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.
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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
answer is not right
To calculate the rate of helium effusion from the balloon, we can use Fick's law of diffusion:
Rate of effusion (mol/s) = (Diffusion coefficient x Surface area x Concentration difference) / Thickness
However, the given values are not in the standard SI units, so we need to convert them before using the formula. Let's start by converting the given values to SI units:
Wall thickness: 3.091 x 10^-4 m
Concentration: 0.35 kg/m^3
Surface area: 0.57 m^2
Diffusion coefficient: 4.9 x 10^-9 m^2/s
Now let's calculate the rate of helium effusion:
Step 1: Convert the concentration from kg/m^3 to mol/m^3.
To convert from kg/m^3 to mol/m^3, we need to divide by the molar mass of helium, which is approximately 4 g/mol.
Concentration (mol/m^3) = (0.35 kg/m^3) / (4 g/mol) = 0.0875 mol/m^3
Step 2: Convert the surface area from m^2 to cm^2.
To convert from m^2 to cm^2, we need to multiply by 10,000.
Surface area (cm^2) = 0.57 m^2 x 10,000 = 5700 cm^2
Step 3: Calculate the rate of effusion in mol/s.
Using Fick's law of diffusion formula:
Rate of effusion (mol/s) = (Diffusion coefficient x Surface area x Concentration difference) / Thickness
Rate of effusion (mol/s) = (4.9 x 10^-9 m^2/s) x 5700 cm^2 x (0.0875 mol/m^3) / (3.091 x 10^-4 m)
Step 4: Convert the rate of effusion from mol/s to g/hr.
To convert from mol/s to g/hr, we need to multiply by the molar mass of helium and adjust the units accordingly.
Rate of effusion (g/hr) = (Rate of effusion in mol/s) x (molar mass of helium) x (3600 seconds/hour) x (1000 g/kg)
Molar mass of helium: 4 g/mol
Rate of effusion (g/hr) = (Rate of effusion in mol/s) x (4 g/mol) x (3600 seconds/hour) x (1000 g/kg)
Now you can substitute the values into the equation to calculate the rate of helium effusion in g/hr.