Really stuck on this question on Combined gas law, not sure where to start...

The year is 2050. Coca Cola wants to film a commercial on another planet where the temperature can go as high as 400K. The carbon dioxide in the bottled coke is under 1.5atm pressure 20 degrees celsius, the cap will withstand a pressure of 2.3 atm. Will they be able to take a regular bottle of coke to this planet, or will they have affix a tighter cap?

need help =p

Question

Really stuck on this question on Combined gas law, not sure where to start...

The year is 2050. Coca Cola wants to film a commercial on another planet where the temperature can go as high as 400K. The carbon dioxide in the bottled coke is under 1.5atm pressure 20 degrees celsius, the cap will withstand a pressure of 2.3 atm. Will they be able to take a regular bottle of coke to this planet, or will they have affix a tighter cap?

need help =p

anonymous · Answer

I had a similar question like that not sure but i'll search it up

anonymous · Answer

thank you, however I literally wrote the question word for word and couldn't find it, it's probably because my teacher handed a sheet that was from 1994 sooo...

anonymous · Answer

good luck

anonymous · Answer

Yeah just searched it up but no result……..i think you should search the topic and some examples on it and you’ll probably understand it more but if you still can’t let me know

anonymous · Answer

well then ok

danjs · Answer

T1 = 20 C = 293 K
P1 = 1.5 atm

T2 = 400 K
P2 = ???   (Needs to be < or = 2.3 atm.)

$$\frac{ PV }{ T } = constant$$

The Volume in this case is also constant, so you can make the following relation:

$$\frac{ P1 }{ T1 } = \frac{ P2 }{ T2 }$$
$$\frac{ 1.5 ~atm }{ 293~K } = \frac{ P_{2}~atm }{400~K  }$$
$$P _{2} \approx 2.05 ~~atm$$

If the temperature reaches 400K, the pressure in the bottle will reach around 2.05 atm. With an allowable pressure of 2.3 atm, they will be able to take the bottle of coke to the planet.

danjs · Answer

The relationship used is derived from Boyle's law, that the pressure is inversely proportional to the volume, and Charles's law, that the volume is directly proportional to the temperature. 
$$V~~\alpha~~T~~~~~~~~;~~~~~\frac{ V }{ T } = constant$$
$$P~~\alpha \frac{ 1 }{ V }~~~~~~~~~;~~~~~P*V = constant$$

$$P*V = n*R*T$$

Isochoric  / Constant-Volume process in a closed system, with constant number of molecules; n.

anonymous · Answer

thank you so much!!!!! DanJS, your feedback helped alot!!!

anonymous · Answer

btw the reason I was stumped was mainly since I didn't know how I could incorporate the volume into the question.

danjs · Answer

ahh. I see. glad to help out.