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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