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Consider the problem of how plants might lift water from ground level to their leaves. Assume that there us a semipermeable membrane at the roots, with pure water on the outside, and an ideal solution inside a small cylindrical capillary inside the plant. The solute mole fraction inside the capillary is x = 0.001. The radius of the capillary is 0.1 mm. Assuming the density of the solution = 1 g/mL, what is the height of the solution at 298 K? Can osmotic pressure account for raising this water?

What is the fundamental differential equation governing mass transfer in chemical engineering, and how does it relate to Fick's law of diffusion?

A sheet of steel with 100cm2 area has nitrogen(N2) atmospheres on both sides and is permitted to achieve a steady-state diffusion condition. In order to increase the flow rate of N2, which of the following modifications is useful? Steel sheet O Increase the N2 pressure at C1 O Decrease the temperature. O Increase the N2 pressure at C2 O Increase the thickness of the steel sheet.

Catalyst particles are entrapped in the center of a porous membrane material. The purpose of this is to protect the catalyst so that it can be recovered and reused. This structure shown below is immersed in an aqueous solution containing a proprietary reactant called component A. Component A can only diffuse through the top and bottom faces of this structure. The dimensions of the top face and the bottom face are same (10cm x 10cm). The thickness of the top membrane is 0.1cm and the thickness of the bottom membrane is also 0.1cm. Furthermore component A is instantaneously consumed by the catalyst at a constant rate of 144 mg/hour when it enters the compartment where the catalyst is located.   If the effective diffusivity of component A in this application is 2 x 10-5 cm2/s in the membrane calculate the concentration of component A in the surrounding solution that is needed to maintain the consumption rate. (You may assume the surrounding solution is well mixed and thus void of any…

A quiescent body of water has a depth of 600 mm. The DO level at the bottom after 16 days is 3.5 mg/l when the surface is exposed to the atmosphere at a temperature of 25oC. Determine the DO of the water body. The saturated DO at 25oC is 8.5 mg/l and the diffusion coefficient (kd) at 25oC is 2.5 x 10-3 mm2/s.

An input stream contains oil sands, comprising 14.0% oil, the remainder being solid sand particles. In the initial stages of steady-state processing, the oil sands are mixed with warm water and pumped to a settling tank. In this tank three layers are formed. The three layers are: 1. Bottom layer containing 95.0% sand and 5.00% water 2. Middle layer containing 5.00% oil and 95.0% water 3. Top layer containing 70.0% oil and 30.0% water The top layer is skimmed off and sent for further processing, while the bottom two layers are disposed of. How much warm water is added to 200 tonnes of oil sands in this process if 85.0% of the total oil is recovered in the top layer (3 sig. figs)? All percentages given are weight percentages.

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Problem #1: Diffusion-convection problems wherein the species diffusivity is concentration-dependent often provide a differential equation of the following general form: [vLj dC + [DJ dz d [dc where Cis the dimensionless concentration and z is the dimensionless distance. Assume VLID, is a constant. Assume that C=1 at z = 0, and C=0 when z is very large. Solve the above differential equation and provide an exact analytical equation for C=ft).

2. In order to remember the difference between macroscopic and molecular scale energies, I ... Answer: