A latex balloon, wall thickness 3.091 x 10-4 m, contains helium at a concentration of 0.35 kg m-3. Under these conditions the total surface area of the balloon is 0.57 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.
maybe:
0.52*(4.9*10^-9)*(concentration in mole/0.52)
then multiply solution (molar flow rate) with molar mass of helium.
solution should be effusion rate.
its just a suggestion, all other interested are invited to post their opinion/formula...
Could someone insert the data into the formula?
This is a question from the second midterm of 3.091x by edx. Stop cheating, it's silly and pointless.
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 Law of diffusion, which states that the rate of diffusion (J) is equal to the diffusion coefficient (D) multiplied by the concentration gradient (∇C) divided by the thickness of the material (∇x). The equation is given by:
J = -D * (∇C / ∇x)
Here's how we can use this equation to solve the problem:
1. Convert the thickness of the wall from meters to centimeters:
∇x = 3.091 x 10^(-4) m * 100 cm/m = 3.091 x 10^(-2) cm
2. Convert the concentration of helium from kg/m^3 to g/cm^3:
Concentration = 0.35 kg/m^3 * 10^3 g/kg = 350 g/m^3
3. Calculate the concentration gradient (∇C) by subtracting the concentration inside the balloon from the concentration outside. Since there's no information about the concentration outside the balloon, we can assume it is zero:
∇C = 350 g/m^3 - 0 g/m^3 = 350 g/m^3
4. Calculate the rate of diffusion (J) by plugging the given values into Fick's Law equation:
J = -D * (∇C / ∇x) = -4.9 x 10^(-9) m^2/s * (350 g/m^3 / 3.091 x 10^(-2) cm)
5. Convert the rate of diffusion from grams per second to grams per hour:
There are 3600 seconds in an hour, so we can multiply J by (3600 s/hr) to get the rate in g/hr.
By following these steps, you should be able to calculate the rate of helium effusion from the balloon in grams per hour.