A latex balloon, wall thickness 3.091 x 10-4 m, contains helium at a concentration of 0.92 kg m-3. Under these conditions the total surface area of the balloon is 0.26 m2. The diffusion coefficient of He in latex at room temperature is 4.9 x 10-9 m2s-1. Calculate the rate of helium effusion (in g/hr) from the balloon.
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Fick’s Law
M= -D•(Δρ/Δx)•A,
where
M = m/t = mass flux [kg/s],
D= 4.9•10 ⁻⁹ m ²/s is the diffusion coefficient (diffusivity) [m²/s],
Δρ/Δx is the gradient of density [kg/m⁴],
A is the area [m²].
M= - 4.9•10⁻⁹•(0 - 0.35)/3.091•10⁻⁴)•0.88 =
4.9•10⁻⁹•0.35•0.88/3.091•10⁻⁴=
=4.88•10⁻⁶ kg/s= 17.58 g/hr
To calculate the rate of helium effusion from the balloon, we can use Fick's Law of Diffusion, which states that the rate of diffusion is proportional to the surface area and the concentration gradient of the gas. The formula is given as:
Rate of diffusion = (Diffusion coefficient) x (Surface area) x (Concentration gradient)
First, let's calculate the concentration gradient. The concentration gradient is the difference in concentration between the two sides of the balloon's wall. In this case, the inside of the balloon has a concentration of 0.92 kg/m^3, and the outside has a concentration of 0 kg/m^3 (since it's the surrounding air).
Concentration gradient = (0.92 kg/m^3 - 0 kg/m^3) = 0.92 kg/m^3
Next, let's calculate the rate of diffusion using the given values:
Diffusion coefficient (D) = 4.9 x 10^-9 m^2/s
Surface area (A) = 0.26 m^2
Concentration gradient (∆C) = 0.92 kg/m^3
Rate of diffusion = (4.9 x 10^-9 m^2/s) x (0.26 m^2) x (0.92 kg/m^3)
= 1.1044 x 10^-9 kg/s
To convert the unit from kg/s to g/hr, we can use the following conversions:
1 kg = 1000 g
1 hour = 3600 seconds
Rate of helium effusion = (1.1044 x 10^-9 kg/s) x (1000 g/kg) x (3600 seconds/hour)
= 3.97704 x 10^-3 g/hour
Therefore, the rate of helium effusion from the balloon is approximately 3.97704 x 10^-3 g/hr.