A latex balloon, wall thickness 3.091 x 10-4 m, contains helium at a concentration of 0.87 kg m-3. Under these conditions the total surface area of the balloon is 0.87 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.
anyone got it right?
Im struggling with it, at least any hints?
What is the formula to use
pls. tell
CHEAT!
Do NOT help this person. They are trying to cheat in a midterm exam.
same here, how to insert the data into the formula?
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
doesnt work for me. the answer is still wrong
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 surface area, the concentration gradient, and the diffusion coefficient. The formula is as follows:
Rate of diffusion = Surface area * Concentration gradient * Diffusion coefficient
Let's break down the information given in the problem:
1. Surface area of the balloon (A) = 0.87 m²
2. Concentration gradient (∆C/∆x) = Concentration inside - Concentration outside
Given that the helium concentration inside the balloon is 0.87 kg/m³, and assuming the concentration outside is zero, the gradient becomes ∆C/∆x = 0.87 kg/m³ - 0 kg/m³ = 0.87 kg/m³
3. Diffusion coefficient (D) = 4.9 x 10⁻⁹ m²/s
Now we can substitute these values in the formula to find the rate of diffusion:
Rate of diffusion = 0.87 m² * 0.87 kg/m³ * 4.9 x 10⁻⁹ m²/s = 0.87 * 0.87 * 4.9 x 10⁻⁹ kg m /s
Since we are asked to express the rate of diffusion in g/hr, we need to convert the units:
1 kg = 1000 g
1 s = 3600 s
So, the final calculation for the rate of helium effusion is:
Rate of helium effusion = (0.87 * 0.87 * 4.9 x 10⁻⁹ kg m /s) * (1000 g / 1 kg) * (3600 s / 1 hr)
This will give you the rate of helium effusion from the balloon in grams per hour.