Question

Consider steady one-dimensional mass diffusion through a wall. Mark these statements as being True or False. (a) Other things being equal, the higher the density of the wall, the higher the rate of mass transfer. (b) Other things being equal, doubling the thickness of the wall will double the rate of mass transfer. (c) Other things being equal, the higher the temperature, the higher the rate of mass transfer. (d) Other things being equal, doubling the mass fraction of the diffusing species at the high concentration side will double the rate of mass transfer.

Short answer

Question: Determine if the following statements are True or False: a) Other things being equal, the higher the density of the wall, the higher the rate of mass transfer. b) Other things being equal, doubling the thickness of the wall will double the rate of mass transfer. c) Other things being equal, the higher the temperature, the higher the rate of mass transfer. d) Other things being equal, doubling the mass fraction of the diffusing species at the high concentration side will double the rate of mass transfer. Answer: a) False b) False c) True d) True

Step-by-step solution

(Statement a: Wall density and mass transfer rate)

(Considering the statement: "Other things being equal, the higher the density of the wall, the higher the rate of mass transfer." We should evaluate the relationship between wall density and mass transfer rate. Though the density of a wall might affect the diffusion rate for a particular substance, this relationship is not directly proportional. In fact, the mass transfer rate also depends on factors such as diffusion coefficient, concentration gradient, and wall thickness. Thus, the statement is False.)

(Statement b: Wall thickness and mass transfer rate)

(Considering the statement: "Other things being equal, doubling the thickness of the wall will double the rate of mass transfer." We should evaluate how the thickness of the wall impacts the mass transfer rate. For steady-state mass diffusion through a wall, the mass transfer rate is inversely proportional to the wall thickness, as shown by Fick's law: J = -D (ΔC/Δx), where J is the mass transfer rate, D is the diffusion coefficient, ΔC is the change in concentration, and Δx is the wall thickness. Doubling the wall thickness would actually decrease the mass transfer rate by half. Therefore, the statement is False.)

(Statement c: Temperature and mass transfer rate)

(Considering the statement: "Other things being equal, the higher the temperature, the higher the rate of mass transfer." We have to investigate how temperature affects the mass transfer rate. Temperature generally increases the diffusion coefficient, which in turn increases the mass transfer rate since J = -D (ΔC/Δx). Elevated temperatures result in a higher kinetic energy for diffusing molecules, allowing them to move more freely. Consequently, the statement is True.)

(Statement d: Mass fraction and mass transfer rate)

(Considering the statement: "Other things being equal, doubling the mass fraction of the diffusing species at the high concentration side will double the rate of mass transfer." We need to see if the mass fraction affects the mass transfer rate in the manner described. Doubling the mass fraction of the diffusing species at the high concentration side increases the concentration gradient, which will influence the mass transfer rate according to Fick's law: J = -D (ΔC/Δx). When the mass fraction doubles, the concentration gradient doubles as well, and so does the mass transfer rate. Therefore, the statement is True.)