UNIVERSITI TEKNOLOGI PETRONAS

CHEMICAL ENGINEERING DEPARTMENT

CCB2053 Assignment-1

1. Ammonia gas (A) and nitrogen gas (B) are diffusing in counterdiffusion through a straight

glass tube 1m long with an inside diameter of 30mm at 298 K and 101.32 kPa. Both ends of

the tube are connected to large mixed chambers at 101.32 kPa. The partial pressure of NH3 is

constant at 40.0 kPa in one chamber and 13.333 kPa in the other. The diffusivity at 298 K

and 101.32 kPa is 2.30 × 10−5

m2/s.

a. Calculate the diffusion of NH3 in kg mol/s.

b. Calculate the diffusion of N2.

Calculate the partial pressures at a point (0.5 m) in the tube and plot ρA, ρB, and P versus

distance z.

2. Mass transfer is occurring from a sphere of toluene having a radius of 10 mm. The sphere is

in a large volume of still air at 298.9 K and 1 atm abs pressure. The vapor pressure of toluene

at 298.9 K is 1.0 mm Hg. The diffusivity of naphthalene in air at 298.9 K is 8.6 × 10−6

m2/s.

a. Calculate the rate of evaporation of naphthalene from the surface in kg mol/s · m2.

b. Calculate the time in seconds for complete evaporation.

3. Water at 25°C is flowing in a covered pipe below ground. Every 150 ft there is a vent line 1.5

in. inside diameter and 2.0 ft long to the outside atmosphere at 25°C. There are 20 vents in

the 3000-ft pipe. The outside air can be assumed to be dry. Calculate the total evaporation

loss of water in kg/day. Assume that the partial pressure of water vapor at the surface of the

water is the vapor pressure, 24.24 mm Hg at 25°C. Use the diffusivity of vapor to air 2.6x10-5

m2/s.

4. Ammonia (A)–water (B) solution at 278 K and 4.0 mm thick is in contact at one surface with

an organic liquid at this interface. The concentration of ammonia in the organic phase is held

constant and is such that the equilibrium concentration of ammonia in the water at this

surface is 2.0 wt % ammonia (density of aqueous solution 991.7 kg/m3) and the concentration

of ammonia in water at the other end of the film 4.0 mm away is 10 wt % (density 961.7

kg/m3). Water and the organic are insoluble in each other. The diffusion coefficient of NH3 in

water is 1.24×10−9

m2/s.

a. At steady state, calculate the flux NA in kg mol/s·m2.

b. Calculate the flux NB. Explain.

5. A layer of gelatin in water 5 mm thick containing 5.1 wt % gelatin at 293 K separates two

solutions of sucrose. The concentration of sucrose in the solution at one surface of the gelatin

is constant at 2.0 g sucrose/100 mL solution, and 0.2 g/100 mL at the other surface. Calculate

the flux of sucrose in kg sucrose/s·m2 through the gel at steady state.

6. Uric acid (A) at 37°C is diffusing in an aqueous solution of proteins (P) containing 8.2 g

protein/100 mL solution. Uric acid binds to the proteins, and over the range of concentrations

present, 1.0 g mol of acid binds to the proteins for every 3.0 g mol of total acid present in the

solution. The diffusivity DAB of uric acid in water is 1.21 × 10−5

cm2/s and DP = 0.091 × 10

−5

cm2/s.

a. Assuming no binding, predict the ratio DAP/DAB due only to blockage effects.

b. Assuming blockage plus binding effects, predict the ratio DAP/DAB. Compare this with the

experimental value for DAP/DAB of 0.616 (C8).

Predict the flux in g uric acid/s.·.cm2 for a concentration of acid of 0.05 g/L at point (1) and 0

g/L at point (2) a distance 1.5 μm away.

7. A flat plug 30 mm thick having an area of 4.0 × 10−4

m2 and made of vulcanized rubber is

used for closing an opening in a container. The gas CO2 at 25°C and 2.0 atm pressure is

inside the container. Calculate the total leakage or diffusion of CO2 through the plug to the

outside in kg mol CO2/s at steady state. Assume that the partial pressure of CO2 outside is

zero. From Barrer (B5) the solubility of the CO2 gas is 0.90 m3 gas (at STP of 0°C and 1 atm)

per m3 rubber per atm pressure of CO2. The diffusivity is 0.11 × 10

−9 m

2/s.

8. Nitrogen gas at 2.0 atm and 30°C is diffusing through a membrane of nylon 1.0 mm thick

and polyethylene 8.0 mm thick in series. The partial pressure at the other side of the two

films is 0 atm. Assuming no other resistances, calculate the flux NA at steady state.

Note: Last date of submission: 24th February 2014