Question

I'm working on a worksheet, and my answer- that I've rechecked four times- conflicts with the answer key. Can someone check my work, and help me figure this one out? The problem:

"A monatomic ideal gas at pressure P= 10^5 Pa is in a container of volume V= 12m^3, while at temperature T= 50 degrees Celsius. How many molecules of gas are in the container?

A) 447
B) 2888
C) 6.0x10^23
D) 2.69x10^26
E) 1.74x10^27"

The AP answer key says the answer is D, but... The key had been wrong before. I need to verify wether or not it is again. Here's my work:

Answer 1

OS limited the number of characters in my original post, so here's my work:

PV = nRT
(10^5)(12) = n(8.31)(50 + 273.15)
(1,200,00) = n(8.31)(323.15)
1,200,00 = n(2,685.3765)
________________________
2,685.3765
n = (446.86473)
= 447

Also, I should say that before today, I've tried this one before. Previously, I wasn't converting the temperature to Kelvin, and was getting it wrong so I tried Kelvin, thinking it was a better choice, considering the other Ideal Gas Laws' units are in Kelvin when referring to temperature. Yet still, the answer key is contrary to what. I got.
Any and all help is greatly appreciated!! :)

Answer 2

@zepdrix

Answer 3

If you multiply that with Avogadro's number do you get the answer?

Answer 4

If not, check if the constant R you are using corresponds to your other units in the formula.

Answer 5

Yes... I do, now that I've googled Avogadro's number lol. My teacher never mentioned this number... BUT doing that gives me the answer the AP answer key has. So, just because I am unfamiliar, what IS Avogadro's number? How does it relate to fluid & thermal dynamics?

Answer 6

Ah well Avogadro's number is the number of objects(atoms/molecules) in one mol of a substance.

Answer 7

. . . That totally makes sense. . . Wow. I shall talk to my teacher about this. :)
Thank you so much!

Answer 8

Sure thing. Also, since it is a monoatomic substance in this case, your answer is as what we did. If it is a substance with molecules, you will have to multiply with the number of atoms in each molecule, get it?

Answer 9

Yessss... Er meh gerd, you're amazing. Yeah, I get it. And why haven't I learned this before now? There's Goddamn public schooling for ya... ;)

Answer 10

Haha nah. I went to public school btw ;) Maybe your teacher forgot or you missed it.

Answer 11

Went, as in you're graduated?
And yeah, I'm hardcore going over my notes!

Answer 12

Yeah. I'm a junior in college now.