A latex balloon, wall thickness 3.091 x 10-4 m, contains helium at a concentration of 0.92 kg m-3. Under these conditions the total surface area of the balloon is 0.26 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.
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
plz answer
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 of a gas is directly proportional to the surface area and the concentration gradient, and inversely proportional to the thickness of the material.
The formula for Fick's Law of Diffusion is:
Rate of diffusion = (Diffusion coefficient * Surface area * Concentration gradient) / Thickness
Now let's break down the given values:
Thickness of the latex balloon wall (t) = 3.091 x 10^(-4) m
Concentration of helium (C) = 0.92 kg/m^3
Surface area of the balloon (A) = 0.26 m^2
Diffusion coefficient of helium (D) = 4.9 x 10^(-9) m^2/s
Before we proceed, we need to convert the concentration of helium into grams per cubic meter, as the final answer is required in grams per hour.
1 kg = 1000 grams, so 0.92 kg/m^3 = 0.92 * 1000 g/m^3 = 920 g/m^3
Next, we'll calculate the rate of diffusion of helium:
Rate of diffusion = (D * A * (C2 - C1)) / t
Since the concentration outside the balloon (C1) is negligible compared to the concentration inside (C2), we can assume C1 = 0.
Rate of diffusion = (D * A * C2) / t
Plugging in the given values, we get:
Rate of diffusion = (4.9 x 10^(-9) m^2/s) * (0.26 m^2) * (920 g/m^3) / (3.091 x 10^(-4) m)
Calculating this expression:
Rate of diffusion ≈ 3.374 g/hr
Therefore, the rate of helium effusion from the balloon is approximately 3.374 grams per hour.