A latex balloon, wall thickness 3.091 x 10-4 m, contains helium at a concentration of 0.82 kg m-3. Under these conditions the total surface area of the balloon is 0.39 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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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 can use Fick's Law of Diffusion, which states that the rate of diffusion is proportional to the concentration gradient and the surface area.
First, let's calculate the concentration gradient of helium across the balloon wall. The concentration gradient can be found by taking the difference in concentration between the inside and outside of the balloon:
Concentration gradient (ΔC) = C_inside - C_outside
Given that the concentration of helium inside the balloon is 0.82 kg m-3 and the concentration outside is assumed to be zero since the balloon is in the open, we have:
ΔC = 0.82 kg m-3 - 0 kg m-3
= 0.82 kg m-3
Next, we need to calculate the thickness of the balloon wall in meters. The wall thickness is given as 3.091 x 10-4 m.
Now, we can calculate the rate of diffusion using Fick's Law of Diffusion:
Rate of diffusion (R) = (Diffusion coefficient x ΔC x A) / d
Where:
- Diffusion coefficient (D) = 4.9 x 10-9 m2s-1
- ΔC = 0.82 kg m-3 (concentration gradient)
- A = 0.39 m2 (total surface area of the balloon)
- d = 3.091 x 10-4 m (wall thickness)
Plugging in the values into the formula:
R = (4.9 x 10-9 m2s-1) * (0.82 kg m-3) * (0.39 m2) / (3.091 x 10-4 m)
Calculating this expression will give you the rate of helium effusion in kg/s. To convert this to g/hr, you can use the following conversion factors:
1 kg = 1000 g
1 s = 3600 hr
So, we need to multiply the rate of diffusion by 1000 to convert from kg to g, and then divide by 3600 to convert from seconds to hours.
Final Rate of helium effusion = R * 1000 / 3600
By substituting the value of R into this equation, you will get the rate of helium effusion from the balloon in g/hr.