AAMC exam 8 #37

[kabtq9s]

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I am a little rusty on the mole stuff so I would appreciate an explanation to the question in the link

http://mysowar.files.wordpress.com/2011/06/37.png

here are my specific questions about it


-How did they find the molar mass of Na2CO3*10H2O ? I calculated it and it came out to be 142

-0.0250 is the total number of moles present in the Na2CO3*10H2O and it represents all atoms in the compound because we took into account the number of atoms of each element present in the compound when we calculated the molar mass (for example when we calculated the molar mass of Na we multiplied it by 2 because of the Na2 in the compound) so why do we have to multiply the moles again by 2 ?

-Doesn't the 0.0250 mol pertain to the whole compound ? why are we treating it as if it pertains to the Na and multiplying it by 2 (ie. the amount of Na should only be a fraction of the 0.0250 mol)?


Thanks in advance

 

[Catburr]

-How did they find the molar mass of Na2CO3*10H2O ? I calculated it and it came out to be 142

Na2CO3 = 106 g/mol
H2O = 18g/mol, so 10 H2O's would be 180 g/mol
Add em up, 286g/mol

-0.0250 is the total number of moles present in the Na2CO3*10H2O and it represents all atoms in the compound because we took into account the number of atoms of each element present in the compound when we calculated the molar mass (for example when we calculated the molar mass of Na we multiplied it by 2 because of the Na2 in the compound) so why do we have to multiply the moles again by 2 ?

0.0250 is JUST the number of moles of Na2CO3*10H2O.

Think of it this way. If I point at a container and say, "that's one mole of water," how many moles of hydrogen are in there? Two. Why two? Because how many atoms are in one molecule of water? Two.

Two atoms of hydrogen plus one atom of oxygen are in every molecule of water. Two moles of hydrogen plus one mole of oxygen are in every mole of water.

Still seems weird? Ok now I point to a full carton of eggs and say, "that's one carton of eggs." But how many eggs are in there? 12. Why 12? Well, because you can count them separately and call it 12 eggs. Or you can call it one dozen eggs. Dozen is just a word we came up with to represent the number 12. Similarly, mole is a word we came up with to represent the number 6.02x10^23.

-Doesn't the 0.0250 mol pertain to the whole compound ? why are we treating it as if it pertains to the Na and multiplying it by 2 (ie. the amount of Na should only be a fraction of the 0.0250 mol)?

It does directly pertain to the whole compound. If you want to know about the components of the compound, you multiply by their "frequency" in the compound, so to speak.

You want to know how much total Na you have. So you need to know how many Na are in each molecule, and then how many total molecules you have.

 

[kabtq9s]

Thanks so much Catburr for your reply. However, I'm still 😕

Still seems weird? Ok now I point to a full carton of eggs and say, "that's one carton of eggs." But how many eggs are in there? 12. Why 12? Well, because you can count them separately and call it 12 eggs. Or you can call it one dozen eggs. Dozen is just a word we came up with to represent the number 12. Similarly, mole is a word we came up with to represent the number 6.02x10^23.

In the problem it says that the number of moles of Na2CO3*10H2O is 0.0250. So the 0.0250 is composed of many atoms. In order to make this simpler I will modify your example of the eggs.

Lets just hypothetically assume that one dozen is equal 6 eggs and 6 carrots. So 3 eggs and 3 carrots would make 0.5 of a dozen. Does it make sense that in order to find the amount of carrots we should multiply the 3 by 0.5 (which is similar to how they solved it)?

I can see the facepalms coming 😳

 

[Catburr]

Lets just hypothetically assume that one dozen is equal 6 eggs and 6 carrots. So 3 eggs and 3 carrots would make 0.5 of a dozen. Does it make sense that in order to find the amount of carrots we should multiply the 3 by 0.5 (which is similar to how they solved it)?

I can see the facepalms coming 😳

No facepalms here! Let me see, I'm not the best teacher, and this is a topic that seems counterintuitive in some ways I guess.

At one point you said "0.0250 is the total number of moles present in the Na2CO3*10H2O and it represents all atoms in the compound because we took into account the number of atoms of each element present in the compound when we calculated the molar mass."

I think this might be the point at which you're getting lost. (Maybe not!) Number of moles isn't directly associated with a particular molar mass. It's just a count of how many molecules you have. You CAN multiply (number of moles) x (molar mass) = (weight of that number of moles).

