Electrochemical Nature of Heterogeneous Reactions Quiz

Fick's First Law

In the direction of low concentration

Fick's Second Law

The slowest step

Homogeneous reactions

The rate increases

$\frac{k_2}{k_1} = \frac{E_A}{R} \left(\frac{1}{T_1} - \frac{1}{T_2}\right)$

Solid-gas

Lattice defects and vacancies

Area of the interface

$r = rac{dM}{dt} = kAC$

Formation of new bonds

Autocatalytic reaction

Non-porous nature of the product

The rate increases with time

The adhesion of the fluid to the surface and the viscosity of the fluid

$\delta = 2r_0S_h$

The rate increases

Temperature only slightly affects diffusion-controlled reactions

$r_A = -D \nabla C_A$

Mass transfer coefficient

Case 1: ks << km

$r_A = -k_sC_s$

The rate of a chemical reaction is directly proportional to the concentrations of reactants.

The Arrhenius equation is given by $\frac{d \ln k},{dT} = \frac{E_A},{RT^2}$ and it describes the relationship between the rate constant of a chemical reaction and the temperature.

The van't Hoff's equation is similar to the Arrhenius equation and is given by $\frac{d \ln k},{dT} = \frac{\Delta H},{RT^2}$, where $\Delta H$ is the enthalpy change of the reaction.

The activation energy is the energy barrier that must be overcome for a chemical reaction to occur. It can be determined using the Arrhenius equation by plotting the natural logarithm of the rate constant against the reciprocal of the temperature.

Heterogeneous reactions involve reactants and products in different phases, while homogeneous reactions occur in a single phase.

Nucleation plays an important role in heterogeneous processes such as thermal decomposition in solids, crystallization, precipitation of solids from liquids, gas evolution in liquids, deposition of solids from gases and roasting.

The three steps involved in nucleation are: 1) nucleation stage or induction period, 2) formation and growth of the reaction interface during the period of acceleration, and 3) propagation of the reaction interface.

If a porous product layer is formed, the rate of reaction is not affected by the coating and resistance may be due only to diffusion through the boundary layer. However, if a non-porous product layer is formed, the rate of reaction may be controlled by diffusion through this layer.

An autocatalytic reaction is a type of reaction in which the liquid product reacts further with the solid reactant, leading to an increasing rate of reaction.

The mass of the solid, the concentration of the reagent, and the solid/liquid ratio (pulp density) can all affect the rate of a solid-liquid reaction.

The five categories of heterogeneous processes based on the nature of the interface are: (i) Solid-gas, (ii) Solid-liquid, (iii) Solid-solid, (iv) Liquid-gas, and (v) Liquid-liquid.

The various lattice defects that can occur in a crystal include: (i) Schottky type of lattice defect, (ii) Frenkel type of lattice defect, (iii) Non-metal deficiency, (iv) Excess metal ions in interstitial cations, and (v) Non-metal excess.

The rate of a heterogeneous reaction depends on the area of the interface. Reactions involving fine particles have a higher rate compared to those involving coarse particles.

The geometry of the interface is an important factor in determining the rate of a reaction. For plates or discs, the surface area remains constant throughout the reaction, resulting in a constant rate. However, for spheres or pellets, the surface area changes as the reaction proceeds, leading to a changing rate.

For a solid-liquid reaction assuming constant concentration, the rate expression is given by $r = \frac{dM},{dt} = kAC$, where $M$ is the mass of solid at time $t$, $A$ is the surface area of the solid, $C$ is the concentration of the fluid reactant, and $k$ is the rate constant.

$J = -D\frac{dc}{dx}

$Sh = \frac{k_ml}{D}

The steps involved are: 1. diffusion of reacting molecules from the bulk of fluid to the interface, 2. adsorption at the interface, 3. reaction at the interface, 4. desorption of reaction products from the interface, and 5. diffusion of reaction products from the interface into the bulk of fluid.

The mechanism of the reaction may change from diffusion to chemical reaction control with increasing reagent concentration.

$E_a = R\cdot T_A - R\cdot T_B$

The steps involved in solid-fluid reactions are:1. External mass transfer between the bulk fluid and the external surface of the solid.2. Diffusion of reactants and products within the pores of the solid.3. Adsorption of reactants and products on the reaction surface.4. Migration of reactants and products on the reaction surface.5. Chemical reaction between the reactants from the fluid phase and components in the solid.

Fick's First Law states that the rate of diffusion of substance A per unit cross section of a solid is proportional to the concentration gradient in the direction of diffusion. The equation for the diffusion flux is $J_A = -D \nabla C_A$. Where $J_A$ is the diffusion flux, $D$ is the diffusivity (diffusion coefficient), and $\nabla C_A$ is the concentration gradient.

Fick's Second Law applies when the concentration gradient changes with time as a result of diffusion itself. The equation for the diffusion flux in the case of unsteady-state diffusion is $J_A = D \nabla^2 C_A$. Where $J_A$ is the diffusion flux, $D$ is the diffusivity (diffusion coefficient), and $\nabla^2 C_A$ is the concentration gradient.

The overall rate of a heterogeneous reaction is determined by the slowest step, also known as the rate-controlling step. The reaction conditions can affect which step becomes rate-controlling. It is important to understand how each step relates to the other in order to determine the overall rate of the process.

If the rate of mass transfer, $n_A$, is defined per unit surface area, then the chemical reaction rate, $r_A$, at the same surface must be defined per unit area of that surface for any comparison of both rates to be done. The equations are:Rate of mass transfer: $\frac{dn_A},{dt} = \frac{km(C_b - C_s)},{\Delta x}$Rate of reaction: $\frac{dN_A},{dt} = \frac{k_r S},{\Delta x}$.Where $km$ is the mass transfer coefficient, $C_b$ and $C_s$ are the concentrations of A in the bulk and at the surface respectively, $\Delta x$ is the thickness of the stagnant film, $S$ is the area of the reaction interface, and $k_r$ is the rate constant of the chemical reaction.

Sh = 2.0 + 0.6Re^{1/2}

Sh = 2.0 + 0.6Re^{1/2}Sc^{1/3}

Cs = -\frac{ks}{km + ks}Cb

rA = -D\nabla CA

rA = -ksCb