Mole Theory Moles and Grams Conversions

A Quick Review In your last exercise, you worked to develop the ability to calculate the formula weight of a given compound. Remember that formula weight is the total mass (weight) of all of the atoms in a chemical formula.

A Quick Example Suppose that you were tasked with determining the formula weight of the compound sodium hydroxide.

Step #1 You would need to write the formula for the compound using “SOCCR”. This would give Na (OH) +1 And you would end up with: NaOH

Now for the Formula Weight The compound has the inventory »Na =1 »O=1 »H=1 From the periodic chart, Sodium has a mass of 23, Oxygen has a mass of 16, and Hydrogen has a mass of 1.

Finishing this up… The formula weight will be calculated as: fw = 1(23) + 1(16) + 1(1) = 40

Now for the New Stuff: The technical units of this formula weight are amu’s (atomic mass units) since we have actually determined the mass of a single molecule. But, we do not typically care about the mass of single molecules. (Note though, that we will care about single molecules in some of our discussions later in the year.)

Continuing… Instead, we will deal with the mass of 6.02 x molecules at a time. (Remember that number ????) By definition, that many molecules of a compound is called 1 mole of that substance.

Putting the Parts Together: Each of the molecules will have the same formula weight. (40 amu’s in our example) Therefore, the total mass of the Avogadro’s number of molecules will be 6.02 x molecules x 40 amu/ molecule which will give you a whole lot of amu’s. (do not bother to calculate this out, it will get easier in just a second)

Finishing this Part: There is an actual mass (in grams) associated with the atomic mass unit – but is so small that it is incomprehensible. (and I have concerns that all of you honors types will memorize it – so it will not appear here) But, it turns out that if you multiply the actual mass of the amu x the number of amu’s that would be calculated in the last slide, you would get an answer of 40 grams… the same numerical value as the formula weight in amu’s.

Therefore… We will define the formula weight as the mass in grams of 1 mole of molecules of a given compound. So… the formula weight of the compound Sodium Hydroxide will be quoted as 40 grams / mole

Formula Weight as a “Component” in Other Calculations Since the actual mass of the atoms (and therefore compounds too) is set by nature, we may take the value of the formula weight as a “fact of life” and use it in other calculations. The fact that science created the measuring system is irrelevant, nature built the atoms.

What does this Mean ? Simply put, since 1 mole = the formula weight in grams, we are free to use the formula weight as a conversion factor. Let’s use the formula weight of sodium hydroxide for the following examples. (since we already know it)

Example #1 The Problem: What mass in grams is equivalent to 3.75 moles of sodium hydroxide ? The Logic: We have already determined that the formula weight of NaOH is 40 grams/mole. Therefore, 1 mole of NaOH will have a mass equal to 40 grams.

Continuing… The problem does not ask for the mass of 1 mole of NaOH, it wants the mass of 3.75 moles of this compound. Obviously, all we have to do is multiply 3.75 x 40 to get a numerical answer. Doing so will give you the answer 150. But why does this work ???

With units… Remember that we have assigned units to formula weight – specifically… grams/mole. The problem actually sets up like this: 3.75 moles NaOH 40 grams NaOH 1 mole NaOH x = = 150 grams NaOH The calculated formula weight Note how the units “moles NaOH” are set up to cancel.

Now for Example #2 The Problem: How many moles are equivalent to a mass of 320 grams of sodium hydroxide? The Logic: We still know that the formula weight of this compound is 40 grams/mole. Therefore, we may still use it as a factor to convert one measurement to the other.

Continuing… Since 1 mole is equivalent to 40 grams (of this compound – remember that it will be different for other compounds), all that we need to do here is divide the 320 grams by 40 grams to obtain the answer “8 moles”. But again, why does it work ???

With units… The problem will set up like this: 320 grams NaOH 1 mole NaOH x 40 grams NaOH =8 moles NaOH Notice that this is still the formula weight, just inverted so that the units will cancel.

To Summarize This type of conversion will be central to a lot of the problems that we see – you need to become really good at it…. The first step will be to write a correct chemical formula (if it is not given to you). Then you will have to determine a correct formula weight. Finally, do the calculation, being sure to set up the “factor” so as to cancel out units.