Question

1. On a summer day, you take a road trip through Death Valley, California, in an antique car. You start out at a temperature of 21°C, but the temperature in Death Valley will reach a peak of 51°C. The tires on your car hold 15.6 L of nitrogen gas at a starting pressure of 249 kPa. The tires will burst when the internal pressure (Pb) reaches 269 kPa. Answer the following questions and show your work.

Answer 1

• How many moles of nitrogen gas are in each tire?
• What will the tire pressure be at peak temperature in Death Valley?
• Will the tires burst in Death Valley? Explain.
• If you must let nitrogen gas out of the tire before you go, to what pressure must you reduce the tires before you start your trip? (Assume no significant change in tire volume.)

Answer 2

aaronq

Answer 3

aaronq can you help

Answer 4

"How many moles of nitrogen gas are in each tire?"

use the ideal gas law PV=nRT

"What will the tire pressure be at peak temperature in Death Valley?"

use \(\dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2}\)

"Will the tires burst in Death Valley? Explain."

does the pressure go past 269 kPa?

Answer 5

see i tried that but its confusing to me

Answer 6

im not sure how that is done i never really picked it up well in my class and my teacher cant seem to explain it that well for me to understand :/ ive tried to do it that way but i get lost and end up making it a big mess

Answer 7

to find the number of moles, we first determine what each variable is, use the first set of data (not at the canyon).

first, you need temp in kelvin: T=273.15+ 21°C = 294.15 K
V= 15.6 L
P= 249 kPa
R= (these you look up to match the units) http://en.wikipedia.org/wiki/Gas_constant
=8.314 L*kPa/K*mol

so rearrange the formula for moles, n: \(PV=nRT \rightarrow n=\dfrac{PV}{RT}\)

\(n=\dfrac{(249 kPa)*(15.6 L)}{(8.314 L*kPa/K*mol)*(294.15~K)}=1.5883 ~moles~ of ~N_2\)

Answer 8

think you can try the second part?

Answer 9

so then it is 8.3140 kPa L/(K mol) (kilopascal liters per kelvin mole)?

Answer 10

yeah, notice i chose it because it matches the pressure (kPa) and volume (L).

Answer 11

okay lets see if i can do the second one :)

Answer 12

sounds good. first determine which variable is which.

Answer 13

Peak temperature in Death Valley is 51 C. However, you can only use proportions with Kelvin temperature so you need to convert Celsius to Kelvin by adding 273. You have to set up another proportion. The volume and temperature of a confined sample of gas are directly proportional. P1/T1 = P2/T2. The temperatures MUST be in Kelvin. So plug in your numbers. 249 kPa/ (21 + 273) K = P2/ (51 + 273)
Solve that.
If I did the math right, the pressure at the peak temperature would be 274 kPa.

Since the peak temperature in Death Valley will cause the pressure in the tires to expand to 274 kPa which exceeds the maximum pressure value, the tires will burst.

269 kPa/ 324 = p2/ 294
p2= 245 kPa. would that be correct?

Answer 14

yes

Answer 15

awesome! okay then now im confused on the the third point how would i say that or i mean how would i explain it

Answer 16

just say Since the peak temperature in Death Valley will cause the pressure in the tires to expand to 274 kPa which exceeds the maximum pressure value, the tires will burst.

Answer 17

for the last point I dont understand whats so ever i feel like the question doesnt give me enough info to solve

Answer 18

I'm kinda confused with what you posted earlier, the answer is \(P_2\)=274.40 kPa

so this "269 kPa/ 324 = p2/ 294
p2= 245 kPa. would that be correct?"

is not correct.

Answer 19

:c se i told you im horrible at this lol :/

Answer 20

*see

Answer 21

haha it's weird, because you wrote the correct value a few sentences earlier, in the same post.

Answer 22

so for the last question, you need to determines the amount of moles, so:

just use \(n=\dfrac{PV}{RT}\) when P<269 kPa

Answer 23

at the temperature of the canyon.

Answer 24

hmm im a little lost what to put :/

Answer 25

PV = nRT

A) V = nRT/P
to convert deg C to Kelvin add 273 = -4 + 273 = 269 K
use R value 0.08206 Latm/Kmol

V =1.40 mol x 0.08206 Latm/Kmol x 269 K / (1.25atm) = 24.7 L

B) T = PV/nR
V = 488/1000 = 0.488 L
1 atm = 760mmHg
to covert mmHg to atm divide by 760
755mmHg x (1 atm/760mmHg) = 0.993 atm
use R value 0.08206 Latm/Kmol
Plug in the equation and solve for T

1 atm = 101 325 pascals = 101.325 kPa
11.15kPa x (1 atm/ 101.325 kPa) = 0.110 atm

Answer 26

that is what i have but i feel like i am very very wrong and off

Answer 27

that is incorrect. First use the conditions at the grand canyon to the determine the amount of gas (moles) you need to have so the pressure remains below 269 kPa.

then use those moles and the conditions not at the canyon to determine the new pressure your tires should be at.

Answer 28

okay wait, that is a little confusing to me, I don't know how to get that particular pressure that is "below" I guess that is where i am getting confused

Answer 29

use 268.9 kPa

Answer 30

in real life you would use much lower value.

Answer 31

wait isnt that what i did? I used that number but w/o the .9

Answer 32

ohhh okay lol i get it now thank yo so so much :)

Answer 33

nope, you copied n pasted from here http://answers.yahoo.com/question/index?qid=20131101133503AAIZZao but it's not the right question :S

Answer 34

that answer i got was from my sister :/ i guess she got it form there grrr i am sorry for that she always looks things up if she doesnt get them.

Answer 35

i guess that would make sense as to why i am confused.

Answer 36

lol

Answer 37

i asked her for help and she seemed to know what she talking about

Answer 38

it's fine to look things up, but don't take things blindly, check em out for yourself :)

Answer 39

yeah i know but i get mad when she lookes things up for me b/c i get into trouble for puting them as my answers

Answer 40

because it can be considered an act of plagiarism in my school.

Answer 41

but i will definatley take your advice about checking them out for myself before making them my answer

Answer 42

good stuff. yeah, copying and pasting can get you kicked out of school :S, be careful and good luck !

Answer 43

okay and thank you so much for your help! :) also do you think you could fan me back?? please so i can pm you when your available you have it set to wear those who are not your fans can not pm you

Answer 44

oh yeah, sure! sorry, i didn't notice you added me. i get a lot of notifications :S