Question

A 14.5 gram sample of gas is found to have a volume of 2.8 liters at 275 K and 1.10 atm. What is the molar mass of this gas? Show all of the work used to solve this problem.

Answer 1

@AccessDenied

Answer 2

please help I have a few like this i just need a formula

Answer 3

Have you tried Ideal Gas Law here? You can put the information about grams of gas aside and find the moles of gas, then convert using the same "mass / molar mass = moles" formula. Both of these formulas were featured in the last problem. :)

Answer 4

PV=nRT??

Answer 5

Pn=VRT
n=VRT/P
n=(14.5)(0.0821)(275)/(1.10)
n=297.61

Answer 6

i have this so far but I dont think it's right

Answer 7

What happened between:
PV = n RT
and
Pn = V RT

Answer 8

I really dont know I found it on yahoo and a few other places but now I'm using it it looks wrong

Answer 9

Alright. This will be an Algebra step. Note that everything here is being multiplied right now:
P * V = n * R * T.
To solve for n, we have to use inverse operations, so multiplying's inverse is dividing, to solve for n. And an equation is only correct if we do the same operation on both sides. Keep those two details in mind.
There's an R multiplied next to n. So we can divide both sides by R. And there's also the T multiplied, so we divide that as well. The whole step is just dividing (R*T) off from both sides:
\( \displaystyle \frac{P \times V}{R \times T} = \frac{n \times R \times T}{R \times T} \)
Things in both numerator and denominator cancel, because anything divided by itself has to be 1.
\( \displaystyle \frac{P \times V}{R \times T} = \frac{n \cancel{\times R \times T}}{\cancel{R \times T}} \)
So in the end we have:
\( \displaystyle \dfrac{PV}{RT} = n \)
Does anything here seem unclear? The next step will be to plug in all the information!

Answer 10

So
(1.10)(24.5) / (0.0821)(275) = n
26.95 / 22.5775 = n
1.1937 = n

Answer 11

Looks good!
Now that we have moles of gas under these conditions, and we know the mass (grams) of the gas as well, we just use the mass / molar mass = moles of gas formula.
\( \dfrac{m}{M} = n \)
We just have to multiply both sides by M (molar mass) to get it back on top.
\( m = n \times M \)
Then divide both sides by n (moles):
\( \dfrac{m}{n} = M \)
If everything looks good here, you have the mass (m) and moles (n) you just found, so you plug in one more time!

Answer 12

Ohh, hang on.
(1.10)((((24.5))) / (0.0821)(275) = n
This 24.5 looks like a typo. Volume was 2.8 liters in the problem. The other values were correct.

Answer 13

With this change, it seems you get:
n = ((1.10)*(2.8))/((0.0821)*(275)) = 0.1364 mol
Apologies for not catching that typo earlier!

Answer 14

Sorry i left for a second lol so where do you go from there?? Or is that the answer?

Answer 15

And I was looking at another problem at the same time thats probably where the 24.65 came from sorry

Answer 16

That was the corrected value of n. I didn't catch in your earlier response that you had V = 24.5, when V should be 2.8.

So from here, we'd have to use the formula for mass / molar mass = moles.

Oh, no problem.

Answer 17

So its be molar mass = moles x mass?

Answer 18

itd

Answer 19

not quite, mass divided by moles.
The units make sense then: Molar mass (in grams per mole) = mass (grams) divided by moles (mol).

Answer 20

how do you find the mass if the gas isn't named?

Answer 21

sorry

Answer 22

That part was given: "A 14.5 gram sample of gas ..."
And we have moles = 0.1364 mol, that was found a bit ago. Just to make sure it was corrected.
So molar mass = mass (14.5 g) / moles (0.1364 mol).

Answer 23

so molar mass =106.3049

Answer 24

Alright, that looks good now. :)

(Originally I checked the end result with the moles = 1.1 to be about 12 g/mol, which was carbon... but gaseous carbon is unheard of at 275 K (room temperature...)

Answer 25

I know it's ridiculous haha

Answer 26

Aye, so everything makes sense there? Anything else you might need help with? :)

Answer 27

Would I use the same formulas and everything for :A sample of gas at 298 Kelvin and 0.98 atmospheres has a density of 1.45 g/L, what is the molar mass of this gas? Show all of the work used to solve this problem.

Answer 28

It will be the same formula, except some more tricky work.
Density is mass per volume, and PV = n RT only has the volume. But we do know that other relationship of n (moles) = mass (grams) / molar mass (grams/mol).
Let's make that substitution:
\( PV = n RT \) \( n = \dfrac{m}{M} \)
\( P\times V = \dfrac{m}{\color{red}{\mathbf{M}}}\times R \times T \)
Because we want molar mass (highlighted red now), we need to solve for that. What should end up happening is that we'll have \(\dfrac{m}{V} \) somewhere, which is the same as density.

Answer 29

So the steps from that point would just be, multiply both sides by M (to get it on top). Then divide both sides by P*V, which will isolate M. I left out the details now so I don't have 400 lines, but I can explain it if needed. You'll get to this point:
\( M = \color{green}{\dfrac{m}{V}} \times \dfrac{R\times T}{P \times V} \)
And now we just replace m / V by density. Usually density is written as a greek letter, rho \(\rho\), but most people will cann it p anyways.
\( M = \mathbf{\color{green}\rho} \times \dfrac{R \times T}{P \times V} \)

Answer 30

call*, not cann. lol

Answer 31

Okay give me a minute to do this lol

Answer 32

Brain fart, one thing:
\( M = \color{green}{\dfrac{m}{V}} \times \dfrac{R\times T}{P} \)

\( M = \color{green}{\rho} \times \dfrac{R\times T}{P} \)
I moved V underneath m, but then I made another one next to P. There wasn't really anything to substitute for V anyways. I'm not doing very well with typos today. o.o

Answer 33

okay i was just about to ask lol dont worry about it

Answer 34

I'm stuck on plugging things in

Answer 35

nevermind brain fart

Answer 36

afk sorry and thank you so much

Answer 37

I havePV=(m/M)RT
M=p(RT/P)
M=1.45(0.98)(298)/(0.0821)
M=1.45(292.04)/(0.0821)
M=423.458/(0.0821)
M=5,157.8319

Answer 38

Looks like you just flipped around R and P.
R = 0.0821, and P = 0.98