A latex balloon, wall thickness 3.091 x 10-4 m, contains helium at a concentration of 0.53 kg m-3. Under these conditions the total surface area of the balloon is 0.2 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. Can I get the formula please
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
how did you find the density gradient and the area?
To calculate the rate of helium effusion from the balloon, you can use Fick's Law of Diffusion. The formula is:
Rate of effusion (mol/s) = -D * (Δc/Δx) * A
where:
- D is the diffusion coefficient of helium in latex (m2/s),
- Δc/Δx is the concentration gradient of helium (kg/m3/m),
- A is the surface area of the balloon (m2).
To convert the rate of effusion from mol/s to g/hr, we need to consider the molar mass of helium, which is approximately 4 g/mol. We'll also convert the time from seconds to hours.
Formula for rate of helium effusion (g/hr) = Rate of effusion (mol/s) * Molar Mass of He (g/mol) * (3600 s/hr)
Now, let's calculate each value step by step:
1. Calculate the concentration gradient:
Δc/Δx is the change in helium concentration per unit thickness (m) of the balloon.
Given concentration = 0.53 kg/m3
Balloon thickness = 3.091 x 10-4 m
So, Δc/Δx = (0.53 kg/m3) / (3.091 x 10-4 m) = 1715 kg/m4
2. Calculate the rate of effusion:
D = 4.9 x 10-9 m2/s
A = 0.2 m2
Rate of effusion (mol/s) = -D * (Δc/Δx) * A = -4.9 x 10-9 m2/s * 1715 kg/m4 * 0.2 m2
Rate of effusion (mol/s) = -1.6782 x 10-5 mol/s
3. Convert mol/s to g/hr:
Rate of effusion (g/hr) = -1.6782 x 10-5 mol/s * 4 g/mol * 3600 s/hr
Rate of effusion (g/hr) = -0.2418 g/hr
Note: The negative sign indicates that the helium gas is escaping from the balloon.
Therefore, the rate of helium effusion from the balloon is approximately 0.2418 g/hr.