Chapter 14

Benzene-free air at \(25^{\circ} \mathrm{C}\) and \(101.3 \mathrm{kPa}\) enters a \(5-\mathrm{cm}\)-diameter tube at an average velocity of $5 \mathrm{~m} / \mathrm{s}$. The inner surface of the 6-m-long tube is coated with a thin film of pure benzene at \(25^{\circ} \mathrm{C}\). The vapor pressure of benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) at \(25^{\circ} \mathrm{C}\) is $13 \mathrm{kPa}$, and the solubility of air in benzene is assumed to be negligible. Calculate \((a)\) the average mass transfer coefficient in \(\mathrm{m} / \mathrm{s}\), (b) the molar concentration of benzene in the outlet air, and \((c)\) the evaporation rate of benzene in $\mathrm{kg} / \mathrm{h}$.

Air at \(52^{\circ} \mathrm{C}, 101.3 \mathrm{kPa}\), and 20 percent relative humidity enters a \(5-\mathrm{cm}\)-diameter tube with an average velocity of $6 \mathrm{~m} / \mathrm{s}$. The tube inner surface is wetted uniformly with water, whose vapor pressure at \(52^{\circ} \mathrm{C}\) is \(13.6 \mathrm{kPa}\). While the temperature and pressure of air remain constant, the partial pressure of vapor in the outlet air is increased to \(10 \mathrm{kPa}\). Detemine \((a)\) the average mass transfer coefficient in $\mathrm{m} / \mathrm{s}\(, \)(b)$ the log-mean driving force for mass transfer in molar concentration units, \((c)\) the water evaporation rate in $\mathrm{kg} / \mathrm{h}\(, and \)(d)$ the length of the tube.

The basic equation describing the diffusion of one medium through another stationary medium is (a) \(j_{A}=-C D_{A B} \frac{d\left(C_{A} / C\right)}{d x}\) (b) \(j_{A}=-D_{A B} \frac{d\left(C_{A} / C\right)}{d x}\) (c) \(j_{A}=-k \frac{d\left(C_{A} / C\right)}{d x}\) (d) \(j_{A}=-k \frac{d T}{d x}\) (e) none of them

For the absorption of a gas (like carbon dioxide) into a liquid (like water) Henry's law states that partial pressure of the gas is proportional to the mole fraction of the gas in the liquid-gas solution with the constant of proportionality being Henry's constant. A bottle of soda pop \(\left(\mathrm{CO}_{2}-\mathrm{H}_{2} \mathrm{O}\right)\) at room temperature has a Henry's constant of \(17,100 \mathrm{kPa}\). If the pressure in this bottle is \(140 \mathrm{kPa}\) and the partial pressure of the water vapor in the gas volume at the top of the bottle is neglected, the concentration of the \(\mathrm{CO}_{2}\) in the liquid \(\mathrm{H}_{2} \mathrm{O}\) is (a) \(0.004 \mathrm{~mol}-\mathrm{CO}_{2} / \mathrm{mol}\) (b) \(0.008 \mathrm{~mol}-\mathrm{CO}_{2} / \mathrm{mol}\) (c) \(0.012 \mathrm{~mol}-\mathrm{CO}_{2} / \mathrm{mol}\) (d) \(0.024 \mathrm{~mol}-\mathrm{CO}_{2} / \mathrm{mol}\) (e) \(0.035 \mathrm{~mol}-\mathrm{CO}_{2} / \mathrm{mol}\)

A rubber object is in contact with nitrogen \(\left(\mathrm{N}_{2}\right)\) at \(298 \mathrm{~K}\) and \(250 \mathrm{kPa}\). The solubility of nitrogen gas in rubber is \(0.00156 \mathrm{kmol} / \mathrm{m}^{3}\).bar. The mass density of nitrogen at the interface is (a) \(0.049 \mathrm{~kg} / \mathrm{m}^{3}\) (b) \(0.064 \mathrm{~kg} / \mathrm{m}^{3}\) (c) \(0.077 \mathrm{~kg} / \mathrm{m}^{3}\) (d) \(0.092 \mathrm{~kg} / \mathrm{m}^{3}\) (e) \(0.109 \mathrm{~kg} / \mathrm{m}^{3}\)

