A latex balloon, wall thickness 3.091 x 10-4 m, contains helium at a concentration of 0.72 kg m-3. Under these conditions the total surface area of the balloon is 0.17 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 first law of diffusion, which states that the rate of diffusion of a gas across a membrane is directly proportional to the surface area and concentration difference, and inversely proportional to the thickness of the membrane.
The formula for Fick's first law of diffusion is:
Rate of Diffusion = (Diffusion Coefficient * Surface Area * Concentration Difference) / Thickness
Let's plug in the given values:
Diffusion Coefficient = 4.9 x 10^-9 m^2s^-1
Thickness (t) = 3.091 x 10^-4 m
Surface Area (A) = 0.17 m^2
Concentration Difference = 0.72 kg m^-3 (assuming the concentration inside the balloon is 0 kg m^-3)
Now we can calculate the rate of diffusion:
Rate of Diffusion = (4.9 x 10^-9 m^2s^-1) * (0.17 m^2) * (0.72 kg m^-3) / (3.091 x 10^-4 m)
Note: We multiply by 0.72 kg m^-3 to convert the concentration difference from kg m^-3 to gm^-3.
Simplifying the equation:
Rate of Diffusion = (4.9 x 0.17 x 0.72) / 3.091
Now, calculate the value:
Rate of Diffusion = 0.16 gm / hr (approximately)
Therefore, the rate of helium effusion from the balloon is approximately 0.16 grams per hour.