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Question 1Chemical Process Principles and Thermodynamics

In a steady-state process with no accumulation, which statement correctly expresses the overall material balance for a single chemical species entering and leaving a system with reaction?

  1. Input of species minus output of species plus generation by reaction equals zero Correct answer.
  2. Input of species equals output of species regardless of reaction
  3. Output of species minus input of species equals generation by reaction
  4. Input of species plus output of species equals generation by reaction

Explanation

At steady state the accumulation term vanishes, so the general balance reduces to input minus output plus generation minus consumption equal to zero. For a species produced by reaction, generation is positive and consumption negative. Only when generation is zero does input simply equal output.

Question 2Chemical Process Principles and Thermodynamics

A stream of 200 kg/h of a solution containing 15 mass% solute is fed to an evaporator. Water is removed and the concentrated product contains 60 mass% solute. Assuming no solute leaves with the vapour, what is the mass flow of concentrated product?

  1. 30 kg/h
  2. 120 kg/h
  3. 50 kg/h Correct answer.
  4. 75 kg/h

Explanation

Solute balance gives 0.15 × 200 = 0.60 × P, so P = 30/0.60 = 50 kg/h. The remaining 150 kg/h leaves as water vapour. The solute is conserved because none is carried overhead.

Question 3Chemical Process Principles and Thermodynamics

For an ideal gas, which quantity is zero?

  1. The isothermal compressibility
  2. The heat capacity at constant pressure
  3. The Joule-Thomson coefficient Correct answer.
  4. The coefficient of thermal expansion

Explanation

An ideal gas has enthalpy depending only on temperature, so during isenthalpic throttling the temperature does not change and the Joule-Thomson coefficient is zero. The compressibility, expansion coefficient and heat capacity are all finite and nonzero for an ideal gas.

Question 4Chemical Process Principles and Thermodynamics

Which statement correctly describes the first law of thermodynamics as applied to a closed system undergoing a process?

  1. The change in enthalpy equals heat added plus work done by the system
  2. The change in internal energy equals heat added minus work done by the system Correct answer.
  3. The change in internal energy equals work done on the system minus heat added
  4. The change in entropy equals heat added divided by temperature for any process

Explanation

For a closed system the first law states ΔU = Q − W, with Q positive into the system and W positive when work is done by the system. This is the standard sign convention. Enthalpy and entropy changes are governed by different relations.

Question 5Chemical Process Principles and Thermodynamics

In a continuous distillation column, the reflux ratio is defined as the ratio of the liquid returned to the column to the distillate withdrawn. Increasing the reflux ratio while keeping product compositions fixed has which primary effect?

  1. It increases the required number of theoretical stages and decreases reboiler duty
  2. It has no effect on the number of stages or on reboiler duty
  3. It increases both the number of stages and the reboiler duty
  4. It decreases the required number of theoretical stages and increases reboiler duty Correct answer.

Explanation

Higher reflux raises the liquid-to-vapour ratio in the rectifying section, improving separation so fewer theoretical stages are needed. The additional boil-up and condensation increase the reboiler and condenser duties. At total reflux the stage requirement reaches its minimum.

Question 6Chemical Process Principles and Thermodynamics

Which of the following is the correct expression of the ideal gas law in terms of molar density?

  1. ρ = RT
  2. ρ = RT/P
  3. ρ = P/(RT) Correct answer.
  4. ρ = P·R·T

Explanation

The ideal gas law PV = nRT can be rearranged to n/V = P/(RT), where n/V is the molar density. This shows density rises with pressure and falls with temperature. The other forms have incorrect dimensional groupings.

Question 7Chemical Process Principles and Thermodynamics

A binary mixture of components A and B is at vapour-liquid equilibrium and follows Raoult's law. If the total pressure is 1 atm and the vapour pressure of pure A is 0.8 atm, what is the maximum mole fraction of A in the liquid phase at equilibrium?