Nitrogen gas at high pressure and \(298 \mathrm{~K}\) is contained in a \(2-\mathrm{m} \times 2-\mathrm{m} \times 2-\mathrm{m}\) cubical container made of natural rubber whose walls are \(3 \mathrm{~cm}\) thick. The concentration of nitrogen in the rubber at the inner and outer surfaces are $0.067 \mathrm{~kg} / \mathrm{m}^{3}\( and \)0.009 \mathrm{~kg} / \mathrm{m}^{3}$, respectively. The diffusion coefficient of nitrogen through rubber is $1.5 \times 10^{-10} \mathrm{~m}^{2} / \mathrm{s}$. The mass flow rate of nitrogen by diffusion through the cubical container is (a) $8.1 \times 10^{-10} \mathrm{~kg} / \mathrm{s}$ (b) \(3.2 \times 10^{-10} \mathrm{~kg} / \mathrm{s}\) (c) \(3.8 \times 10^{-9} \mathrm{~kg} / \mathrm{s}\) (d) \(7.0 \times 10^{-9} \mathrm{~kg} / \mathrm{s}\) (e) \(1.60 \times 10^{-8} \mathrm{~kg} / \mathrm{s}\)

A recent attempt to circumnavigate the world in a balloon used a helium-filled balloon whose volume was \(7240 \mathrm{~m}^{3}\) and surface area was $1800 \mathrm{~m}^{2}\(. The skin of this balloon is \)2 \mathrm{~mm}$ thick and is made of a material whose helium diffusion coefficient is $1 \times 10^{-9} \mathrm{~m}^{2} / \mathrm{s}$. The molar concentration of the helium at the inner surface of the balloon skin is \(0.2 \mathrm{kmol} / \mathrm{m}^{3}\) and the molar concentration at the outer surface is extremely small. The rate at which helium is lost from this balloon is (a) \(0.26 \mathrm{~kg} / \mathrm{h}\) (b) \(1.5 \mathrm{~kg} / \mathrm{h}\) (c) \(2.6 \mathrm{~kg} / \mathrm{h}\) (d) \(3.8 \mathrm{~kg} / \mathrm{h}\) (e) \(5.2 \mathrm{~kg} / \mathrm{h}\)

Carbon at \(1273 \mathrm{~K}\) is contained in a \(7-\mathrm{cm}\)-innerdiameter cylinder made of iron whose thickness is \(1.2 \mathrm{~mm}\). The concentration of carbon in the iron at the inner surface is $0.5 \mathrm{~kg} / \mathrm{m}^{3}$ and the concentration of carbon in the iron at the outer surface is negligible. The diffusion coefficient of carbon through iron is $3 \times 10^{-11} \mathrm{~m}^{2} / \mathrm{s}$. The mass flow rate of carbon by diffusion through the cylinder shell per unit length of the cylinder is (a) \(2.8 \times 10^{-9} \mathrm{~kg} / \mathrm{s}\) (b) \(5.4 \times 10^{-9} \mathrm{~kg} / \mathrm{s}\) (c) \(8.8 \times 10^{-9} \mathrm{~kg} / \mathrm{s}\) (d) \(1.6 \times 10^{-8} \mathrm{~kg} / \mathrm{s}\) (e) \(5.2 \times 10^{-8} \mathrm{~kg} / \mathrm{s}\)

The surface of an iron component is to be hardened by carbon. The diffusion coefficient of carbon in iron at \(1000^{\circ} \mathrm{C}\) is given to be $3 \times 10^{-11} \mathrm{~m}^{2} / \mathrm{s}$. If the penetration depth of carbon in iron is desired to be \(1.0 \mathrm{~mm}\), the hardening process must take at least (a) \(1.10 \mathrm{~h}\) (b) \(1.47 \mathrm{~h}\) (c) \(1.86 \mathrm{~h}\) (d) \(2.50 \mathrm{~h}\) (e) \(2.95 \mathrm{~h}\)

A natural gas (methane, \(\mathrm{CH}_{4}\) ) storage facility uses 3 -cm- diameter by 6 -m-long vent tubes on its storage tanks to keep the pressure in these tanks at atmospheric value. If the diffusion coefficient for methane in air is \(0.2 \times 10^{-4} \mathrm{~m}^{2} / \mathrm{s}\) and the temperature of the tank and environment is \(300 \mathrm{~K}\), the rate at which natural gas is lost from a tank through one vent tube is (a) \(13 \times 10^{-5} \mathrm{~kg} / \mathrm{day}\) (b) \(3.2 \times 10^{-5} \mathrm{~kg} / \mathrm{day}\) (c) \(8.7 \times 10^{-5} \mathrm{~kg} / \mathrm{day}\) (d) \(5.3 \times 10^{-5} \mathrm{~kg} / \mathrm{day}\) (e) \(0.12 \times 10^{-5} \mathrm{~kg} / \mathrm{day}\)