A latex balloon, wall thickness 3.091 x 10-4 m, contains helium at a concentration of 0.3 kg m-3. Under these conditions the total surface area of the balloon is 0.33 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. Fick's Law states that the rate of diffusion is directly proportional to the surface area and concentration gradient, and inversely proportional to the thickness of the material.
The formula for Fick's Law is as follows:
Rate of diffusion = (Diffusion coefficient * Surface area * Concentration gradient) / Thickness
Let's calculate each component step by step:
1. Diffusion coefficient (D) = 4.9 x 10^(-9) m^2/s
2. Surface area (A) = 0.33 m^2
3. Concentration gradient (ΔC) = difference in concentration between the inside and outside of the balloon. Since the concentration of helium inside the balloon is 0.3 kg/m^3 and assuming the concentration outside the balloon is negligible, the concentration gradient can be taken as 0.3 kg/m^3.
4. Thickness (l) = 3.091 x 10^(-4) m
Now, we can plug in these values into Fick's Law equation:
Rate of diffusion = (4.9 x 10^(-9) m^2/s * 0.33 m^2 * 0.3 kg/m^3) / (3.091 x 10^(-4) m)
Performing the calculation:
Rate of diffusion = 0.5146 g/hr
Therefore, the rate of helium effusion from the balloon is approximately 0.5146 g/hr.