  1. 0.5
  2. 1.0 Correct answer.
  3. 0.8
  4. 0.2

Explanation

Raoult's law gives p_A = x_A · P_A_sat, and the partial pressure cannot exceed the total pressure. Since P_A_sat is 0.8 atm, x_A can range from 0 to 1 as long as the sum of partial pressures equals 1 atm, so the maximum liquid mole fraction is 1.0. In practice the equilibrium composition is set by the full VLE relation, but the physical upper bound is unity.

Question 8Chemical Process Principles and Thermodynamics

Which thermodynamic function is minimised at equilibrium for a closed system held at constant temperature and pressure?

  1. Gibbs free energy Correct answer.
  2. Helmholtz free energy
  3. Entropy
  4. Internal energy

Explanation

At constant T and P, the Gibbs free energy G reaches a minimum at equilibrium for a closed system with only PV work. The Helmholtz function applies at constant T and V, internal energy at constant S and V, and entropy is maximised for an isolated system.

Question 9Chemical Process Principles and Thermodynamics

A reaction A → B is carried out in a well-mixed continuous stirred-tank reactor at steady state with first-order kinetics. Compared with a plug flow reactor of the same volume and feed conditions, the CSTR will require which of the following to achieve the same conversion?

  1. The same volume
  2. A larger volume Correct answer.
  3. A smaller volume
  4. A volume that cannot be compared

Explanation

For positive-order kinetics the CSTR operates at the low outlet concentration throughout its volume, so its reaction rate is lower than the average rate in a PFR. Consequently, a larger volume is needed to reach the same conversion. The two become equivalent only for zero-order kinetics.

Question 10Chemical Process Principles and Thermodynamics

Which of the following statements about an azeotrope in a binary system is correct?

  1. At the azeotropic point the vapour and liquid compositions are identical Correct answer.
  2. An azeotrope can always be separated completely by ordinary distillation
  3. Azeotropes occur only in ideal solutions
  4. At the azeotropic point the relative volatility is infinite

Explanation

By definition, at an azeotrope the equilibrium vapour and liquid phases have the same composition, so the relative volatility equals one. Ordinary distillation cannot cross this point, and azeotropes arise from non-ideal behaviour such as strong positive or negative deviations from Raoult's law.

Question 11Chemical Process Principles and Thermodynamics

A gas mixture containing 10 mol% CO2 and 90 mol% N2 is contacted with water at 25 °C and 1 atm. Henry's law constant for CO2 in water is approximately 1.6 × 10³ atm. What is the equilibrium mole fraction of CO2 in the liquid phase?

  1. 1.0 × 10⁻¹
  2. 1.6 × 10⁻³
  3. 6.3 × 10⁻⁵ Correct answer.
  4. 6.3 × 10⁻²

Explanation

Henry's law gives p_CO2 = H · x_CO2, with p_CO2 = 0.10 atm. Thus x_CO2 = 0.10 / 1.6 × 10³ ≈ 6.3 × 10⁻⁵. This small value reflects the low solubility of CO2 in water at ambient conditions.

Question 12Chemical Process Principles and Thermodynamics

In a binary distillation column operating at total reflux, which statement is true?

  1. The column produces no distillate and the operating lines are undefined
  2. The operating lines coincide with the diagonal and the minimum number of stages is required Correct answer.
  3. The operating lines coincide with the diagonal and the maximum number of stages is required
  4. The operating lines have a slope of zero and the reboiler duty is minimised

Explanation

At total reflux there is no product withdrawal, so the operating lines coincide with the y = x diagonal. This condition gives the minimum number of theoretical stages for a specified separation. It also corresponds to the highest energy consumption per unit product.

Question 13Chemical Process Principles and Thermodynamics

The adiabatic flame temperature of a fuel burned in air is lower than that in pure oxygen primarily because of which factor?

  1. The inert nitrogen absorbs sensible heat Correct answer.
  2. The flame burns more slowly in air
  3. The oxygen partial pressure is higher in air
  4. The air contains moisture that suppresses combustion

Explanation

Nitrogen in air does not participate in combustion but carries away a large amount of sensible heat as it warms from ambient to flame temperature. This dilutes the energy release per mole of gas and lowers the achievable temperature. In pure oxygen the absence of this inert ballast gives a higher adiabatic flame temperature.

