Question

There is 12.45 mol of oxygen gas contained in a balloon at 34.6
C. The balloon is in an air-tight room in which the
gauge pressure is adjusted to 0.400 atm.
a.) What is the volume of the gas?
b.) If the volume of the gas is cut in half while the gauge pressure is adjusted to 1.55 atm, what is the temperature?
the answers are supposed to be a) 0.225 m^3 and b)280 K, but I don't know how to get that

Answer 1

A)

Apply
\[ PV=nRT\]
where
P is the pressure (.4 atm = 40530 Pa = 40530 N/m^2 -> 1atm = 1*101325 Pa) (SEE BELOW)
V is the volume (in m^3)
n is the number of moles
R is the ideal gas constant (units J/ mol K -> 1 J = 1Nm)
T is the temperature (in Kelvin, so here 34.6ºC = 307.75K -> 0ºC = 0+ 273.15 K)

******So for the first part, I kept getting the wrong answer using .4 atm - you get the correct answer with P=1.4atm. Is there some definition of the "gauge pressure" that you've used in class? Like it's calibrated to 1 atm beforehand? Or maybe the balloon itself has an atmosphere of pressure or something along those lines? In any case

\[V=\frac{nRT}{P} = \frac{(12.45 \ mol)(8.314 \ J/mol \ K)(307.75 \ K)}{141855 \ N/m^2} = .225 \ m^3\]

B)
Again, this only works if you add an extra atmosphere of pressure, P=2.55 atm, so there's some bit of info that is unclear to me. Following through though
\[T=\frac{PV}{nR} = \frac{(258378.75 \ N/m^2)(.225/2 \ m^3)}{(12.45 \ mol)(8.314 \ J/mol \ K)}=280 \ K\]

Answer 2

Do you have an idea about the pressures?

Answer 3

thank you so much!! I'm not really sure about the pressures because we never really learned about gauge pressure but this was to helpful!

Answer 4

^_^ Welcome!

Answer 5

Typically, gauge pressure = absolute pressure - atm pressure.

So 0.4 atm gauge is 1.4 atm absolute. 6 psig = 21 psia approx

Answer 6

Ah! That makes much more sense! ^_^