A latex balloon, wall thickness 3.091 x 10-4 m, contains helium at a concentration of 0.55 kg m-3. Under these conditions the total surface area of the balloon is 0.78 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 can use Fick's law of diffusion, which states that the rate of diffusion is proportional to the surface area, the concentration gradient, and the diffusion coefficient.

First, we need to calculate the concentration gradient, which is the difference in helium concentration between the inside and outside of the balloon. Since the balloon contains helium at a concentration of 0.55 kg/m^3, we need to find out the helium concentration outside the balloon.

Assuming atmospheric pressure and temperature, we can use the ideal gas law to calculate the concentration of helium outside the balloon. The ideal gas law equation is:

PV = nRT

Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature

Since we are considering atmospheric conditions, the pressure and temperature remain constant. Therefore, we can rewrite the ideal gas law equation as:

V / n = constant

This means that the ratio of volume to the number of moles is constant. As the volume increases, the number of moles of helium required to maintain atmospheric conditions inside the balloon is also greater.

Now, we can calculate the helium concentration outside the balloon using the ideal gas law equation. Let's assume atmospheric pressure at sea level (1 atm) and room temperature (approximately 298 K). The ideal gas constant, R, is 8.314 J/(mol·K). Since we know the volume of the balloon and can assume it is filled to capacity, we can calculate the number of moles of helium outside the balloon.

Next, we can calculate the concentration gradient by subtracting the helium concentration inside the balloon from the helium concentration outside the balloon.

Once we have the concentration gradient, we can use Fick's law of diffusion to calculate the rate of helium diffusion. The equation is:

diffusion rate = (surface area) x (concentration gradient) x (diffusion coefficient)

In this case, the diffusion coefficient of helium in latex is given as 4.9 x 10^-9 m^2/s, and the surface area of the balloon is given as 0.78 m^2. Plug in the values to calculate the diffusion rate.

Finally, convert the diffusion rate from kg/s to g/hr by converting the units accordingly.

Follow these steps to calculate the rate of helium effusion from the balloon.