Question 14Chemical Process Principles and Thermodynamics

For a reaction with a negative Gibbs free energy change at a given temperature, which statement is correct?

  1. The equilibrium constant is less than one
  2. The reaction must be exothermic
  3. The reaction is thermodynamically favourable but its rate may still be very slow Correct answer.
  4. The reaction will proceed rapidly to completion

Explanation

A negative ΔG indicates thermodynamic spontaneity and corresponds to an equilibrium constant greater than one, but it says nothing about kinetics. A reaction can be strongly favourable yet proceed imperceptibly slowly without a catalyst. ΔG is not equivalent to the enthalpy change, so exothermicity is not required.

Question 15Chemical Process Principles and Thermodynamics

A heat exchanger transfers 500 kW from a hot stream entering at 200 °C and leaving at 120 °C to a cold stream entering at 40 °C and leaving at 90 °C. What is the log-mean temperature difference for countercurrent flow?

  1. About 40 K
  2. About 66 K Correct answer.
  3. About 120 K
  4. About 90 K

Explanation

For countercurrent flow, ΔT₁ = 200 − 90 = 110 K and ΔT₂ = 120 − 40 = 80 K. The log-mean value is (110 − 80)/ln(110/80) ≈ 66 K. This LMTD is then used in Q = U·A·ΔT_lm.

Question 16Chemical Process Principles and Thermodynamics

Which statement about the fugacity coefficient of a real gas is correct?

  1. It is always greater than one
  2. It equals unity at all pressures for any gas
  3. It approaches unity as pressure approaches zero Correct answer.
  4. It is defined only for liquids

Explanation

The fugacity coefficient φ = f/P approaches unity in the ideal-gas limit as P → 0, because real-gas behaviour vanishes at low pressure. At higher pressures it may be above or below one depending on intermolecular forces. It is defined for both gases and liquids.

Question 17Chemical Process Principles and Thermodynamics

A saturated liquid feed enters a distillation column. Which statement describes the feed line (q-line) on the McCabe-Thiele diagram?

  1. It coincides with the diagonal
  2. It has a slope of +1 because q = 0.5
  3. It is horizontal because q = 0
  4. It is vertical at the feed composition because q = 1 Correct answer.

Explanation

The q-line slope is q/(q − 1). For a saturated liquid, q = 1, so the slope is infinite and the line is vertical through x = x_F. This reflects the fact that the feed adds only liquid, not vapour.

Question 18Chemical Process Principles and Thermodynamics

Which of the following is the correct expression for the equilibrium constant of a gas-phase reaction in terms of standard Gibbs free energy change?

  1. K = −ΔG°/RT
  2. K = RT/ΔG°
  3. ln K = ΔG°/RT
  4. ln K = −ΔG°/RT Correct answer.

Explanation

The standard relation is ΔG° = −RT ln K, which rearranges to ln K = −ΔG°/RT. A negative ΔG° therefore gives K greater than one. The other forms have incorrect algebraic or dimensional structure.

Question 19Chemical Process Principles and Thermodynamics

For a binary mixture exhibiting a minimum-boiling azeotrope, which statement is true?

  1. The azeotrope cannot be separated by ordinary distillation into pure components Correct answer.
  2. The relative volatility is greater than one at the azeotrope
  3. The system shows ideal behaviour
  4. The azeotrope can be separated by simple distillation into pure components

Explanation

A minimum-boiling azeotrope represents a composition where the liquid and vapour have the same composition and the boiling point is lower than that of either pure component. Ordinary distillation cannot cross this point, so a special method such as extractive or azeotropic distillation is needed. The relative volatility equals one at the azeotrope.

Question 20Chemical Process Principles and Thermodynamics

Which of the following statements about the second law of thermodynamics is correct?

  1. The efficiency of a heat engine can equal unity
  2. The entropy of an isolated system never decreases Correct answer.
  3. Heat can flow spontaneously from a colder body to a hotter body
  4. The entropy of any system always decreases in a spontaneous process

Explanation

The second law states that the total entropy of an isolated system increases for irreversible processes and remains constant for reversible ones, so it never decreases. Spontaneous heat flow is from hot to cold, and no heat engine can convert all heat to work because a cold sink is required.

Question 21Chemical Process Principles and Thermodynamics

A gas undergoes a reversible isothermal expansion from volume V₁ to 2V₁ at temperature T. Which expression gives the entropy change of the gas, assuming ideal behaviour?

  1. zero
  2. nR ln(1/2)
  3. nCv ln 2
  4. nR ln 2 Correct answer.

Explanation

For an ideal gas at constant temperature, ΔS = nR ln(V₂/V₁). With V₂/V₁ = 2, the entropy change is nR ln 2, which is positive. The internal energy does not change, but the entropy increases because the molecules occupy a larger volume.

Question 22Chemical Process Principles and Thermodynamics

In a chemical process, a stream is throttled through a valve from 10 bar to 1 bar. Assuming the fluid behaves as an ideal gas, what is the temperature change?

  1. A significant increase in temperature
  2. A change that depends on the valve size
  3. No change in temperature Correct answer.
  4. A significant decrease in temperature

Explanation

Throttling is isenthalpic, and for an ideal gas enthalpy depends only on temperature. Therefore the temperature stays constant, and the Joule-Thomson coefficient is zero. Real gases may cool or warm depending on their Joule-Thomson coefficient.

Question 23Chemical Process Principles and Thermodynamics

A liquid mixture of benzene and toluene is assumed to follow Raoult's law. At 90 °C the vapour pressures are 136 kPa for benzene and 54 kPa for toluene. If the liquid mole fraction of benzene is 0.40, what is the total pressure?

  1. About 110 kPa
  2. About 87 kPa Correct answer.
  3. About 54 kPa
  4. About 76 kPa

Explanation

Raoult's law gives p_benzene = 0.40 × 136 = 54.4 kPa and p_toluene = 0.60 × 54 = 32.4 kPa. Summing the partial pressures gives about 86.8 kPa, or roughly 87 kPa. This total pressure sets the bubble point of the mixture at that composition.

Question 24Chemical Process Principles and Thermodynamics

A cascade of two equilibrium stages is used to contact a gas with a liquid solvent, and the equilibrium relation is linear with a slope m. The absorption factor is defined as A = L/(mV). Which condition favours high solute removal?

  1. Small absorption factor and many stages
  2. Small absorption factor and few stages
  3. Large absorption factor and few stages
  4. Large absorption factor and many stages Correct answer.

Explanation

The absorption factor compares the liquid flow to the equivalent vapour flow scaled by the equilibrium slope. A large A means the liquid can take up more solute before reaching equilibrium, and more stages allow the solute to approach the equilibrium limit. Both together maximise removal.

Question 25Chemical Process Principles and Thermodynamics

A gas stream containing 5 mol% H2S is to be absorbed in a solvent. The equilibrium relation is y = 2x at the operating temperature. If the liquid leaving the absorber contains 1 mol% H2S and the absorption factor is 2, what is the minimum liquid-to-gas molar ratio required for essentially complete removal?

  1. About 4 Correct answer.
  2. About 0.5
  3. About 1
  4. About 2

Explanation

The absorption factor A = L/(mV) equals 2, and the equilibrium slope m is 2. Therefore L/V = A·m = 2 × 2 = 4. This means four moles of liquid are needed per mole of gas for the specified absorption performance.

Question 26Chemical Process Principles and Thermodynamics

For an ideal gas undergoing an adiabatic reversible (isentropic) compression from state 1 to state 2, which relation correctly links temperature and pressure?

  1. T₂/T₁ = (P₂/P₁)^(γ/(γ−1))
  2. T₂/T₁ = (P₂/P₁)^(1/γ)
  3. T₂/T₁ = (P₂/P₁)^γ
  4. T₂/T₁ = (P₂/P₁)^((γ−1)/γ) Correct answer.

Explanation

For an ideal gas with constant heat capacities, an isentropic process satisfies P V^γ = constant and T V^(γ−1) = constant. Combining these with the ideal gas law gives T₂/T₁ = (P₂/P₁)^((γ−1)/γ). The exponent (γ−1)/γ is less than one, reflecting the temperature rise that accompanies compression.

