A latex balloon, wall thickness 3.091 x 10-4 m, contains helium at a concentration of 0.5 kg m-3. Under these conditions the total surface area of the balloon is 0.72 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.

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what is the formula?

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

To calculate the rate of helium effusion from the balloon, we need to use Fick's first law of diffusion, which states that the rate of diffusion is proportional to the surface area, the concentration gradient, and the diffusion coefficient.

First, let's calculate the concentration gradient. The concentration gradient is given by the change in concentration divided by the thickness of the wall.

Concentration gradient = (final concentration - initial concentration) / wall thickness

In this case, the final concentration is 0 (since the gas is escaping), and the initial concentration is given as 0.5 kg/m3. The wall thickness is given as 3.091 x 10-4 m.

Concentration gradient = (0 - 0.5 kg/m3) / 3.091 x 10-4 m

Next, we can calculate the diffusion rate using Fick's first law of diffusion:

Diffusion rate = (diffusion coefficient) * (surface area) * (concentration gradient)

The diffusion coefficient is given as 4.9 x 10-9 m2/s, and the surface area is given as 0.72 m2.

Diffusion rate = (4.9 x 10-9 m2/s) * (0.72 m2) * (concentration gradient)

Now, we can solve for the diffusion rate:

Diffusion rate = (4.9 x 10-9 m2/s) * (0.72 m2) * [(0 - 0.5 kg/m3) / 3.091 x 10-4 m]

After calculating this, you will get the diffusion rate in units of kg/s. To convert it to g/hr, you need to multiply it by 3600 (to convert seconds to hours) and by 1000 (to convert kg to g).

Diffusion rate (g/hr) = Diffusion rate (kg/s) * 3600 * 1000

Plug in the values and calculate the diffusion rate in g/hr.