A balloon is filled with helium gas. The concentration of helium inside the ball

Question

A balloon is filled with helium gas. The concentration of helium inside the balloon is 0.3 kg/m^3 and the concentration of helium outside is negligible. The diffusion coefficient for helium in rubber is 5.8 times 10^-9 m^2/s. The surface area of the inflated balloon is 1 m^2 and the wall of the balloon is 0.2 mm thick What is the concentration gradient of helium through the wall of the balloon? a) 1.5 kg/m^3 b) 60 kg/m^4 c) 1500 kg/m^4 I don't know At what rate will helium diffuse through the wall of the balloon? a) 1.74 times 10^-9 kg/s b) 8.7 times 10^-6 kg/s c) 2 58 times 10^11 kg/s d) I don't know

Explanation / Answer

Concentration gradient = -dCA/dx

Where dCA= (0-0.3) kg/m3= -0.3 kg/m3 and dx= thickness = 0.2 mm= 0.2*10-3 m

Hence -dCA/dx= 0.3/(0.22*10-3)=1500 kg/m4 ( C is the correct answer)

b) flux of helium= DAB*(-dCA/dx)= 5.8*10-9 m2/s*1500 kg/m4= 0.0000087 kg/s.m2

Rate of helium diffusion through the wall = 0.0000087kg/s,m2*1m2= 0.0000087 kg/s ( b is correct)

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