Chemical Reaction Engineering — Part 1 MCQs with Explanations

For a first-order reaction, the relationship between time and conversion can be derived using the half-life formula. The half-life (t 1/2 ) of a first-order reaction is constant and is given by: t 1/2 = 0.693 / k Let the initial concentration be C 0 and concentration at time t be C. Using the first-order equation: C = C 0 * e -kt If t = 3 * t 1/2 , then: C / C 0 = e -k(3t 1/2 ) = e -3 * 0.693 = e -2.079 ≈ 0.125 Conversion (X) = 1 - (C / C 0 ) = 1 - 0.125 = 0.875 Therefore, the conversion at time equal to three times the half-life is 0.875. Alternate Solution First-order reactions have a special property: their half-life (t 1/2 ) is constant. This means it always takes the same amount of time for half of the reactant to be consumed, regardless of the initial amount. The question states the time is three times the half-life (3 * t 1/2 ) . Let's break it down step-by-step: After 1 half-life (t 1/2 ), the conversion is 50% (0.5). After 2 half-lives (2 * t 1/2 ), half of the remaining reactant is converted. So, half of 0.5 (which is 0.25) is converted, resulting in a total conversion of 0.5 + 0.25 = 0.75. After 3 half-lives (3 * t 1/2 ), half of the remaining reactant is converted again. Half of what's left after 2 half lives = Half of 0.25 = 0.125 The total conversion after 3 half lives is 0.5 + 0.25 + 0.125 = 0.875 Therefore, the conversion after three half-lives is 0.875 . So the answer is: Option A: 0.875

In chemical reaction engineering , the energy balance for a tubular reactor under transient (unsteady-state) conditions involves time-dependent and position-dependent variables such as temperature and concentration. This results in a balance that includes both time and spatial derivatives , making it a partial differential equation (PDE) . Due to the presence of temperature-dependent properties (like reaction rate constants, heat capacities, and heat generation terms), the equation typically contains non-linear terms . Therefore, the energy balance under these conditions is expressed as a non-linear partial differential equation . Option A: An ordinary non-linear differential equation is incorrect because it doesn't account for spatial variation. Option B: An algebraic differential equation is incorrect because the energy balance is not algebraic — it involves derivatives. Option C: A linear partial differential equation is incorrect because the equation is usually non-linear due to reaction kinetics and temperature dependencies. Correct answer: A non-linear partial differential equation.

Concept: In a solid-catalyzed reaction, reactant molecules must diffuse through the pores of the catalyst to reach the active sites where the reaction takes place. Pore diffusion control: When pore diffusion is the controlling step, the overall reaction rate is limited by the movement of reactants within the pores rather than by the surface reaction itself. Importance of porosity: Higher porosity provides more void space for reactant molecules to diffuse easily, reducing internal mass transfer resistance and improving access to active sites. Reason: If the porosity is low, diffusion is hindered, and a large portion of the catalyst's active surface remains underutilized, decreasing the overall efficiency of the catalyst. Conclusion: When pore diffusion controls the reaction, porosity is very important for effective catalyst performance.

According to the Arrhenius equation, the rate constant (k) increases with an increase in temperature. The Arrhenius equation is given by: $$k = A \exp \left( -\frac{E_a}{RT} \right)$$ . Here, k is the rate constant, A is the pre-exponential factor, E a is the activation energy, R is the gas constant, and T is the temperature in Kelvin. As the temperature T increases, the exponential term becomes larger, leading to an increase in the rate constant.

The molecularity of an elementary reaction represents the number of molecules or particles that come together to react and form the products. In the given elementary reaction: P + Q → R + S There are two reactant molecules (P and Q) that come together to form two product molecules (R and S). Therefore, the molecularity of this elementary reaction is 2 . So, the correct answer is Option B: 2 .

