A latex balloon, wall thickness 3.091 x 10-4 m, contains helium at a concentration of 0.35 kg m-3. Under these conditions the total surface area of the balloon is 0.88 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.
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
Thank you Elena
To calculate the rate of helium effusion from the balloon, we can use Fick's law of diffusion.
Fick's law of diffusion states that the rate of diffusion of a substance is proportional to the surface area and the concentration gradient of the substance, and inversely proportional to the thickness of the barrier through which it is diffusing.
The formula for Fick's law of diffusion is:
Rate of diffusion = (Diffusion coefficient) x (Surface area) x (Concentration gradient) / (Thickness of barrier)
Given:
Diffusion coefficient (D) = 4.9 x 10^-9 m^2/s
Surface area (A) = 0.88 m^2
Concentration gradient (ΔC) = concentration difference between the inside and outside of the balloon
Thickness of the barrier (δ) = 3.091 x 10^-4 m
We need to calculate the concentration difference (ΔC) in order to determine the rate of diffusion.
First, let's convert the concentration of helium from kg/m^3 to g/m^3:
0.35 kg/m^3 = 350 g/m^3
Next, let's calculate the concentration difference:
ΔC = Concentration inside balloon - Concentration outside balloon
The concentration outside the balloon is assumed to be 0 (assuming no helium in the surrounding air). Therefore:
ΔC = 350 g/m^3 - 0 g/m^3
ΔC = 350 g/m^3
Now, we can substitute the values into Fick's law of diffusion to calculate the rate of helium effusion:
Rate of diffusion = (4.9 x 10^-9 m^2/s) x (0.88 m^2) x (350 g/m^3) / (3.091 x 10^-4 m)
Simplifying the equation, we get:
Rate of diffusion = (4.9 x 0.88 x 350) / 3.091 x 10^-4 g/s
Finally, let's convert the rate of diffusion from g/s to g/hr:
Rate of diffusion (g/hr) = (Rate of diffusion (g/s)) x (3600 s/hr)
Now you can plug in the calculated value for the rate of diffusion (in g/s) and calculate the final answer for the rate of helium effusion in g/hr.