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23 Nov 2019

Calculate an estimate of how long it would take for a gaseousair-borne cold virus of molar mass 100 kg/mol to travel a distanceof 1.0 m by diffusion in still, 25 ^oC air at 1.0 atm.Assume the bulk density of the virus is the same as that ofwater.

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The self-diffusion coefficient of H₂O molecules in water is 2.26 x 10^-5 cm² s^-1 at 25 ^oC. Estimate how long it takes for an H₂O molecule to travel:

1.0 cm at 25 ^oC

2.0 cm at 25 ^oC

2.0 cm at 50 ^oC (this one will take some creativityâ¦assume that water molecules are weakly bound (1 kJ mol^-1) and assume it takes about half that energy to move a molecule through the water)

Hint: the argument in the error function relationship for Fick's Second Law [x/(2*(Dt)^.5] must be a constant since the error function is constant, therefore:

x = K' 2 (Dt)^0.5

where x is the diffusion distance and t is time and D is the diffusion constant. We can just assume K' =1 which is not usually the case but at least can help us get order of magnitude estimates for diffusion distances.

The equilibrium partitioning of a chemical in a three-phase system comprised of air, soil and water can be approximated as follows:

Total mass = mass in air + mass in water + mass in soil

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Assume a system with a volume 1 L that it is divided into 600 mL water, 200 mL air and 200 mL soil. The soil has a bulk density (r_b) of 2.0 g/cm³ and a fraction organic matter of 2.5 percent. Into this system we introduce 100 mg pyrene, which has a Henryâs Law constant of 10^2.05 (mol/L-atm) and log Kow = 5.13 (L/kg). What would the mass of pyrene be in the air, soil and water phases at equilibrium? How does this compare to our estimate conducted in class? (Hints: pay attention to the units and determine a dimensionless Henryâs Law constant, which the text discusses)

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Calculate an estimate of how long it would take for a gaseousair-borne cold virus of molar mass 100 kg/mol to travel a distanceof 1.0 m by diffusion in still, 25 ^oC air at 1.0 atm.Assume the bulk density of the virus is the same as that ofwater.

Related textbook solutions

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Principles of Chemistry Molecular Approach

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Calculate an estimate of how long it would take for a gaseousair-borne cold virus of molar mass 100 kg/mol to travel a distanceof 1.0 m by diffusion in still, 25 oC air at 1.0 atm.Assume the bulk density of the virus is the same as that ofwater.

Related textbook solutions

Basic Chemistry

Principles of Chemistry Molecular Approach

Principles of Chemistry Molecular Approach

Chemistry: Structure and Properties

Chemistry: A Molecular Approach

Chemistry: A Molecular Approach

Principles of Chemistry: A Molecular Approach

Chemistry: The Central Science

Related questions

Weekly leaderboard

Calculate an estimate of how long it would take for a gaseousair-borne cold virus of molar mass 100 kg/mol to travel a distanceof 1.0 m by diffusion in still, 25 ^oC air at 1.0 atm.Assume the bulk density of the virus is the same as that ofwater.