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Molar Math 2

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ALL mole chemistry problems you have from here on out are simply extensions of the skill of being able to find the correct conversion ratio which cancels unwanted units and leaves wanted units. EASY!


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 to get the answer.

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 can use TWO conversion factors to get our answer.

Set it up like this:

Start units --> Liters.  End units --> molecules.  Conversion set up:  Liters x (?/?) x (?/?) = molecules.

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

Conversion set up:  Liters x (mole/Liters) x (molecules/mole) = molecules.  Middle two ratios are labeled conversion factors.  Units of Liters cancel.  Units of mole cancel.

Finally, plug in the numbers and do the calculation.

54.6 Liters x (mole/22.4 Liters) x (6.022 x 10exp23 molecules/mole) =  ? molecules.  Units of Liters cancel.  Units of mole cancel.  = 14.678 x 10exp23 molecules.  = 1.4678 x 10exp24 molecules.  (Round to 3 significant figures, because of 54.6 Liters and 22.4 Liters.)  = 1.47 x 10exp24 molecules - FINAL ANSWER.

Notice that the entire strategy for solving problems like this, even with more than one conversion factor, is simply setting up the starting and ending units and 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. EASY!


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. Although any given substance has the same unchanging, constant molar mass, each different substance has its own molar mass. Look at the three examples below.

A mole of hydrogen molecules (which are made up of two hydrogen atoms bonded together) has a mass of 2 grams.

2.0 grams/mole H2  or  1 mole H2/2.0 grams

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

4.0 grams/mole He  or  1 mole He/4.0 grams

A mole of water has a mass of 18.0 grams.

18.0 grams/mole H2O  or  1 mole H2O/18.0 grams

If you do not know how to find the molar mass of a substance, click here. [Not active yet.]

Now let’s use molar mass to solve problems.

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.”

Start units --> grams.  End units --> moles H2O.  Conversion set up:  grams x (?/?) = moles H2O

For water, the two possible ratios are:

18.0 g/mole or 1 mole/18.0 g

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

Starting units are grams.  Ending units are moles H2O.

Hopefully you chose the conversion factor shown below.

Conversion factor units are mole H2O over grams.

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

45.0 grams x (1 mole H2O/18.0 grams) = ? moles H2O.  Units of grams cancel.  = 2.50 moles H2O -- FINAL ANSWER.

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

Start units --> moles H2.  End units --> grams.  Conversion set up:  moles H2 x (?/?) = grams

Choose the correct conversion ratio.

2.0 grams/mole H2  or  1 mole H2/2.0 grams

Write in the numbers, cancel units, do the calculation, determine significant figures and report the answer in final form.

5.7 moles H2 x (2.0 grams/1mole H2) = ? grams.  Units of mole cancel.  = 11.4 grams.  (2 significant figures, because of 5.7 and 2.0)   = 11 grams - FINAL 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) The condition of 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.

Set up the problem.

Start units --> grams.  End units --> Liters.  Conversion set up:  grams x (?/?) x (?/?) = Liters.

Find and choose the correct conversion ratios.

Two sets of possible conversion factors:  First set = 16.0 grams/mole CH4  or  1 mole CH4/16.0 grams.  Second set = 22.4 Liters/mole  or  1 mole/22.4 Liters.

Put in the numbers, cancel units, do the calculation, determine correct number of significant figures and report the final answer.

25.3 grams x (1 mole CH4/16.0 grams) x (22.4 Liters/mole) = ? Liters.  Units of grams cancel.  Units of mole CH4 cancel.  = 35.42 Liters CH4.  (Round to 3 significant figures, because of 25.3, 16.0 and 22.4.)  = 35.4 Liters CH4 - FINAL ANSWER.

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