A latex balloon, wall thickness 3.091 x 10-4 m, contains helium at a concentration of 0.79 kg m-3. Under these conditions the total surface area of the balloon is 0.47 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.

Question

A latex balloon, wall thickness 3.091 x 10-4 m, contains helium at a concentration of 0.79 kg m-3. Under these conditions the total surface area of the balloon is 0.47 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.

Answer 1

CHEAT

This question is from a mid-teem exam. It shluldn't be posted here. This individual is violating the honor code.

Please do NOT help them

Answer 2

Fick’s Law

M= -D•(Δρ/Δx)•A,
where
M = m/t = mass flux [kg/s],
D= 4.9•10 ⁻⁹ m ²/s is the diffusion coefficient (diffusivity) [m²/s],
Δρ/Δx is the gradient of density [kg/m⁴],
A is the area [m²].

M= - 4.9•10⁻⁹•(0 - 0.35)/3.091•10⁻⁴)•0.88 =
4.9•10⁻⁹•0.35•0.88/3.091•10⁻⁴=
=4.88•10⁻⁶ kg/s= 17.58 g/hr

Answer 3

To calculate the rate of helium effusion from the balloon, we can use Fick's Law of diffusion. Fick's Law states that the rate of diffusion is proportional to the concentration gradient and the surface area, and inversely proportional to the thickness of the material.

The equation for Fick's Law in this case can be written as:

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

First, let's convert the thickness of the balloon wall from meters to centimeters:

Thickness = 3.091 x 10^-4 m * 100 cm/m = 3.091 x 10^-2 cm

Next, let's calculate the concentration gradient. The concentration gradient is the difference in concentration between the inside and outside of the balloon. In this case, the concentration inside the balloon is given as 0.79 kg/m^3.

Since the units for the concentration are in kg/m^3, we should convert it to g/cm^3 for consistency:

Concentration = 0.79 kg/m^3 * (1000 g / 1 kg) * (1 cm / 100 m)^3 = 7.9 x 10^-3 g/cm^3

Now we have all the necessary values to calculate the rate of effusion. Plugging them into the equation:

Rate of effusion = (4.9 x 10^-9 m^2/s) * (0.47 m^2) * (7.9 x 10^-3 g/cm^3) / (3.091 x 10^-2 cm)

Cancelling out units, we get:

Rate of effusion = 6.9695 x 10^-5 g/s

Finally, we can convert the rate of effusion from seconds to hours:

Rate of effusion = (6.9695 x 10^-5 g/s) * (3600 s / 1 hr) = 0.25 g/hr

Therefore, the rate of helium effusion from the balloon is 0.25 g/hr.