Option A: Always the same irrespective of the reaction This option suggests that the half-life period of a first-order reaction is always the same regardless of the reaction. This statement is correct. For a first-order reaction, the half-life period (t₁/₂) is constant and does not depend on the initial concentration of the reactants. Option B: Dependent on initial concentration of the reactants This option suggests that the half-life period of a first-order reaction depends on the initial concentration of the reactants. This statement is incorrect. The half-life of a first-order reaction is independent of the initial concentration and remains constant throughout the reaction. Option C: Proportional to the initial concentration of reactants This option suggests that the half-life period of a first-order reaction is proportional to the initial concentration of the reactants. This statement is incorrect. In a first-order reaction, the half-life is not proportional to the initial concentration; it remains constant regardless of the concentration. Option D: Half the specific rate constant This option suggests that the half-life period of a first-order reaction is half the specific rate constant. This statement is incorrect. The half-life of a first-order reaction is related to the rate constant (k) by the formula t₁/₂ = 0.693/k. It is not half the rate constant but rather a function of the rate constant. Conclusion: The correct answer is Option A: Always the same irrespective of the reaction because, for a first-order reaction, the half-life period is constant and does not depend on the initial concentration of the reactants.

Step 1: Understanding the given information. The reaction given is X → Y, and it follows the rate equation: Rate = k * C x n It is observed that when the concentration of 'X' is doubled, the reaction rate quadruples. Step 2: Setting up the rate equation. Let the initial concentration of 'X' be C x . The initial rate is: Rate 1 = k * (C x ) n When the concentration is doubled, the new rate is: Rate 2 = k * (2C x ) n Step 3: Establishing the relationship. Since it is given that the reaction rate quadruples: Rate 2 = 4 * Rate 1 Substituting the expressions: k * (2C x ) n = 4 * (k * (C x ) n ) Step 4: Solving for 'n'. Dividing both sides by k * (C x ) n : (2C x ) n / (C x ) n = 4 2 n = 4 Since 4 = 2 2 , we get: n = 2 Final Answer: The value of 'n' is 2. The correct answer is Option D: 2.

$$\frac{1}{{{{\text{k}}_{\text{e}}}{\text{ff}}}} = \frac{1}{{\text{k}}} + \frac{1}{{{{\text{k}}_{\text{g}}}}}$$ is the correct answer to “A first order gaseous phase reaction is catalysed by a non-porous solid. The kinetic rate constant and the external mass transfer co-efficients are k and $${{\text{k}}_{\text{g}}}$$ respectively. The effective rate constant (k e ff) is given by”. This question is standard in competitive examination syllabi for Chemical Reaction Engineering.

$$\frac{{0.693}}{{\text{K}}}$$ is the correct answer to “The half life period of a first order reaction is given by (where, K = rate constant. )”. This question is standard in competitive examination syllabi for Chemical Reaction Engineering.

Increases the speed of a is the correct answer to “Catalyst is a substance, which __________ chemical reaction.”. This question is standard in competitive examination syllabi for Chemical Reaction Engineering.

None of these is the correct answer to “A chemical reaction is of zero order, when the reaction rate is (where, CA = concentration of reactant)”. This question is standard in competitive examination syllabi for Chemical Reaction Engineering.

Slower rate of reaction is the correct answer to “Higher free energy of activation of a chemical reaction (at a given temperature) implies”. This question is standard in competitive examination syllabi for Chemical Reaction Engineering.

Free energy of activation is higher is the correct answer to “If the rate of a chemical reaction becomes slower at a given temperature, then the”. This question is standard in competitive examination syllabi for Chemical Reaction Engineering.

0 is the correct answer to “The eddy diffusivity for a liquid in plug flow must be”. This question is standard in competitive examination syllabi for Chemical Reaction Engineering.

CSTR is the correct answer to “The most suitable reactor for carrying out an auto-thermal reaction is a”. This question is standard in competitive examination syllabi for Chemical Reaction Engineering.

All of the above is the correct answer to “In an ideal tubular-flow reactor”. This question is standard in competitive examination syllabi for Chemical Reaction Engineering.

High pressure batch reactor is the correct answer to “A reactor is generally termed as an autoclave, when it is a”. This question is standard in competitive examination syllabi for Chemical Reaction Engineering.

Liquid phase reactions is the correct answer to “A batch reactor is suitable for”. This question is standard in competitive examination syllabi for Chemical Reaction Engineering.

< 0.5 is the correct answer to “If Thiele modulus is __________ , then the pore diffusion resistance in a catalyst may be considered as negligible.”. This question is standard in competitive examination syllabi for Chemical Reaction Engineering.

