Question

Q: A molecule of water's volume is 10^-27 m^3 (meters cubed)

(a) How many molecules are there in 1 m^3 of water? If you wrote your answer in full, how many zero digits would there be?
(b) If you assume that a water molecule is in the form of a cube, show that its side length is 10^-9m
(c) If a number of water molecules were placed touching each other in a straight line, how many would there be in a line 1 cm long?
(d) The volume of a cup of tea is 200 cm^3. How many molecules of water would the cup hold? If all these were placed end to end in a straight line, how long would the line be?

Answer 1

continuing part (d) : Take the circumference of the Earth to be 40,000 km. How many times would the line of molecules go around Earth?

Answer 2

you're given :
"water molecule volume" = \(10^{-27} m^3\)

Answer 3

for part a,
divide the "water molecule's volume" by the "water volume"

Answer 4

number of water molecules = (water volume) / (water molecule's volume)

Answer 5

= \(\large \frac{1~ m^3}{10^{-27}~ m^3} = 10^{27}\)

Answer 6

so, there will be \(10^{27}\) "molecules" in 1 m^3 volume of water

Answer 7

if that makes some sense...

Answer 8

can u tell how many zeroes will be there in that number ha ? :)

Answer 9

27 zeroes, right?

Answer 10

Correct !

Answer 11

thats pretty huge number !!
looks like there are very huge number of molecules in just 1m^3 of water !

Answer 12

yeah, according to this question anyway~ :)
Okay, I think I understand parts a,b, and c pretty well, but the part that I'm really just stuck at is (d). Please help me!~

Answer 13

oh ok... good :) let me go thru it quick..

Answer 14

sure, thanks!

Answer 15

part d requires answer from part c

Answer 16

wat did u get as answer for part c ?

Answer 17

10^7

Answer 18

thats right for part c !

Answer 19

so, in 1cm long line, u can place 10^7 molecules

Answer 20

so, in 1cm^3 BOX, u can place (10^7)^3 = 10^21 molecules

Answer 21

that means, in 200 cm^3 BOX, u can place how many molecules ?

Answer 22

200*10^21 molecules?..

Answer 23

perfect !!!

Answer 24

you may also write it as :

2*10^23 molecules

Answer 25

Oh okay, I understand that part :)

Answer 26

good :) wat about next part

Answer 27

If all these were placed end to end in a straight line, how long would the line be?

Answer 28

think a bit,
u knw that there are a total of : 2*10^23 molecules

Answer 29

and u want to place them in a straight line... next to eachother

Answer 30

and u want to knw how long the straight line wud be

Answer 31

il give u hint maybe : u need to use answer from part b

Answer 32

divide 2*10^23 by 10^-9?...

Answer 33

nope

Answer 34

if one molecule is 10^-9 meters long,

Answer 35

then 2*10^23 molecules will be how much long ?

Answer 36

u need to multiply here okay ?

Answer 37

If I multiplied it, it would come out as (2*10^23)*10^-9...which would be 2*10^14?

Answer 38

But then, the answer in my textbook is 2*10^16 cm...

Answer 39

think a bit

Answer 40

if one molecule is 10^-9 meters long,
^^^^^^

Answer 41

then 2*10^23 molecules will be how much long ?

Answer 42

2*10^23 * 10^-9 meters

Answer 43

if u convert it to cm, u wud get the same answer in ur textbook

Answer 44

2*10^23 * 10^-9 meters

2*10^14 meters

2*10^16 centi meters

Answer 45

Oh, I think I get it now. To change it to cm, I'd have to times 2*10^14 by 100, which would be 2*10^16, right? Haha, sorry took the long way to explain it. Just wanted to make sure that I understood it right! Thanks a lot, a lot! :)

Answer 46

you got it :))