A helium filled balloon has a volume of 208 l and it contains 9.95 moles of gas. If the pressure of the ballon is 1.26 atm determine the temperature in Celsius degrees?

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Answer 1 · 2018-01-13T05:40:24

#48.1^@C#

We are going to use the ideal gas law, which states that

#PV=nRT#

#P# is the pressure in atmospheric pressures (for this case)

#V# is the volume in liters (for this case)

#n# is the number of moles of the substance

#R# is the gas constant

#T# is the temperature in Kelvin

Since our pressure is in atms, volume in liters, we have to use #R=0.082 l \ atm \ mol^-1 \ K^-1#.

Plugging in for #P=1.26atm#, #V=208l#, #n=9.95mol#, #R=0.082 l \ atm \ mol^-1 \ K^-1#, we get that

#1.26atm*208l=9.95mol*0.082l \ atm \ mol^-1 \ K^-1*T#

#T=(1.26atm*208l)/(9.95mol*0.082l \ atm \ mol^-1 \ K^-1)#

#T=(262.08cancel(atm) \ cancell)/(0.8159 cancel(mol) \ cancell \ cancel(atm) \ cancel(mol^-1) \ K^-1)#

#T=321.22/K^-1=321.22K#

We know that

#K="^@C+273.15#

#"^@C=K-273.15#

We know that #K=321.22#

#:."^@C=321.22-273.15=48.07~~48.1#

or

#T=48.1^@C#