A latex balloon, wall thickness 3.091 x 10-4 m, contains helium at a concentration of 0.87 kg m-3. Under these conditions the total surface area of the balloon is 0.87 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 0.87 kg m-3. Under these conditions the total surface area of the balloon is 0.87 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!

Do NOT help this person. They are trying to cheat in a midterm exam.

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 need to 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) across which diffusion occurs.

The formula can be written as:

J = -D * (∆C/∆x) * A

In this case, we are given the diffusion coefficient (D) as 4.9 x 10^(-9) m^2s^(-1), the surface area (A) as 0.87 m^2, and the concentration of helium (C) as 0.87 kg m^(-3).

First, we need to find the concentration gradient (∆C/∆x). The concentration gradient for the balloon can be determined by dividing the change in concentration (∆C) by the change in distance (∆x). In this case, ∆C is the difference between the concentration of helium inside and outside the balloon, and ∆x is the thickness of the wall of the balloon.

Next, substitute the given values into the formula:

J = -D * (∆C/∆x) * A

J = -4.9 x 10^(-9) m^2s^(-1) * (∆C/3.091 x 10^(-4) m) * 0.87 m^2

Calculate ∆C:
∆C = 0.87 kg m^(-3) - 0 kg m^(-3) (assuming no helium outside the balloon)

Now, substitute the values for ∆C and solve for J:

J = -4.9 x 10^(-9) m^2s^(-1) * (0.87 kg m^(-3)/3.091 x 10^(-4) m) * 0.87 m^2

Using the given unit conversion:

1 kg = 1000 g
1 hour = 3600 seconds

J = -4.9 x 10^(-9) m^2s^(-1) * (0.87 * 1000 g) / (3.091 x 10^(-4) m) * 0.87 m^2 * 3600 s / 1 hr

By calculating this expression, you will find the rate of helium effusion in grams per hour from the balloon.