Question

Word Problem in comments.. Please help :(

Answer 1

The smallest piece there is of any substance is called a molecule. A single water molecule is the smallest thing that can still be called water. It is small. Very small. It is so very small that the typical half-liter water bottle holds about 16,700,000,000,000,000,000,000,000 water molecules.

Just to get an idea of why scientific notation is important, try writing 16,700,000,000,000,000,000,000,000 ten times without getting frustrated. Now write 1.67 x 1025. It is easier, right?

There is a rule that lets us calculate how much of a substance takes up a particular space. According to this rule, 18 grams of water contain a total of 6.02x1023 molecules of water. It looks like a lot, but consider that 18 grams weigh only about 2/3 of one ounce and fill less than half an inch in a half-liter water bottle.

Again, the rule is that 18 grams of water contains about 6.02*1023 water molecules.

Question #1:

Consider Bob, who weighs 180 pounds. On Earth, a kilogram weighs 2.2 pounds, and just for reference, a kilogram is one thousand grams. About 60% of a person is water.

Approximately how many molecules of water are in Bob? Give your answer in scientific notation rounded to the nearest hundredth and in standard notation. SHOW THE STEPS USED TO FIND THESE VALUES IF YOU WISH TO RECEIVE CREDIT.

Answer 2

Question #2

Now you will go backwards. Consider Irene, who has about 1.28*1027 water molecules in her. How much does she weigh? Round to the nearest hundredth of a pound. REMEMBER TO SHOW ALL STEPS

Answer 3

They say that "the rule is that 18 grams of water contains about 6.02*1023 water molecules"

So you need to convert 180 pounds to grams

Answer 4

how do we do this?

Answer 5

any ideas?

Answer 6

I was thinking maybe dividing, but I wasn't sure :(

Answer 7

In the problem, we're given this

1 kilogram = 2.2 pounds

1 kilogram = 1000 grams


we'll use these two facts to convert from pounds to grams


First convert 180 pounds to kg


(180 pounds)*(1 kilogram/2.2 pounds) = 180/2.2 = 81.818181818 kilograms


So

180 pounds = 81.818181818 kilograms


Now convert this to grams

(81.818181818 kilograms)*(1000 grams/1 kilogram) = 81.818181818*1000 = 81818.181818 grams


So

81.81818 kilograms = 81818.181818 grams (roughly)


-------------------------------------------------------

This means that


180 pounds = 81818.181818 grams (roughly)

Answer 8

So if Bob weighs 180 pounds, then he also weighs about 81818.181818 grams

Answer 9

How much of this weight (in grams) is water?

Answer 10

wow interesting.. Hmm 60% of his weight

Answer 11

so 60% of 81818.181818 grams is...?

Answer 12

49090.90909? I hope that's right.. I'm not really good at percentages.

Answer 13

that's correct

Answer 14

thank you so much

Answer 15

So Bob is composed of roughly 49090.90909 grams of pure water

Answer 16

awesome

Answer 17

Now you can use this to figure out how many molecules of water are in Bob

Answer 18

okay thank you Jim :)

Answer 19

sure thing

Answer 20

and it might be easier to convert 49090.90909 to scientific notation to get 4.909 x 10^4

Answer 21

since the number is an approximation, you can get away with dropping a few decimal places

Answer 22

yeah, I almost forgot about that
thank you again, you are great

Answer 23

you're welcome

Answer 24

So, 60% of his weight in grams, 81818.181818, is 49090.90909..

Scientific Notation: 4.909 x 10^4

SO, if 18 grams of water contains about 6.02 x 10^23 water molecules, then
6.02 x 10^23 divided by 4.909 x 10^4

equals 1.226296296 x 10^19
so there are 1.226296296 x 10^19 molecules of water in Bob..
I hope that is correct.. wasn't sure if I should divide or multiply

Answer 25

18 grams of water = 6.02 x 10^23 water molecules


So since we want to find out how many molecules of water are in 4.909 x 10^4 grams, we do the following


(4.909 x 10^4 grams)*(6.02 x 10^23 water molecules/18 grams)


(4.909 x 10^4 grams)*(6.02 x 10^23 water molecules/1.8 *10^1 grams)


(4.909 x 10^4 grams)*(3.344444 x 10^(23-1) water molecules/1 gram)


(4.909 x 10^4 grams)*(3.344444 x 10^22 water molecules/1 gram)


4.909 x 10^4 * 3.344444 x 10^22


(4.909* 3.344444) x (10^4 * 10^22)


16.417875596 x (10^4 * 10^22)


1.6418 x 10^1 x (10^4 * 10^22)


1.6418 x (10^1*10^4 * 10^22)


1.6418 x (10^(1+4+22) )


1.6418 x 10^(27)


So in the end, there are roughly 1.6418 x 10^(27) water molecules in 4.909 x 10^4 grams of water


This rounds to 1.64 x 10^(27) when rounding to the nearest hundredth

===============================================

Question:

Approximately how many molecules of water are in Bob?

-------------------------

Answer:

Approximately 1.64 x 10^(27) molecules of water

Answer 26

Oh wow, I was far off lol thank you..
and so I'm guessing that for the second question:
"Question #2

Now you will go backwards. Consider Irene, who has about 1.28 x 10^27 water molecules in her. How much does she weigh? Round to the nearest hundredth of a pound. REMEMBER TO SHOW ALL STEPS"

I would possibly have to divide 1.28 x 10^27 by 6.02 x 10^23/18 grams ?