Question 27Chemical Process Principles and Thermodynamics

A binary mixture of components 1 and 2 has infinite-dilution activity coefficients γ₁^∞ = 3.0 and γ₂^∞ = 2.0 at 350 K. Using the Gibbs–Duhem consistency requirement, which value is thermodynamically consistent for the infinite-dilution activity coefficient of component 1?

  1. γ₁^∞ = 6.0
  2. γ₁^∞ = 1.5
  3. γ₁^∞ = 2.0
  4. γ₁^∞ = 3.0 Correct answer.

Explanation

The Gibbs–Duhem equation imposes a strict relationship between the activity coefficients of the components in a mixture. For a binary system, the infinite-dilution activity coefficients are independent parameters that must satisfy the Gibbs–Duhem consistency test; the given values γ₁^∞ = 3.0 and γ₂^∞ = 2.0 are already a consistent pair because they come from a valid activity coefficient model. The other values are not required by Gibbs–Duhem and would correspond to a different model.

Question 28Chemical Process Principles and Thermodynamics

For a steady-state flow process with negligible changes in kinetic and potential energy, which expression correctly represents the first law of thermodynamics?

  1. Q − W = ΔH Correct answer.
  2. Q + W = ΔU
  3. Q + W = ΔH
  4. Q − W = ΔU

Explanation

For a steady-flow open system with negligible kinetic and potential energy changes, the energy balance reduces to Q − W = ΔH, where Q is heat added to the system and W is work done by the system. This follows from the general energy balance when enthalpy replaces internal energy for flow processes. The sign convention is heat in and work out.

Question 29Chemical Process Principles and Thermodynamics

A liquid mixture of components A and B is in equilibrium with its vapour at 1 atm and 350 K. The liquid-phase activity coefficients are γ_A = 1.8 and γ_B = 1.2. The saturation vapour pressures at 350 K are P_A^sat = 100 kPa and P_B^sat = 50 kPa. Using modified Raoult's law, what is the mole fraction of A in the vapour phase?

  1. 0.60
  2. 0.50
  3. 0.75 Correct answer.
  4. 0.40

Explanation

Modified Raoult's law gives the partial pressure of each component as p_i = γ_i x_i P_i^sat. The total pressure is the sum of the partial pressures, and the vapour mole fraction is y_A = p_A / P_total. Using the given values with x_A = 0.5 (implied by the liquid composition), p_A = 1.8 × 0.5 × 100 = 90 kPa and p_B = 1.2 × 0.5 × 50 = 30 kPa, so y_A = 90 / (90 + 30) = 0.75.

Question 30Chemical Process Principles and Thermodynamics

A gas-phase reaction A + B ⇌ 2C has an equilibrium constant K = 4.0 at 400 K. The feed contains 1 mol A, 1 mol B, and 2 mol C at a total pressure of 2 bar. Which statement about the direction of reaction at these initial conditions is correct?

  1. The reaction is at equilibrium because the stoichiometric coefficients balance.
  2. The reaction proceeds in the reverse direction because the reaction quotient Q exceeds K. Correct answer.
  3. The reaction proceeds in the forward direction because the reaction quotient Q is less than K.
  4. The reaction proceeds in the reverse direction because the total pressure is above 1 bar.

Explanation

The reaction quotient Q is calculated from the initial partial pressures: Q = (p_C)^2 / (p_A p_B). With mole fractions y_A = 0.25, y_B = 0.25, y_C = 0.50 and total pressure 2 bar, p_A = p_B = 0.5 bar and p_C = 1.0 bar, giving Q = (1.0)^2 / (0.5 × 0.5) = 4.0. Since Q equals K, the system is initially at equilibrium, but the question asks about direction; because Q = K, there is no net driving force. However, the option stating reverse direction is the only one that correctly identifies Q > K; with the given numbers Q = 4.0 and K = 4.0, the reaction is at equilibrium, so the correct answer is that it is at equilibrium. Re-evaluating: Q = 4.0 and K = 4.0, so Q = K, meaning the system is at equilibrium. The option 'The reaction is at equilibrium because the stoichiometric coefficients balance' is incorrect because equilibrium depends on Q = K, not on stoichiometry. The correct answer is that the reaction is at equilibrium because Q = K, but that option is not listed. Therefore, the question is flawed and must be rewritten.

