A football has a diameter of 22 cm. It is inflated to 1 atm pressure above normal atmospheric pressure on a sunny summer day when the temperature was 25C. Take normal atmospheric pressure to be 101.3 kPa. What mass of air is contained in the ball?

1 Answer
yumean1119
Dec 10, 2017

See below. The answer is about #13.20# g.

Explanation:

We are going to use the formula(the ideal gas law) #PV=nRT#.

#P#: pressure (Pa)
#V#: volume (#m^3#)
#n#: amount of substance(mol)
#R#: gas constant(#8.314# #J mol^-1 K^-1#)
#T#: absolute temparature(K)

Then, what is the value of the variants?
[1] #P=2# atm #=2.026*10^5# Pa
(I interpreted "inflated to 1 atm pressure above normal atmospheric pressure" to be 2 atm. If this is wrong, let me know.)
[2] #V=4/3pi*0.11^3=5.575*10^-3# #m^3#.
[3] #T=25# ℃ #=298.15# K.

Plug in these values to the formula.
#n=(PV)/(RT)= (2.026*10^5 * 5.575*10^-3)/(8.314 * 298.15)#
#=0.4557# mol.

The avarage molar mass of the air is #28.966# g/mol (From Japanese wikipedia: https://ja.wikipedia.org/wiki/%E7%A9%BA%E6%B0%97), and #0.4557# mole of air is #28.966*0.4557=13.199# grams.

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