So in the problem, they first needed to know, based on 7g being present, how many molecules there were. Once they had number of molecules of the compound, they were able to figure out how many Na atoms there are. How? By multiplying by 2, since there's 2 Na+ per 1 Na2HCO3*10(H2O).

Now let's think about the food example -consider it this way - Let's call your complete breakfast invention a "carton of egg-arrots" and say that it has a given molecular formula, say Eg6Ct6. If I tell you that I went nuts at costco, and bought 20 cartons of egg-arrots, how would you know how many carrots I had?

It would be 20 x (carrots per "molecule"), right? Similarly, if I told you I went to the corner store and bought one of those miniature, cut-in-half cartons, how would you count my carrots? It would now be 0.5 x 6.

Does that make sense?

See it wouldn't be 0.5 x 3, because you just defined the molecular formula (one dozen, in your example. I'm calling it a "carton of egg-arrots" because that's just how I roll) as 6 carrots 6 eggs. So you multiply by how many carrots there are in ONE UNIT.

Let's move back to chemistry then. They figured out that their pile of Na2HCO3*10(H2O) is 0.0250 moles of the stuff right? That's like saying they have 0.0250 x (6.02x10^23) molecules of the stuff.

Now here's the key part. Each of those molecules has TWO molecules of sodium. Just like each carton of egg-arrots has 6 carrots.

Any better this way?

 

[kabtq9s]

Yep, after reading it two times, I think I got it. Thanks to the egg-arrots 🙂

I will explain what I understood just to make sure that I have the correct understanding.

1 mol of Na2HCO3*10(H2O) will have 2 moles of Na atoms

just like 1 dozen egg-arrots will have 6 carrots

If 1 mole of Na2HCO3*10(H2O) has 2 moles of Na then how many moles of Na are there in 0.0250 moles of Na2HCO3*10(H2O), so se can set it up like a ration

This is the same as saying if 1 dozen of egg-arrots will have 6 carrots then how many carrots are there in 0.5 of a dozen egg-arrots?

But unlike the egg-arrots example we can go a further step that allows us to find the exact number of molecules in the moles we are using. We do this by keeping in mind that 1 mole of any substance = (6.02x10^23) molecules of that substance. So if we know the number of moles of Na in the 0.0250 moles of Na2HCO3*10(H2O) we can calculate the molecules of Na by multiplying it by 6.02x10^23.

When I read my previous questions to you I return to my old state of confusion, but luckily the egg-arrots theory comes to the rescue just in time.

Thanks so much Catburr, I can't thank you enough for your time and patience with me, and I wish you the best in your future plans. 👍

 

[Catburr]

No problem, really. Kept me awake at work while waiting for stuff to incubate and all.

1 mol of Na2HCO3*10(H2O) will have 2 moles of Na atoms

Yup, just like it has 3 moles of oxygen, 1 mole of carbon, etc.

If 1 mole of Na2HCO3*10(H2O) has 2 moles of Na then how many moles of Na are there in 0.0250 moles of Na2HCO3*10(H2O), so se can set it up like a ration

Yup: Moles of Na = [(2 moles Na)/(1 mole Na2HCO3*10H2O)] * (# of moles of Na2HCO3*10H2O you're given)

But unlike the egg-arrots example we can go a further step that allows us to find the exact number of molecules in the moles we are using. We do this by keeping in mind that 1 mole of any substance = (6.02x10^23) molecules of that substance. So if we know the number of moles of Na in the 0.0250 moles of Na2HCO3*10(H2O) we can calculate the molecules of Na by multiplying it by 6.02x10^23.

Yup! Because a mole is just a number

When I read my previous questions to you I return to my old state of confusion, but luckily the egg-arrots theory comes to the rescue just in time.

Just try to keep the definitions straight for mole, molecular weight, molar mass. Always write units, I think that helps me. Try not to jump a step ahead of yourself. Remember molecular weight is g/mol for a given substance, molar mass is weight of one mole of a given substance (so unit is just g), and mole is 6.02x10^23 of ANYTHING, and how much it weighs varies drastically based on what you're counting.

Kinda like the cheesy joke/riddle, "Which is heavier, a pound of feathers or a pound of bricks?" Neither, they're equally heavy, because we're talking about pounds. But if they say, "a mole of feathers, or a mole of bricks?" then the bricks would be heavier.

Thanks so much Catburr, I can't thank you enough for your time and patience with me, and I wish you the best in your future plans. 👍

That's very sweet of you to say, thanks! All the best to you too. If you keep up this approach you've got going of making sure you really go back and understand everything that trips you up at first, you'll kick ass on the MCAT, that's for sure.