Introduction to Mass Transfer

Flashcards covering fundamental concepts, definitions, phase transfer examples, applications, and mathematical formulations of Fick's Law of Diffusion from Chapter 1: Introduction to Mass Transfer.

How is mass transfer defined in engineering?

It is an engineering term for physical processes that involve the molecular and convective transport of atoms and molecules within physical systems, occurring in gas mixtures, liquid solutions, or solids.

What condition is required for mass transfer to occur, and what is its direction?

It requires the presence of two regions with different chemical compositions (a concentration gradient), causing species to move from a high-concentration region toward a lower-concentration region.

How are a solution, a solute, and a solvent defined?

A solution is a mixture consisting of a solute and a solvent. A solute is the component present in the lesser amount, and a solvent is the component present in the greater amount.

What is the general definition of concentration in a solution?

Concentration is the amount of a solute present in a solution per standard amount of solvent.

What are the three ways to quantify concentration and their respective units?

1. Mass concentration: Mass of $i$ per unit volume ($\text{kg/m}^3$\n2. Molar concentration: Number of moles of $i$ per unit volume ($\text{kmol/m}^3$\n3. Number of molecules: Number of molecules of each species present per unit volume ($\text{molecules/m}^3$)

Why is quantifying mass transfer important in engineering?

It allows for the design and manufacture of separation equipment to meet specified requirements and enables the estimation of outcomes in real-life situations, such as chemical spills.

What are two everyday examples of mass transfer mentioned in the lecture?

1. The addition of sugar to coffee.\n2. The evaporation of water from a pond to the atmosphere driven by the difference in concentration of water vapor between the water surface and surrounding air.

What are biological process examples of mass transfer?

The oxygenation of blood and the transport of ions across membranes within the kidney.

What are five common chemical separation processes based on mass transfer?

Adsorption, liquid-liquid extraction, distillation, drying, and gas absorption.

What are examples of solid-to-gas and gas-to-liquid mass transfer?

Solid-to-gas: Dry ice ($\text{solid CO}_2$) shrinking over time as $\text{CO}_2$ molecules diffuse into the air.\nGas-to-liquid: A small fraction of $\text{O}_2$ in air diffusing into water to meet the oxygen needs of marine animals.

What are examples of solid-to-solid mass transfer?

The diffusion of carbon into iron during case-hardening, and the doping of semiconductors and transistors.

What are the two primary modes of mass transfer?

Molecular diffusion and convective mass transfer.

What is the general governing equation for the molecular transport process of mass?

$$\text{Rate of transfer process} = \frac{\text{driving force}}{\text{resistance}}$$

How is molecular diffusion (molecular transport) defined?

The transfer or movement of individual molecules through a fluid by means of the random, individual movements of the molecules.

What is Fick's Law of diffusion for a stationary binary mixture expressed in terms of the concentration of component A ($c_A$)?

$$J_{AZ}^* = -D_{AB} \frac{dc_A}{dz}$$

What does each variable in the equation $J_{AZ}^* = -c D_{AB} \frac{dx_A}{dz}$ represent along with its units?

$J_{AZ}^*$: Molar flux of component A in the z direction ($\text{kmol A}/(\text{s}\cdot\text{m}^2)$).\n$c$: Total concentration of A and B ($\text{kmol (A + B)}/\text{m}^3$).\n$D_{AB}$: Molecular diffusivity of molecule A in B ($\text{m}^2/\text{s}$).\n$x_A$: Mole fraction of A in the mixture.\n$z$: Distance of diffusion ($\text{m}$).

What is the integrated form of Fick's Law for molecular diffusion of ideal gases between positions $z_1$ and $z_2$ in terms of partial pressures?

$$J_{Az}^* = \frac{D_{AB}(p_{A1} - p_{A2})}{RT(z_2 - z_1)}$$

A mixture of He and $N_2$ gas is contained in a pipe at $298\,\text{K}$ and $1\,\text{atm}$. At $z_1$, $p_{A1} = 0.6\,\text{atm}$; at $z_2 = 0.2\,\text{m}$, $p_{A2} = 0.2\,\text{atm}$. If $D_{AB} = 0.687 \times 10^{-4}\,\text{m}^2/\text{s}$ and $R = 82.057 \times 10^{-3}\,\text{m}^3\cdot\text{atm}/(\text{kmol}\cdot\text{K})$, what is the molar flux of He at steady state?

$$5.62 \times 10^{-6}\,\text{kmol}/(\text{s}\cdot\text{m}^2)$$