A latex balloon, wall thickness 3.091 x 10-4 m, contains helium at a concentration of 0.66 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.
To calculate the rate of helium effusion from the balloon, we need to use Fick's Law of Diffusion, which states that the rate of diffusion (J) is proportional to the surface area (A), the concentration gradient (ΔC/Δx), and the diffusion coefficient (D).
The formula for Fick's Law of Diffusion is:
J = -D * (ΔC/Δx) * A
Given information:
- Wall thickness (Δx) = 3.091 x 10^(-4) m
- Concentration of helium (ΔC) = 0.66 kg/m^3
- Surface area of the balloon (A) = 0.88 m^2
- Diffusion coefficient (D) = 4.9 x 10^(-9) m^2/s
Now, let's calculate the rate of helium effusion:
1. Calculate the concentration gradient (ΔC/Δx):
We need to find the difference in concentration across the thickness of the balloon wall. Since the helium concentration is uniform throughout the balloon, the concentration gradient will be:
ΔC/Δx = ΔC / Δx (Note that Δ represents the difference)
2. Calculate the rate of helium effusion (J):
J = -D * (ΔC/Δx) * A
3. Convert the rate of helium effusion from kg/s to g/hr:
Since the given rate of diffusion is in kg/m^3, we can convert it to g/hr by multiplying by (1000 g/kg * 3600 s/hr).
Now, let's plug the values into the formula and calculate the rate of helium effusion:
1. Calculate ΔC/Δx:
Since the helium concentration is uniform throughout the balloon, ΔC/Δx = 0.66 kg/m^3 / 3.091 x 10^(-4) m
2. Calculate J:
J = (-4.9 x 10^(-9) m^2/s) * (0.66 kg/m^3 / 3.091 x 10^(-4) m) * (0.88 m^2)
3. Convert J from kg/s to g/hr:
J = J * (1000 g/kg * 3600 s/hr)
By following these steps and plugging in the given values, you should be able to calculate the rate of helium effusion from the balloon in g/hr.