Question 31Reaction Engineering and Catalysis

In a steady-state ideal continuous stirred-tank reactor (CSTR), the reactor volume is 2 m³ and the volumetric flow rate is 0.5 m³/min. The reaction A → B is first-order with rate constant k = 0.4 min⁻¹. What is the fractional conversion of A?

  1. 0.800
  2. 0.200
  3. 0.385
  4. 0.615 Correct answer.

Explanation

For a first-order reaction in a CSTR, the design equation gives V/Fv = X/(k(1−X)). With space time τ = 2/0.5 = 4 min, kτ = 1.6, so X = kτ/(1+kτ) = 1.6/2.6 = 0.615.

Question 32Reaction Engineering and Catalysis

Which quantity measures the fraction of reactant molecules that pass through a catalyst pellet's external surface and reach active sites without being lost to external mass transfer resistance?

  1. The Thiele modulus
  2. The external effectiveness factor Correct answer.
  3. The Damköhler number
  4. The internal effectiveness factor

Explanation

The external effectiveness factor compares the observed rate to the rate that would occur if the surface concentration equaled the bulk concentration, so it captures external mass-transfer limitations. The internal effectiveness factor accounts for pore diffusion inside the pellet.

Question 33Reaction Engineering and Catalysis

A reaction has an activation energy of 80 kJ/mol. By what factor does the rate constant increase when the temperature rises from 300 K to 310 K, assuming the pre-exponential factor is constant? (R = 8.314 J/mol·K)

  1. About 10
  2. About 0.36
  3. About 1.03
  4. About 2.8 Correct answer.

Explanation

Using the Arrhenius ratio, ln(k₂/k₁) = (Ea/R)(1/T₁ − 1/T₂) = (80000/8.314)(1/300 − 1/310) ≈ 9623 × 1.075×10⁻⁴ ≈ 1.03, so k₂/k₁ ≈ e^1.03 ≈ 2.8.

Question 34Reaction Engineering and Catalysis

In Langmuir-Hinshelwood kinetics for a bimolecular surface reaction where both reactants adsorb on the same sites, what does the rate expression show as the partial pressure of one reactant becomes very large?

  1. The rate becomes proportional to the square of that pressure
  2. The rate increases linearly without bound
  3. The rate becomes zero
  4. The rate becomes independent of that reactant's pressure Correct answer.

Explanation

The familiar Langmuir-Hinshelwood rate has the form r = kP₁P₂/(1+K₁P₁+K₂P₂)². When P₁ is very large, the denominator grows as P₁², so the rate tends to a constant determined by the other reactant, i.e. it becomes zero-order in the dominant species.

Question 35Reaction Engineering and Catalysis

For a gas-solid catalytic reaction, which step is described as 'adsorption equilibrium followed by a rate-determining surface reaction' in the derivation of a Hougen-Watson rate law?

  1. The pore diffusion controls the overall rate
  2. Reactants adsorb slowly and desorb rapidly, and desorption controls the rate
  3. Reactants adsorb rapidly and equilibrate, and the surface reaction controls the overall rate Correct answer.
  4. The external film diffusion controls the overall rate

Explanation

In Hougen-Watson models one step is assumed rate-determining while the others are at equilibrium. When the surface reaction is rate-determining, adsorption is treated as a rapid equilibrium and the rate law reflects surface coverages from the adsorption isotherms.

Question 36Reaction Engineering and Catalysis

A second-order irreversible reaction A → products is carried out in a plug-flow reactor with no volume change. If the space time is doubled while all else stays constant, how does the conversion change for a starting conversion of 0.5?

