A latex balloon, wall thickness 3.091 x 10-4 m, contains helium at a concentration of 0.7 kg m-3. Under these conditions the total surface area of the balloon is 0.52 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 0.7 kg m-3. Under these conditions the total surface area of the balloon is 0.52 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

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 2

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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 diffusion is proportional to the concentration gradient and the surface area and inversely proportional to the thickness.

First, we need to calculate the concentration difference or the concentration gradient. The concentration inside the balloon is given as 0.7 kg/m^3. Since helium is escaping the balloon, the concentration outside the balloon is effectively zero (assuming an infinite volume of air).

Next, we can find the concentration difference (ΔC) by subtracting the outside concentration from the inside concentration:

ΔC = 0.7 kg/m^3 - 0 kg/m^3 = 0.7 kg/m^3

Now, we can calculate the flux (J) using Fick's Law:

J = -D * (ΔC / Δx)

Where:
J is the flux or rate of diffusion
D is the diffusion coefficient
ΔC is the concentration difference
Δx is the thickness of the latex balloon

Substituting the given values:

J = - (4.9 x 10^-9 m^2/s) * (0.7 kg/m^3) / (3.091 x 10^-4 m)

Simplifying, we get:

J = - 1.3994 x 10^-4 kg / (m^2 * s)

Since the flux (J) has a negative sign, it represents the rate of effusion. However, we need to convert this to grams per hour:

To convert the rate of effusion from kg/s to g/hr, we need to multiply by the appropriate conversion factors:

J = - 1.3994 x 10^-4 kg / (m^2 * s) * (1000 g / 1 kg) * (3600 s / 1 hr)

Simplifying, we get:

J = -503.784 g / (m^2 * hr)

Therefore, the rate of helium effusion from the balloon is approximately 503.784 g/hr.