A perfectly spherical balloon is inflated. The circumference is measured by a pi

Question

A perfectly spherical balloon is inflated. The circumference is measured by a piece of string around the balloon and is found to be 36 cm. The total gas pressure inside the balloon is 1.04 bar at a temperature of 26degreeC. Consider the air inside the balloon to be normal atmospheric air without water (i.e. dry air). (for this question you will also need a conversion factor and this one should not be as difficult to find as the last assignment!) Calculate the number of nitrogen atoms inside the balloon. Calculate the new volume of the balloon if it is taken outside on a cold winter day (-12 degreeC).

Explanation / Answer

circumference of balloon = 36 cm = 2Pir

pi = 3.14 , r = radius of balloon = ?

r = 36/(2*3.14) = 5.732 cm

voulme of ballon = 4/3*pi*r^3

                 = 4/3*3.14*(5.732^3) = 788.4732 cm^3 = 788.4732 ml

so that

V = 0.788 L , P = 1.04 bar = 1.0264 atm

T = 26 C = 299 k   R = 0.0821 l.atm.k-1.mol-1

n = No of moles of air   = PV/RT = 1.0264*0.788/(0.0821*299) = 0.033 mole

in air 78% N2.so that

No of moles of N2 = 0.033*78/100 = 0.02574 mole

at S.T.P

1 mole N2 = 6.023*10^23 molecules

0.02574 mole N2 = 6.023*10^23*0.02574 = 1.55*10^22 molecules.

b) V1/T1= V2/T2

V1 = 0.788 L

T1 = 26 C = 299 K

V2 = ?

T2 = -10 C = 263 K

v2 = 0.788/299*263 = 0.693 L

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