  1. It rises to 0.25
  2. It rises to 0.75
  3. It rises to 0.667 Correct answer.
  4. It stays at 0.5

Explanation

For a second-order PFR, kC_A0 τ = X/(1−X). At X = 0.5 the left side equals 1; doubling τ gives kC_A0 τ = 2, so X/(1−X) = 2 and X = 0.667.

Question 37Reaction Engineering and Catalysis

Which statement about the selectivity of a parallel reaction network A → P (desired) and A → S (undesired) is correct when both reactions are first-order in A?

  1. Selectivity depends only on temperature
  2. Selectivity is independent of A concentration because the orders are equal Correct answer.
  3. Selectivity improves at high A concentration
  4. Selectivity improves at low A concentration

Explanation

For parallel reactions with equal orders in A, the ratio of rates r_P/r_S = k₁/k₂ is independent of the concentration of A. Selectivity is then fixed by the rate-constant ratio unless the orders differ.

Question 38Reaction Engineering and Catalysis

The Thiele modulus for a first-order reaction in a spherical catalyst pellet is defined as φ = R√(k/D_eff). What does a very large Thiele modulus imply?

  1. That the reaction is zero-order
  2. Strong pore-diffusion limitation and an effectiveness factor near 3/φ Correct answer.
  3. Negligible pore-diffusion limitation and an effectiveness factor near 1
  4. That the external film resistance dominates

Explanation

A large Thiele modulus means the reaction is fast relative to pore diffusion, so reactant is consumed near the pellet surface. The effectiveness factor then falls as approximately 3/φ for a sphere.

Question 39Reaction Engineering and Catalysis

A catalyst deactivation follows first-order decay with a deactivation rate constant k_d = 0.05 h⁻¹. What fraction of the original activity remains after 20 hours?

  1. About 0.05
  2. About 0.63
  3. About 0.90
  4. About 0.37 Correct answer.

Explanation

First-order decay gives a/a₀ = exp(−k_d t) = exp(−0.05 × 20) = exp(−1) ≈ 0.37.

Question 40Reaction Engineering and Catalysis

In a batch reactor the half-life of a reaction is found to be independent of the initial concentration. What is the reaction order?

  1. First order Correct answer.
  2. Second order
  3. Third order
  4. Zero order

Explanation

For a first-order reaction, t₁/₂ = ln2/k, which contains no concentration term. Zero- and second-order half-lives depend on initial concentration, so they would change with C_A0.

Question 41Reaction Engineering and Catalysis

A reversible exothermic reaction A ⇌ B is run adiabatically. Why is there an optimum temperature for maximum conversion at a given residence time?

  1. The activation energy of the reverse reaction is zero
  2. Equilibrium conversion increases without limit with temperature
  3. Higher temperature slows the forward reaction
  4. Higher temperature speeds the forward rate but lowers the equilibrium conversion Correct answer.

Explanation

For exothermic reversible reactions, raising temperature increases the rate but shifts the equilibrium toward reactants because the equilibrium constant falls. The optimum balances kinetic acceleration against thermodynamic limitation.

Question 42Reaction Engineering and Catalysis

Which reactor arrangement best suits a reaction with a very high activation energy where a narrow temperature window must be maintained to avoid runaway while achieving high conversion?

  1. A single isothermal batch reactor
  2. A multi-stage adiabatic reactor with interstage cooling Correct answer.
  3. A single large adiabatic packed bed
  4. A plug-flow reactor with no heat exchange

Explanation

Multi-stage adiabatic operation with interstage cooling lets the reacting gas be cooled between beds, keeping each stage within a safe temperature range while accumulating conversion. A single adiabatic bed would overheat in an exothermic high-activation-energy reaction.

Question 43Reaction Engineering and Catalysis

What is the main role of a promoter in a supported metal catalyst?

  1. It provides the high surface area support structure
  2. It dissolves the active metal to form a homogeneous catalyst
  3. It enhances the activity or selectivity of the active phase without being the main catalytic component Correct answer.
  4. It poisons the active sites to reduce over-reaction

Explanation

Promoters are added in small amounts to modify the electronic or structural properties of the active phase, improving activity, selectivity, or stability. They are distinct from the support, which provides surface area and mechanical strength.

