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Chemistry! Help please?!



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Fri Oct 08, 2010 12:45 am
HostofHorus says...



Alright, I have a bunch (like 25) of these problems concerning Avogadro's number, and I was gone when they went over them... So I thought I'd post like two, and see if someone could help me out, and show me how I would go about doing these. Thanks in advance!!!

I. On the day the earth was born 4.8 billion years ago, you began putting hydrogen atoms on an analytical balance at a rate of x atoms per second. Yesterday afternoon at half past three, you found that you had put 1.008 grams of hydrogen atoms on the balance. What is the value of x?

And a harder one....

II. You have heard the story of a fellow who rescued the king's daughter from a dragon and then the king told him to name his own reward and he would have it. The willy character said, "I like rice, so get out a chess board and put one grain of rice on the first square. two on the second, four on the third, eight on the next, and so forth. Then give me all of the rice when you fill up the chess board.

The king, who flunked math, (or I who am going to flunk chemistry... =P) 100 at the Royal University, approved the deal and of course you know that the kingdom went bankrupt somewhere around square # 22.

Your problem is similar. You have Avogadro's number of hydrogen atoms and you put one atom on square one, two on the next, etc. If you have any atoms left over when you have hydrogenated (filled with hydrogen atoms) the whole board then start over on the next chess board with one hydrogen atom on the first square of the second board, and two hydrogen atoms on the next square, four atoms on the next square, and so on until you have filled up the second board. On each new board begin with only one atom on the first square and keep going this way until you have exhausted your supply of hydrogen atoms (Avagadro's number of hydrogen atoms). How many chess boards will you fill? (HINT: There are 64 squares on a chessboard....)

And yeah, I'm stumped.... so any help would be much appreciated! I just need some examples to go off for the rest of the assignment... Thanks!
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Fri Oct 08, 2010 12:55 am
Kale says...



I can help you with these. I just need the aid of pictures as the formulas are not easily read when typed out. Will edit this post with said pictures soon.

First things first: Avogadro's Number

Avogadro's Number is the number of individual particles in one mole of a substance. That number is 6.022*10^23.

In other words, a mole is a larger unit used to measure particles, much as a kilometer is a larger unit to measure distance. Just as the conversion between meters and kilometers is 1000 meters = 1 kilometer, 1 mole of x = 6.022*10^23 particles of x.

Question I

What we know: The problem tells us that at the end of 4.8 billion years, we have 1.008 grams of hydrogen. We also know, from looking at the periodic table, that 1 mole of hydrogen has a mass of 1.008 grams.

What we want to end up with: The problem is asking us for individual particles, atoms in this case, added per year. Wherever we have individual particles, Avogadro's Number comes into play. Recall from earlier that Avogadro's Number is the number of particles in one mole; in other words one mole is equal to 6.022*10^23 particles.

Converting to numbers:

4,800,000,000 years
x atoms of hydrogen / 1 year
1.008g H
1 mole H = 1.008g H
1 mole H = 6.022*10^23 atoms H

Set up: Because we want to end up with atoms in the end, it is best to start with the conversion factor dealing with Avogadro's Number.

step1.jpg
step1.jpg (5.43 KiB) Viewed 472 times

As you can see, we have moles of hydrogen on the bottom. Since we don't want moles in the final answer, we want to cancel the moles out. The only set of numbers dealing with moles is the 1 mole = 1.008g H conversion, so that is what we use.

step2.jpg
step2.jpg (8.1 KiB) Viewed 472 times

Again, we have a unit on the bottom that we do not want to end up with, and so we cancel again, this time using the given 1.008g H.

step3.jpg
step3.jpg (9.98 KiB) Viewed 472 times

With the setup complete, we can go through, cancel all the appropriate units, and calculate the number of atoms of hydrogen we have.

step4.jpg
step4.jpg (12.09 KiB) Viewed 472 times

Now, since we want the rate of atoms released per year, we can divide this number of atoms we've calculated by 4.8 billion to find how many atoms were released each year.

In other words: atoms / 4.8 billion = x

Question II

The formula for calculating the total number of particles on a single chessboard following that pattern is 2^64 * 2 - 1. The reason can be found here. Divide the result into Avogadro's Number. Simple as that.
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Tue Oct 12, 2010 10:21 pm
HostofHorus says...



Thank you so much!!!!
HostofHorus Author, Poet, Dreamer, and Expressionist.
http://JRSStories.com
Stories Poems © As of January 1st 2014

Need a review? Feel free to ask me! :)
  








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