Electrochemical Nature of Heterogeneous Reactions Quiz

Which law describes the rate of diffusion of substance A per unit cross section of a solid?

Fick's Second Law
Newton's Law of Motion
Fick's First Law (correct)
Boyle's Law

What is the direction of diffusion according to Fick's First Law?

In the direction of high concentration
In the direction of low concentration (correct)
In the direction of increasing concentration
In the direction of no concentration gradient

Which law applies to unsteady-state diffusion when the concentration gradient changes with time?

Fick's Second Law (correct)
Newton's Law of Motion
Fick's First Law
Boyle's Law

What determines the overall rate of a heterogeneous reaction?

The slowest step (D) Signup and view all the answers

Which type of reaction involves reactants and products in the same phase?

Homogeneous reactions (C) Signup and view all the answers

According to the Arrhenius equation, how does the rate of chemical reactions change with an increase in temperature?

The rate increases (C) Signup and view all the answers

Which equation is used to determine the activation energy using two temperatures?

$\frac{k_2}{k_1} = \frac{E_A}{R} \left(\frac{1}{T_1} - \frac{1}{T_2}\right)$ (D) Signup and view all the answers

Which category of heterogeneous processes involves reactions between a solid and a gas?

Solid-gas (C) Signup and view all the answers

What is the nature of the interface that plays an important role in determining the kinetics of reactions involving solids?

Lattice defects and vacancies (B) Signup and view all the answers

What factor does the rate of heterogeneous reactions depend on, in addition to the nature of the interface?

Area of the interface (B) Signup and view all the answers

What is the rate expression for solid-liquid reactions assuming constant concentration?

$r = rac{dM}{dt} = kAC$ (A) Signup and view all the answers

Which of the following is NOT a step involved in nucleation in heterogeneous processes?

Formation of new bonds (A) Signup and view all the answers

What type of reaction is possible in solid-liquid reactions when the liquid product reacts further with the solid reactant?

Autocatalytic reaction (C) Signup and view all the answers

What determines the kinetics of a reaction when a solid product is formed on reacting solid?

Non-porous nature of the product (C) Signup and view all the answers

What happens to the rate of reaction in solid-liquid reactions when the volume of reagent is large?

The rate increases with time (A) Signup and view all the answers

Which hydrodynamic factors contribute to the existence of a boundary layer in solid-fluid interactions?

The adhesion of the fluid to the surface and the viscosity of the fluid (D) Signup and view all the answers

What is the formula for the thickness of the boundary layer around a particle?

$\delta = 2r_0S_h$ (B) Signup and view all the answers

How does the rate of a diffusion-controlled reaction change with the decrease in the thickness of the boundary layer?

The rate increases (D) Signup and view all the answers

What is the effect of temperature on diffusion-controlled reactions?

Temperature only slightly affects diffusion-controlled reactions (A) Signup and view all the answers

Which equation represents Fick's 1st Law for mass transfer in porous media?

$r_A = -D \nabla C_A$ (B) Signup and view all the answers

What does the Sherwood number represent in mass transfer?

Mass transfer coefficient (C) Signup and view all the answers

Which case represents external mass transfer offering no resistance and chemical reaction control?

Case 1: ks << km (D) Signup and view all the answers

What is the equation for the overall reaction rate when the reaction is mass transfer controlled in porous media?

$r_A = -k_sC_s$ (A) Signup and view all the answers

What is the relationship between the rate of a chemical reaction and the concentrations of reactants?

The rate of a chemical reaction is directly proportional to the concentrations of reactants. Signup and view all the answers

What is the Arrhenius equation and what does it describe?

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. Signup and view all the answers

What is the van't Hoff's equation and how is it related to the Arrhenius equation?

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. Signup and view all the answers

What is the activation energy and how is it determined using the Arrhenius equation?

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. Signup and view all the answers

What are heterogeneous reactions and how do they differ from homogeneous reactions?

Heterogeneous reactions involve reactants and products in different phases, while homogeneous reactions occur in a single phase. Signup and view all the answers

What is the role of nucleation in heterogeneous processes?

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. Signup and view all the answers

What are the three steps involved in nucleation?

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. Signup and view all the answers

How does the nature of the solid reaction product affect the kinetics of the reaction?

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. Signup and view all the answers

What is an autocatalytic reaction?

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. Signup and view all the answers

What factors can affect the rate of a solid-liquid 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. Signup and view all the answers

What are the five categories of heterogeneous processes based on the nature of the interface?

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. Signup and view all the answers

What are the various lattice defects that can occur in a crystal?

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. Signup and view all the answers

How does the rate of a heterogeneous reaction depend on the area of the interface?

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. Signup and view all the answers

How does the geometry of the interface affect the rate of a reaction?

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. Signup and view all the answers

What is the rate expression for a solid-liquid reaction assuming constant concentration?

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. Signup and view all the answers

What is the equation for the rate of diffusion according to Fick's First Law?

$J = -D\frac{dc}{dx} Signup and view all the answers

What is the equation for the Sherwood number?

$Sh = \frac{k_ml}{D} Signup and view all the answers

What are the steps involved in the interaction between a solid and a fluid?

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. Signup and view all the answers

What is the effect of reagent concentration on the mechanism of solid-liquid reactions?

The mechanism of the reaction may change from diffusion to chemical reaction control with increasing reagent concentration. Signup and view all the answers

What is the equation for the activation energy using two temperatures?

$E_a = R\cdot T_A - R\cdot T_B$ Signup and view all the answers

What are the steps involved in solid-fluid reactions? Explain each step briefly.

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. Signup and view all the answers

What does Fick's First Law state? Write the equation for the diffusion flux.

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. Signup and view all the answers

When does Fick's Second Law apply? Write the equation for the diffusion flux in the case of unsteady-state diffusion.

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. Signup and view all the answers

What determines the overall rate of a heterogeneous reaction? Explain.

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. Signup and view all the answers

How is the rate of mass transfer defined in comparison to the rate of chemical reaction? Provide the equations.

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. Signup and view all the answers

What is the relationship between Sherwood number (Sh) and Reynolds number (Re)?

Sh = 2.0 + 0.6Re^{1/2} Signup and view all the answers

What is the relationship between Sherwood number (Sh) and Schmidt number (Sc)?

Sh = 2.0 + 0.6Re^{1/2}Sc^{1/3} Signup and view all the answers

What is the equation for the steady-state concentration of species A (Cs) in terms of the reaction rate constant (ks) and the bulk concentration of species B (Cb)?

Cs = -\frac{ks}{km + ks}Cb Signup and view all the answers

What is the equation for the overall reaction rate (rA) in a porous solid where the reaction is influenced by pore diffusion?

rA = -D\nabla CA Signup and view all the answers

What is the equation for the overall reaction rate (rA) when external mass transfer offers no resistance and reaction rate is chemical reaction controlled?

rA = -ksCb Signup and view all the answers