Question

How many milligrams of C atoms are in 2.04 x 10^20 molecules of ethanol?

Answer 1

Ethanol: \(\large \text{C}_2\text{H}_6\text{O}\)

Answer 2

So first question, how many moles does 2.04 x 10^20 molecules represent?

Answer 3

its not CH(Sub 6)O?

Answer 4

why did u give Carbon2?

Answer 5

Because that's the formula for Ethanol

Answer 6

It's a 2-carbon alcohol.

Answer 7

\[(6.02 \times 10^{23})(2.04 \times 10^{20})?\]

Answer 8

oh ok

Answer 9

That's incorrect;
\[\large 1 \text{ mole}= 6.02×10^{23}\]

Answer 10

\[\large ? \text{ mole}=2.04×10^{20}\]

Answer 11

That's a proportion and you should have this: \(\LARGE \frac{2.04×10^{20}}{6.02×10^{23}}\)

Answer 12

oh so its divide instead of multiply?

Answer 13

Yes, that's algebraic manipulation.

Answer 14

Once you get that, you'll get the number of moles this quantity of molecules represent, are afterward, you may convert that easily to its mass through the molar mass.

Answer 15

Why 1000?

Answer 16

for milligrams?

Answer 17

Our units are in moles...

Answer 18

\[\large \frac{1 \text{ mole}}{6.02*10^{23} \text{ atoms}}=\frac{x \text{ mole}}{2.04 * 10^{20}\text{ atoms}}\]Multiply both sides by 2.04*10^20\[\large \frac{2.04*10^{20}\text{ atoms}*1 \text{ mole}}{6.02*10^{23} \text{ atoms}}=x \text{ mole}\]

Answer 19

atoms and atoms simplify out, leaving the mole on both sides.\[\large \frac{2.04*10^{20}}{6.02*10^{23}}\text{mole}=x \text{ mole}\]

Answer 20

ok i see

Answer 21

i got .0003 correct?

Answer 22

You'll get as answer: \(\large x\text{ moles}\)

Now you may proceed to transform this using \(\LARGE n=\frac{m}{M}\), where \(\large \text{n}\) is the number of moles, \(\large \text{m}\) is the mass in \(\large \textbf{grams}\) (so you'll need to retransform it into milligrams as you're asked to do) and \(\large \text{M}\) is the molar mass.

Answer 23

Molar mass is 46.07?

Answer 24

Yes

Answer 25

well for ethanol it self right?

Answer 26

would i multiply that by .0003

Answer 27

Exact.

Answer 28

46.68->46.7 sorry

Answer 29

so i got .0140 because i used 46.68*.0003

Answer 30

thats just grams right?

Answer 31

Yep

Answer 32

.0140 x 10^-3 ?

Answer 33

Good, now you'll need to set up another proportion:\[ \frac{\text{Mass of Carbon in 1 mole of Ethanol}}{\text{Molar mass of Ethanol}}=\frac{\text{Mass of Carbon (Unknown) }}{\text{Mass of the Ethanol given to you}}\]

Answer 34

(?/46.68)=(?/.0140x10^-3?)

Answer 35

Mass of carbon in 1 mole of ethanol is a known number, 2*Molar mass of carbon, 12, 2*12 = 24.

Answer 36

oh ok i see where you got that from

Answer 37

(24/46.68) = (?/.0140x10^-3?)

Answer 38

was i correct on the second half too?

Answer 39

I don't know, I didn't push the values in my calculator, I've shown you how to do these kind of problem, all the other mathematical manipulations/calculations should be done by you; the right method is shown so you can take down any question that looks like this.

Answer 40

I was asking about for the mass of the ethanol that the answer i found before right?

Answer 41

Like I said, I don't know :)

Answer 42

Ok so now i simple mult across top and bottom and cancel out to get my answer

Answer 43

simply*

Answer 44

i think i have it

Answer 45

thank you

Answer 46

np