Answer:
563712.04903 Pa
Explanation:
m = Mass of material = 3.3 kg
r = Radius of sphere = 1.25 m
v = Volume of balloon = [tex]\frac{4}{3}\pi r^3[/tex]
M = Molar mass of helium = [tex]4.0026\times 10^{-3}\ kg/mol[/tex]
[tex]\rho[/tex] = Density of surrounding air = [tex]1.19\ kg/m^3[/tex]
R = Gas constant = 8.314 J/mol K
T = Temperature = 345 K
Weight of balloon + Weight of helium = Weight of air displaced
[tex]mg+m_{He}g=\rho vg\\\Rightarrow m_{He}=\rho vg-m\\\Rightarrow m_{He}=1.19\times \frac{4}{3}\pi 1.25^3-3.3\\\Rightarrow m_{He}=6.4356\ kg[/tex]
Mass of helium is 6.4356 kg
Moles of helium
[tex]n=\frac{m}{M}\\\Rightarrow n=\frac{6.4356}{4.0026\times 10^{-3}}\\\Rightarrow n=1607.85489[/tex]
Ideal gas law
[tex]P=\frac{nRT}{v}\\\Rightarrow P=\frac{1607.85489\times 8.314\times 345}{\frac{4}{3}\pi 1.25^3}\\\Rightarrow P=563712.04903\ Pa[/tex]
The absolute pressure of the Helium gas is 563712.04903 Pa
