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hslove142331 · Jan 16, 2010, 03:07 PM

To what temperature must 280mL of CO2 be cooled for its volume to decrease to 130mL if initial temperature is 11C ?

How can I find temperature?
Do we have any formula for this problem?

Thank you

Unknown008 · Jan 17, 2010, 09:00 AM

Yes, you basically start with the equation:

PV=nRT

P = pressure of gas
V = volume of gas
n = no. of moles of gas
R = ideal gas constant
T = temperature of gas in Kelvin

the ideal gas law equation.

Now, since it's a closed system, the number of moles n is a constant.

Then, you can write it as:

$nR = \frac{PV}{T}$

Now, since you have two different situations, with the same constant, you may write:

$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$

Here, since the pressure remains the same, the P crosses out;

$\frac{V_1}{T_1} = \frac{V_2}{T_2}$

Then, replace:
Initial volume = 280 mL
Initial temperature = 11+275 = 286 K
Final volume = 130 mL

$\frac{280}{286} = \frac{130}{T_2}$

Solve for T2, the final temperature in Kelvin. Then convert back to degrees celsius if you want or if it is asked.

hslove142331 · Jan 18, 2010, 02:15 PM

Initial temperature = 11+275 = 286 K

on here I thought 273, Is it just same as 275?

so T2 going to be -140.15C ? Correct?

Unknown008 · Jan 20, 2010, 07:36 AM

Yes, it's 273, I made a typo... last time. :o

Yes, you got the answer! :)

hslove142331 · Jan 20, 2010, 01:54 PM

Thank you so much! Your teaching is more better than ma teacher.

Unknown008 · Jan 21, 2010, 06:22 AM

Lol, the only difference is that I may not be always on time to answer you. I'm myself quite busy with my homework...

Thanks for the compliment! :)