Help with 109 workshop 2 moles to masses table

I expect a lot of you have been struggling with the table on page 41 of your 109 workbook.  Let me try to work through it for you (this is going to be a long post!).

This table looked something like this:

If you read the previous question, you will realise that this table wants values for alanine.  In the previous question you were asked to calculate the relative molecular mass of alanine - remember, this is equivalent to the mass of 1 mole of alanine.  To calculate this, you have to add up the atomic masses of all of the elements that make up alanine, and if you do this you get a relative molecular mass of 89 (which means, 1 mole of alanine weighs 89g).

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A quick re-cap on moles and relative molecular mass....
Remember from my previous post, moles are coming, that a mole is simply a quantity, it is 6.02 x 10²³ of something.  And relative molecular mass equivalent to much 1 mole (or 6.02 x 10²³ of something) weighs.  So, if we know that the relative molecular mass of alanine is 89, this literally means that 1 mole (which is the same as saying 6.02 x 10²³ molecules) of alanine actually weigh 89g! 

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Back to the table.... lets just focus in on the first row:

I have just said that 1 mole of alanine weighs 89 g - this means that we already know what to put in the box on the far right - 89 g!  So that was an easy one to fill in.  But what about the mg and μg boxes.....

Well this is a simple conversion to do.  Remember, 1 g contains 1000 mg.  This means, if you want to convert from grams to milligrams, you have to multiply the grams by 1000.  In this case, we would do 89 x 1000 = 89000 i.e. 89 g is the same as 89000 mg.  Now the question asks for scientific notation, so we have to write 8.9 x 10⁴ mg.

And then you need to convert your answer in mg to μg.  Remember, 1 mg contains 1000 μg. This means, if you want to convert from milligrams to micrograms, you have to multiply the milligrams by 1000.  In this case, we would do 89000 x 1000 = 89000000 i.e. 89000 mg is the same as 89000000 μg.  Now the question asks for scientific notation, so we have to write 8.9 x 10⁷ μg.

So, this is what the table looks like now:

Now we need to start working our way down the table....lets just focus on the next row down:

The way I would approach this, would be to think to myself, how much smaller is 1 μmole than 1 mole, or in other words, how many fewer molecules are there in 1 μmole compared to 1 mole.  

I actually think about this in two jumps...

first I think, ok, 1mmole is 1000 times smaller than 1 mole (because there are 1000 mmoles in 1 mole) 

.....and 1μmole is 1000 times smaller than 1 mmole (because there are 1000 μmoles in 1 mmole).  

This means that 1 μmole is 1000 x 1000 = 1000000 times smaller than 1 mole (or in other words, there are 1000000 μmoles in 1 mole)

Ok, great, now we know that 1 μmole is 1000000 times smaller than 1 mole.  So, in the context of the table, this means that for the second row, we are asking how much weight there is of alanine, in a quantity that is 1000000 times less than what we have in the first row.

This means it is going to be easy to figure out the amounts for the second row - you just need to take each value from the row above, and divide it by 1000000.  This is what you will get (in scientific notation of course!):

Excellent, we are getting there!  Lets look at the next row...

Now this row is ever so slightly more tricky.  You want to know what mass of alanine is in 30 mmoles. To figure this out, just focus in on the top row and the third row:

I would think about this in two stages:

First I would think, how much smaller is 1 mmole than 1 mole, well, as I said before, 1mmole is 1000 times smaller than 1 mole (because there are 1000 mmoles in 1 mole).  So if I wanted to know how many grams of alanine were in 1 mmole, I would take the number of grams of alanine in 1 mole (89 g) and divide this by 1000 (89 / 1000 = 0.089).  So this would tell us that there are 0.089 g of alanine in 1 mmole.....

Then I would think, how much bigger is 30 mmole than 1 mmole - that is easy, 30 mmole is 30 times bigger than 1 mmole.  So, if there are 0.089 g of alanine in 1 mmole, then there must be 0.089 x 30 = 2.67 g of alanine in 30 mmoles.

Once you have figured this out, you can convert your 2.67 g to mg by multiplying by 1000, and then convert the number of mg you have to μg by multiplying by 1000 again (in the same way as we did when filling in row 1 above.

Remember, you will have to give your answer to 2 significant figures, because all information you are given is to 2 significant figures....  So here is what the table will look like now:

Working with this logic, see if you can fill in row 4....if you have trouble/want to check your answers, message us below :)