A latex balloon, wall thickness 3.091 x 10-4 m, contains helium at a concentration of 0.23 kg m-3. Under these conditions the total surface area of the balloon is 0.46 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 is proportional to the surface area and concentration gradient.

The formula for Fick's Law of Diffusion is:

Rate of diffusion = (Diffusion coefficient * Surface area * Concentration gradient) / Thickness

First, let's calculate the concentration gradient of helium across the balloon wall. The concentration gradient is the difference in concentration between the inside and outside of the balloon.

Concentration gradient = Concentration inside - Concentration outside

The concentration inside the balloon is given as 0.23 kg/m^3. The concentration outside can be assumed to be zero, as there is no helium outside the balloon. Therefore, the concentration gradient is 0.23 kg/m^3.

Now, we can substitute the given values into the formula:

Rate of diffusion = (4.9 x 10^-9 m^2/s) * (0.46 m^2) * (0.23 kg/m^3) / (3.091 x 10^-4 m)

Note: In scientific calculations, it is important to use consistent units. Therefore, we need to convert the result to grams per hour.

To convert the rate of diffusion to grams per hour, we can use the following conversions:
1 kg = 1000 g
1 hour = 3600 seconds

Rate of diffusion (in g/hr) = (Rate of diffusion in kg/s) * (1000 g/kg) * (3600 s/hr)

Now, let's go ahead and calculate the rate of helium effusion from the balloon:

Rate of diffusion = (4.9 x 10^-9 m^2/s) * (0.46 m^2) * (0.23 kg/m^3) / (3.091 x 10^-4 m)

Rate of diffusion = 1.108 x 10^-9 kg/s

Rate of diffusion (in g/hr) = (1.108 x 10^-9 kg/s) * (1000 g/kg) * (3600 s/hr)

Rate of diffusion (in g/hr) = 3.9888 x 10^-3 g/hr

Therefore, the rate of helium effusion from the balloon is approximately 3.9888 x 10^-3 grams per hour.