Answer 27

Use the conversion factor

18 grams = 6.02 x 10^23 molecules

so...

(1.28 x 10^27 water molecules)*(18 grams/6.02 x 10^23 molecules)

and tell me what you get

Answer 28

doing this calculation will give you an answer in grams

from there, you convert to kilograms, then to pounds

Answer 29

Okay thank you so much, i'll tell you what I get.

Answer 30

alright sounds great

Answer 31

hmm I'm not so sure about my answer..
I got:
(1.28 x 10^27)(18 grams/6.02 x 10^23)
2.304 x 10^28 /6.02 x 10^23
3.827242525 x 10^50

Answer 32

1.28 x 10^27 * 18

1.28 x 10^27 * 1.8 x 10^1

(1.28*1.8) x (10^27 * 10^1)

2.304 x 10^28

So you got that part correct

-------------------------------


(2.304 x 10^28)/(6.02 x 10^23)

(2.304/6.02) x (10^28)/(10^23)

0.3827242524917 x 10^5 ... This is where you made your error

3.827242524917 x 10^(-1) x 10^5

3.827242524917 x 10^4


-----------------------------------------

So 1.28 x 10^27 molecules tells us that Irene weighs 3.827242524917 x 10^4 grams

This is the same as 38,272.42524917 grams

Now convert to kg, then convert to lbs

Answer 33

ahh okay that makes much more sense

Answer 34

Keep in mind that when you get your final answer in pounds, this answer will be her water weight only (this won't be her actual weight). So you'll then use the fact that she's roughly 60% water to find her true weight.

Answer 35

I nearly forgot about that

Answer 36

Thank you so much for all your help lately.. I do online schooling and none of my teachers are really reliable for help :/
I'm trying to get a few projects done by midnight.. the deadline of my class.. if I get stuck again and you're not busy, could I ask for your assistance?
Thank you

Answer 37

sure you can ask me any time you want

Answer 38

I'm glad I could be of help

Answer 39

okay thank you :)

Answer 40

you're welcome

Answer 41

3.827242524917 x 10^4 /1000
38.27242525 • 2.2
84.19933555 lbs of water?

Answer 42

hmm hopefully that's correct

Answer 43

one moment

Answer 44

okay take your time

Answer 45

yes that's correct

So Irene has 84.19933555 lbs of water that makes up her entire body weight

So what's her total weight?

Answer 46

33.67973422?

Answer 47

you're going backwards

Answer 48

uh oh lol

Answer 49

you're not taking 60% of 84.19933555 lbs because you already know the water weight

Answer 50

okay

Answer 51

You want to take 60% of some unknown total weight, say x, and get 84.19933555 lbs as the result

So

0.6x = 84.19933555

now solve for x

Answer 52

Bob weighs 180 pounds.
180 lb x 2.2 kg/lb = 2.2 x 180 kg

He is only 60% water, so that's 0.6 x 2.2 x 180 kg.

In grams, that's 1000 x 0.6 x 2.2 x 180 g.

Now, to get the number of molecules we do whatever that equals times
6.023 x 10^23 / 18

The best thing to do for such problems is to make sure the units cancel.
For example, at the end here we had

.. grams x molecules / gram

Worry about the units first and the arithmetic second.

Answer 53

@jim_thompson5910 I really hope this isn't incorrect again lol
6.0 (140.3322259) = 84.19933555
x= 140.3322259?

Answer 54

@telliott99 Thank you

Answer 55

that's 100% correct

I did it this way

0.6x = 84.19933555

x = 84.19933555/0.6

x = 140.332225916667

which is exactly what you have

Answer 56

So Irene is roughly 140.3322259 lbs

If you need to round to the nearest pound, then she is roughly 140 pounds

Answer 57

:) yay, thank youuu
you are so awesome, I wouldn't of even been able to do this without you

Answer 58

you're very welcome

Answer 59

I'm sure you could have

Answer 60

yes 140,
now I wont fail my class thank God
are you a teacher by any chance?

Answer 61

I'm a student learning to become one..so half and half i guess

Answer 62

wow thats awesome, well your doing a great job at it :)

Answer 63

why thank you

Answer 64

I appreciate the compliment

Answer 65

better than my teacher lol

Answer 66

your welcome, Jim :)

Answer 67

aww shucks...lol, well I'm sure your teacher is great in his/her own way though

Answer 68

but you said that you couldn't get a hold of your teacher? that's a bit odd and troubling

Answer 69

esp when a project is due

Answer 70

yeah, they slack off a lot LOL
well i've been doing this online schooling for about 2 years now and have been jumping around from diff. schools, and this one is an alternative so they are a bit different here

Answer 71

but I'm sure I'll be fine, I prefer your help anyways lol

Answer 72

that's a shame...if the students are meant to work hard, then the teachers should work just as hard (if not work more)

Answer 73

well that's good, I'm flattered you do lol

Answer 74

lol i agree

Answer 75

well I'm going to try and do my other projects and if I need help I promise to come here lol :)

Answer 76

alright sounds good lol

Answer 77

good luck

Answer 78

thank you :)

Answer 79

sure thing