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Molar Math examples 1

The below lesson is from http://molarmath.info/

Ratio # 1: The Number of Particles in a Mole

602,200,000,000,000,000,000,000, or 6.022 x 10^23 = # of particles in a mole.

In chemistry, particles usually means molecules, ions or electrons.

The value is given BY DEFINITION based on experiments in the real world.

This relationship may be written in one of two ways:

6.022 x 10exp23 particles/mole or 1 mole/6.022 x 10exp23 particles

Remember, it doesn’t matter WHAT the particles are. The number of particles in a mole is ALWAYS the same.

Now let’s use this ratio in solving two example problems. In the first few examples, I go into excruciating detail, but after you get a feel for this kind of problem solving, it goes very quickly and is really very EASY. (My assumption is that you already understand scientific notation and significant figures.)

Problem 1: Find the Number of Particles from Moles

You have 3.0 moles of substance. How many particles of substance do you have?

Analysis: You are given moles and are asked to find particles.
So you start with units of moles and end up with units of particles in your answer.
Before you even begin to worry about the numbers, be sure to place the starting and ending units where they need to go.

conversion set up showing starting units, moles, ending units, particles and a blank horizontal fraction bar in between.  moles x (?/?) = particles.

Notice that we placed the units where they go first, without even worrying about the numbers.

We also left a blank space to write in the conversion ratio, once we determine what that is.

Next, we need to choose the correct version of the ratio between moles and particles to make the conversion work.

Concentrate on just finding the UNITS which will cancel out moles and leave us with particles.

Below we see the two possible ways that units in the Conversion Ratio may be placed. Which one do you think is correct?

two alternate set ups.  A is moles x (particles/mole) = particles.  B is moles x (mole/particles) = particles.

If you chose possibility “A,” you are correct.
That placement allows us to cancel the unit “moles” and keep the unit “particles.”

conversion set up.  moles x (particles/mole) = particles.  But the units of moles are cancelled, leaving us with particles in the end.

Now that our units are placed correctly, we can insert the numbers.
We start with 3.0 moles of substance.
# of particles in a mole is constant, so our conversion factor is constant.
(I have also placed grey numeral “1’s” into the problem to help us remember that even when there are no numbers or units written, the number “1” is always there.)

Putting the numbers in, 3.0 moles x (6.022 x 10exp23 particles/1 mole) = ? particles.  The middle factor, 6.022 x 10exp23 particles/mole is labeled the conversion factor.

Our final steps are to check the unit cancellation, do the calculation, determine significant figures and put the answer in final form.

3.0 moles x (6.022 x 10esp23 particles/mole) = ? particles.  Units of moles cancel, leaving particles.  Now put in numbers.  Get 18.066 x 10exp23 particles =1.8066 x 10exp24 particles (rounded to 2 significant figures, because of 3.0 moles) = 1.8 x 10exp24 particles -- Final Answer

Problem 2: Find the Number of Moles from Particles

Instead of being given moles as in Problem 1, you are now 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.

Analysis: You are given particles and are asked to find how many moles you have.
So this time you start with particles and end up with units of moles in your answer.
Follow the same pattern as before. Begin by placing your units first.

Conversion set up:  particles x (?/?) = moles.

Next, choose which version of the conversion ratio you need :
to cancel out the units you DON’T want and end up with the units you DO want.

Choose A or B:  A -- particles x (particles/mole) = moles    or    B -- particles x (mole/particles) = moles

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.

 B -- particles x (mole/particles) = moles.  Units of particles are cancelled.

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

2.56 x 10exp25 particles x (1 mole/6.022 x 10exp23 particles) =  ? moles.  Units of particles are cancelled.   = 0.4251 x 10exp2 moles = 42.51 moles  (round to 3 significant figures, because of 2.56 x 10exp25 particles.)  = 42.5 moles - FINAL ANSWER.

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Review of the Four Steps to Solve Mole Problems

# of particles in a mole =  6.022 x 10^23.  This is ALWAYS true.

In doing conversions, we can use the 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

This quantity is used specifically ONLY for particles in the gaseous state.
Its value is FIXED at 22.4 Liters per mole at STP (Standard Temperature and Pressure).
STP was arbitrarily set and agreed upon by the scientific community to mean 25 degrees C and 1 atmosphere pressure, the pressure at sea level.

Note: At DIFFERENT temperatures and pressures, the volume occupied by one mole of gas is different and can be calculated using the laws of relationship known as the “gas laws.”

Nevertheless, for many calculations in chemistry, volume is measured and compared at STP, so this is a useful ratio.

The ratio representing the volume of a mole of gas at STP may be written in either of two ways:

22.4 Liters/mole  or  1 mole/22.4 Liters

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: You are given moles and are asked to find Liters.
You start with units of moles and end up with units of Liters. Place your units as shown below.

moles x (?/?) = Liters

Choose the correct conversion ratio to make the unwanted units cancel.

Choose A or B:  A -- moles x (Liters/mole) = Liters  or  B -- moles x (mole/Liters) = Liters.

If you chose “A,” you are correct. Next, insert the numbers, cancel units, do the calculation, round to the correct number of significant figures and report the answer in final form.

4.0 moles x (22.4 Liters/1 mole) = ? Liters.  Units of mole cancel.  = 89.6 Liters.  (Round to 2 significant figures, because of 4.0 moles.)  = 90 Liters.  (Must write the answer in scientific notation to preserve the fact that 0 (zero) in this case counts as a significant figure.)  = 9.0 x 10exp1 Liters --- FINAL ANSWER.

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: You are given Liters and are asked to find moles.
You start with units of Liters and end up with units of moles.
You should place your beginning and ending units as shown below.

Liters x (?/?) = moles

From here, which conversion factor do you choose?
The one which has Liters on top or moles on top?
Choose the correct conversion factor, plug in the numbers and proceed through to the final answer.

49.7 Liters x (1 mole/22.4 Liters) = ? moles.  = 2.21875 moles.  (Round to 3 significant figures, because of both 49.7 and 22.4.)  = 2.22 moles  (Third digit is rounded up to 2 because of 8 being the next digit.)  = 2.22 moles - FINAL ANSWER.

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