A latex balloon, wall thickness 3.091 x 10-4 m, contains helium at a concentration of 0.43 kg m-3. Under these conditions the total surface area of the balloon is 0.68 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.
CHEMISTRY HELP FROM DrBoB22
Sir please help. and give the formula to solve this question
To solve this question, we can use Fick's Law of Diffusion, which states that the rate of effusion (J) is proportional to the diffusion coefficient (D), the concentration gradient (∆C/∆x), and the surface area (A).
The formula for Fick's Law of Diffusion is:
J = -D * (∆C/∆x) * A
In this case, we are given:
- Diffusion coefficient (D) = 4.9 x 10^-9 m^2/s
- Concentration gradient (∆C/∆x) = unknown (to be calculated)
- Surface area (A) = 0.68 m^2
To calculate the concentration gradient, we need to know the initial concentration of helium inside the balloon and the final concentration outside the balloon.
Since we are only given the concentration of helium inside the balloon (0.43 kg/m^3), we'll assume that the concentration outside the balloon is negligible (0 kg/m^3).
The concentration gradient can be calculated as:
∆C/∆x = (C2 - C1) / L
Where C2 is the concentration outside the balloon, C1 is the concentration inside the balloon, and L is the thickness of the balloon wall.
Since C2 = 0 kg/m^3, the concentration gradient simplifies to:
∆C/∆x = -C1 / L
Implementing this in Fick's Law, the rate of helium effusion can be calculated as:
J = -D * (-C1 / L) * A
Given that the thickness of the balloon wall (L) is 3.091 x 10^-4 m, we can plug in the values and solve for J.
Please note that the negative sign indicates that the rate of effusion is in the opposite direction of increasing concentration.
To convert the rate of effusion from kg/s to g/hr, you'll need to multiply J by 3,600,000 (3,600 seconds in an hour and 1000 grams in a kilogram).
I hope this helps!