The Shrinking Core Model

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According to the text, what is the purpose of selecting a reaction model in the design of reaction systems?

To represent actual conditions
To closely correspond to what actually takes place
To accurately predict and describe the actual kinetics (correct)
To simplify the mathematical complexities

What type of reaction model is considered when the particle size decreases as the reaction proceeds with time?

Gasification Model
Shrinking Core Model
Dissolution Model
Shrinking Particle Model (correct)

In the reaction equation A(fluid) + bB(solid) = cR (fluid) + dD(removable solid), what does 'b' represent?

The stoichiometric coefficient of R
The stoichiometric coefficient of A
The stoichiometric coefficient of D
The stoichiometric coefficient of B (correct)

Which factor determines the rate expression of a reaction according to the given text?

The shape of the particle (C) Signup and view all the answers

What is the equation for the reaction rate assuming first-order reaction?

$\frac{d[A]}{d[B]} = -4\pi\rho_B \cdot r_c^2$ (D) Signup and view all the answers

In the reaction of a single porous particle, when no solid product is formed and diffusion offers no resistance, what influences the overall reaction?

Pore diffusion (D) Signup and view all the answers

In the grain model, what assumption is made about the resistance due to external mass transfer?

It is negligible (C) Signup and view all the answers

Which of the following is the correct equation for finding the area of a rectangle?

$A = l imes w$ (C) Signup and view all the answers

What is the value of $x$ in the equation $3x + 5 = 20$?

$x = 8$ (D) Signup and view all the answers

What is the slope of the line passing through the points (2, 5) and (4, 9)?

$m = 2$ (A) Signup and view all the answers

What is the value of $x$ in the equation $2(x - 3) = 10$?

$x = 8$ (B) Signup and view all the answers

What is the value of $x$ in the equation $5x - 8 = 12$?

$x = 6$ (D) Signup and view all the answers

Which equation represents the mass balance for solid reactant B within each solid grain?

$-\rho_B \frac{dC_B}{dt} = b k_s C_B$ (B) Signup and view all the answers

What is the relationship between time and conversion given by the solution?

$t^* \approx gFg(x) + \sigma^2 Fp(x)$ (A), $t^* \approx gFg(x) + \sigma^2 Fp(x)$ (B), $t^* \approx gFg(x) + \sigma^2 Fp(x)$ (C), $t^* \approx gFg(x) + \sigma^2 Fp(x)$ (D) Signup and view all the answers

Which reactor type is commonly used in metallurgical reactions?

Continuous Flow Stirred Tank Reactor (CFSTR) (B) Signup and view all the answers

What is the purpose of reactor design?

To determine the size of the reactor (D) Signup and view all the answers

According to the text, which factors may control the overall process in the Shrinking Core Model?

All of the above (D) Signup and view all the answers

What is the equation for the rate of external mass transport across the boundary layer in the Shrinking Core Model?

$-r_B = \frac{1},{4\pi r_o} \frac{dn_B},{dt} = \frac{b},{k_m} (C_b - C_s)$ (C), $-r_B = \frac{1},{4\pi r_o} \frac{dn_B},{dt} = \frac{b},{k_m} (C_b - C_s)$ (D) Signup and view all the answers

What is the equation for the rate of disappearance of B in the Shrinking Core Model?

$-dn_B = -b \frac{dn_A},{dt} = -\rho_B \frac{dV},{dt} = -4\pi\rho_B r_c^2 \frac{dr_c},{dt}$ (A), $-dn_B = -b \frac{dn_A},{dt} = -\rho_B \frac{dV},{dt} = -4\pi\rho_B r_c^2 \frac{dr_c},{dt}$ (B) Signup and view all the answers

What is the equation for the change in the unreacted core with time in the Shrinking Core Model?

$r^2 \frac{dC_o},{dt} - \rho_B \int_{r_o}^{r_c} \frac{C_b - C},{r_c^2} dr_c = \frac{bD_eC_b},{3} \int_0^t dt$ (C) Signup and view all the answers

Which of the following reactions is an example of a case where a product is formed on the surface of the particle and reaction takes place at the interface between the product layer and the unreacted core?

Reduction of metal oxides (D) Signup and view all the answers

What is the main location of the reaction in a case where a product is formed on the surface of the particle and reaction takes place at the interface between the product layer and the unreacted core?

At the interface between the product layer and the unreacted core (B) Signup and view all the answers

Which of the following is NOT an example of a case where a product is formed on the surface of the particle and reaction takes place at the interface between the product layer and the unreacted core?

Oxidation of metals (A) Signup and view all the answers