N2O2 ⇋ 2NO2 is the correct answer to “Which of the following chemical reactions will be favoured by low pressure”. This question is standard in competitive examination syllabi for Chemical Reaction Engineering.

Employs all the three phases (i.e.. .solid, liquid and gas) is the correct answer to “A trickle bed reactor is the one, which”. This question is standard in competitive examination syllabi for Chemical Reaction Engineering.

Irreversible is the correct answer to “Study of chemical kinetics is the easiest in the case of __________ reactions.”. This question is standard in competitive examination syllabi for Chemical Reaction Engineering.

Activation energy is the correct answer to “The catalyst in a first order chemical reaction changes the”. This question is standard in competitive examination syllabi for Chemical Reaction Engineering.

Conversion is the correct answer to “Limiting reactant in a chemical reaction decides the”. This question is standard in competitive examination syllabi for Chemical Reaction Engineering.

More energy is the correct answer to “In an exothermic chemical reaction, the reactants compared to the products have”. This question is standard in competitive examination syllabi for Chemical Reaction Engineering.

1.60 is the correct answer to “An isothermal aqueous phase reversible reaction, P ⇋ R, is to be carried out in a mixed flow reactor. The reaction rate in k.mole/m 3 .h is given by, r = 0.5C P - 0.125C R . A stream containing only P enters the”. This question is standard in competitive examination syllabi for Chemical Reaction Engineering.

d is the correct answer to “The time needed to achieve the same fractional conversion for particles of different sizes (d) when chemical reaction controls, is proportional to”. This question is standard in competitive examination syllabi for Chemical Reaction Engineering.

Molar concentration of the reactants is the correct answer to “According to the 'law of mass action', the rate of reaction is directly proportional to the”. This question is standard in competitive examination syllabi for Chemical Reaction Engineering.

∞ is the correct answer to “What is the dispersion number for a CSTR”. This question is standard in competitive examination syllabi for Chemical Reaction Engineering.

None of the above is the correct answer to “For an ideal mixed flow reactor (CSTR), the exit age distribution E(t) is given by”. This question is standard in competitive examination syllabi for Chemical Reaction Engineering.

All of the above is the correct answer to “Mean residence time is equal to the space time, when”. This question is standard in competitive examination syllabi for Chemical Reaction Engineering.

The time required to process one reactor volume of feed (measured at specified conditions) is 3 hours is the correct answer to “A space time of 3 hours for a flow reactor means that”. This question is standard in competitive examination syllabi for Chemical Reaction Engineering.

Semi-fluidised bed reactor is the correct answer to “Which of the following will give maximum gas conversion”. This question is standard in competitive examination syllabi for Chemical Reaction Engineering.

Single tubular flow reactor (v = 5 litres) is the correct answer to “For the same residence time, which one will give the maximum conversion”. This question is standard in competitive examination syllabi for Chemical Reaction Engineering.

Dehydration of ethanol is the correct answer to “A typical example of an exothermic reversible reaction conducted at high pressure in industry is”. This question is standard in competitive examination syllabi for Chemical Reaction Engineering.

No change is the correct answer to “Recycling back of outlet stream to the reactor from an ideal CSTR carrying out a first order liquid phase reaction will result in __________ in conversion.”. This question is standard in competitive examination syllabi for Chemical Reaction Engineering.

Sum of A & B is the correct answer to “Threshold energy in a reaction is equal to the”. This question is standard in competitive examination syllabi for Chemical Reaction Engineering.

No change is the correct answer to “In case of calcination of limestone, CaCO 3 CaO + CO 2 , the addition of more of CaO will result in __________ in the concentration of CO 2 .”. This question is standard in competitive examination syllabi for Chemical Reaction Engineering.

Remains unaffected is the correct answer to “The equilibrium constant of chemical reaction __________ in the presence of catalyst.”. This question is standard in competitive examination syllabi for Chemical Reaction Engineering.

Catalytic cracking is the correct answer to “From among the following, choose one which is not an exothermic process.”. This question is standard in competitive examination syllabi for Chemical Reaction Engineering.