Find the Number of Molecules from Liters.

In this problem, you will be using TWO conversion factors.

How many molecules of hydrogen gas are in 54.6 Liters of pure hydrogen at STP?

Analysis: You are asked to start with Liters and end with molecules. (The clue that you

end with molecules is given from the words "how many.")

While we have no direct one-shot conversion between Liters and molecules, we DO have

"Liters to moles" and "moles to molecules." So this time we use 2 conversion factors: Set it up like this:

Next, find the conversion factors needed to do the conversion.

Finally, plug in the numbers and do the calculation.

Notice that the strategy for solving problems, even with more than one conversion factor, is simply setting up the starting and ending units. Then filling in the gaps with ratios - either "right side up" or "upside down" - to make unwanted units cancel, and keep the units you want in the answer.

Ratio #3: The Molar Mass of a Specific Substance Molar mass is different from the first two ratios, because it is NOT a single constant value which never changes. Each different substance has its own molar mass. Look at the examples below. A mole of hydrogen molecules (which are made up of two hydrogen atoms bonded together) has a mass of 2 grams.

A mole of helium gas has a mass of 4.0 grams.

A mole of water has a mass of 18.0 grams.

Problem 6: Find Moles from Grams. How many moles of water are in 45.0 grams of water?

Analysis: The words "how many" point to the needed "ending units."

The words "are in" indicate the "starting units."

For water, the two possible ratios are:

Now choose which of the above ratios can be used to solve this problem.

Hopefully you chose the conversion factor shown below.

Finally, write in the numbers, do the calculation, determine significant figures and report the answer in final form.

Problem 7: Find Grams from Moles. How many grams of diatomic hydrogen gas are in 5.7 moles of hydrogen?

Analysis: The words "how many" point to the ending units.

The words "are in" point to the starting units.

Start by setting up the units

Choose the correct conversion ratio.

Write in the numbers, cancel units, do the calculation, calculate answer.

Using Two Ratios in One Problem (Part 2)

Now let's use molar mass ratios along with the first two molar ratios to solve problems.

Problem 8: Find Liters at STP from Grams.

How many Liters of space will 25.3 grams of methane gas occupy at STP? Analysis: The words "how many" indicate the ending units.

What are the starting units? And what are the conditions? (STP)

STP is important, because the conversion ratio of gas volume at STP is valid ONLY at

standard temperature and pressure. That's why is must be stated explicitly in the problem.

Find and choose the correct conversion ratios.

Put in the numbers, cancel units, do the calculation, & calculate answer.

Ratio #4: The Mole Ratio of Two Substances in a Chemical Equation We find the mole ratio, or mole-mole ratio, from a balanced chemical equation.

In most mole ratio problems, we are given a balanced chemical equation (or we must

balance it before we begin).

How to Find Mole Ratios from a Chemical Equation

A mole ratio is the ratio of moles of one species, in a chemical reaction, to the number of

moles of another.

A "species" means "a particular chemical," such as H2 or O2.

In the equation below, there are three species: H2, O2 and water.

Here is the balanced equation for the formation of water. From it we know that 2 molecules

of hydrogen plus 1 molecule of oxygen combine to make 2 molecules of water.

The coefficients (large numbers) in front of the chemical formulas represent a ratio of

components. Thus, we have a 2:1:2 ratio between the different species in the reaction.

From the above equation, we get 3 different "mole ratios."

We get the mole ratios from the coefficients.

Study the diagram below and see if you can figure out how to find mole ratios

Problem 9: Find Grams of Water from Liters of Hydrogen. Given 17.3 Liters of H2 gas, how many grams of water will be produced, if there is an

excess of oxygen?

Analysis: Start units are "Liters of hydrogen." End units are "grams of water."

Set up the problem. This time there will be 3 conversion ratios.

The middle ratio will be one of the mole/mole ratios from the balanced chemical equation.

We can think about it this way:

How could we use this flow chart? (1) Write the starting units and ending units under the chemical species to which they

pertain. We start with 17.3 Liters of hydrogen gas, so we place 17.3 Liters in the bottom

box directly under hydrogen in the equation.

We are looking for grams of water, so we write "grams" with a question mark under water,

or H2O.

(2) Draw an arrow directly up from the start unit to the mole/mole box and write the word

"moles." (For this problem, it will mean "moles of H2.")

(3) Next, draw an arrow directly down from the mole/mole box pointing towards the ending

units, which in this case are "grams of water." Write the word "moles" in the mole/mole box

where the down arrow begins. This will mean "moles of water."

(4) Finally, draw an arrow from the moles of the starting chemical (in this case, hydrogen

gas) to the moles of the ending chemical (in this case, water).

(5) Once you have these units correctly placed, writing the conversion ratios is simply a matter of following the arrows.

(6) Finally, input the numbers, cancel units, do the calculation, determine significant figures, and write the final answer in correct form.

Problem 10: Find Liters H2 at STP from Grams O2.

If you want to use up 56.7 grams of oxygen to make water, how many Liters of hydrogen

gas at STP will you need?

Analysis: Start units "56.7 grams of oxygen." (The words "use up" are the clue.) End units

"Liters hydrogen gas."

Set up the equation showing start and end units, leaving space for the conversion factors.

Next, set up the "Multiple Conversion Flow Chart"

We are starting with 56.7 grams of O2 and ending with Liters of H2 at STP.

(Notice that the direction of the arrow in the mole/mole box goes in the opposite direction

from the previous problem.)

Next, set up the conversion factor ratios with the units in the correct places for cancelling.

Now input the numbers.

Finally, cancel units to make sure you have them correctly placed, then do the math.

Recognize that we usually don’t drawing a flow chart. Once we get the hang of it, we just apply the pattern. So my actual figuring of the above problem on paper would look more like this

From here, I would cancel the units and do the calculation.