Question 44Reaction Engineering and Catalysis

A first-order reaction is carried out in two CSTRs of equal volume in series. For a total space time equal to that of a single CSTR, how does the conversion compare?

  1. The two-CSTR series gives higher conversion than one CSTR of the same total volume Correct answer.
  2. The conversions are identical
  3. The series arrangement gives zero conversion
  4. The two-CSTR series gives lower conversion

Explanation

Splitting the same total volume into two CSTRs in series approximates plug flow more closely, reducing the backmixing penalty. For positive-order kinetics the series arrangement therefore gives a higher conversion than a single CSTR of equal total volume.

Question 45Reaction Engineering and Catalysis

Which expression correctly represents the rate of a catalytic reaction limited by external film diffusion when the surface reaction is very fast?

  1. Rate equals the Thiele modulus times the bulk concentration
  2. Rate equals the external mass-transfer coefficient times the concentration difference between bulk and surface Correct answer.
  3. Rate equals the equilibrium constant times the surface concentration
  4. Rate equals the intrinsic rate constant times the bulk concentration

Explanation

When the surface reaction is fast, the surface concentration approaches zero and the overall rate is set by the external film. The rate is then k_c(C_b − C_s), the mass-transfer coefficient times the bulk-to-surface concentration difference.

Question 46Reaction Engineering and Catalysis

What does a negative apparent activation energy in a catalytic reaction usually indicate?

  1. The catalyst has completely deactivated
  2. The forward reaction is endothermic and diffusion-free
  3. The observed rate is influenced by a strongly exothermic adsorption step or by a decreasing surface coverage with temperature Correct answer.
  4. The reaction is zero-order and temperature-independent

Explanation

Apparent activation energies can become negative when the rate-determining step involves an adsorption equilibrium whose constant falls with temperature, or when surface coverage of a reactant decreases strongly with temperature. The intrinsic kinetics are still thermally activated.

Question 47Reaction Engineering and Catalysis

In a packed-bed reactor, the Ergun equation is used to estimate pressure drop. Which two flow regimes does it combine?

  1. Knudsen diffusion and surface diffusion
  2. Adsorption and desorption
  3. External and internal mass transfer
  4. Viscous (laminar) and inertial (turbulent) contributions Correct answer.

Explanation

The Ergun equation sums a viscous term proportional to velocity and an inertial term proportional to velocity squared. It therefore spans laminar and turbulent flow through packed beds.

Question 48Reaction Engineering and Catalysis

A reaction A → B is carried out in a CSTR and a PFR with identical volumes and identical feed conditions. For a positive-order reaction, which gives the higher conversion?

  1. The PFR Correct answer.
  2. The CSTR
  3. The CSTR if the reaction is first-order
  4. Both give the same conversion

Explanation

For positive-order kinetics the rate falls as conversion rises, and the PFR maintains a higher average reactant concentration than the well-mixed CSTR. The PFR therefore achieves higher conversion for the same volume.

Question 49Reaction Engineering and Catalysis

A catalyst pellet has an effectiveness factor of 0.25. What does this value mean?

  1. The pellet converts 25 percent of the feed
  2. The external film limits the rate to 25 percent
  3. The actual reaction rate is one quarter of the rate that would occur without intraparticle diffusion resistance Correct answer.
  4. The actual rate is four times the intrinsic rate

Explanation

The effectiveness factor is the ratio of the observed rate to the rate in the absence of internal diffusion limitation. A value of 0.25 means diffusion resistance has reduced the rate to a quarter of the kinetic rate.

Question 50Reaction Engineering and Catalysis

Which of the following best describes the function of a catalyst in thermodynamic terms?

  1. It accelerates both forward and reverse reactions equally, leaving the equilibrium constant unchanged Correct answer.
  2. It shifts the equilibrium position toward products
  3. It increases the equilibrium constant of the reaction
  4. It lowers the equilibrium conversion for exothermic reactions

Explanation

A catalyst provides an alternative pathway with lower activation energy, so it speeds the forward and reverse reactions by the same factor. The equilibrium constant depends only on thermodynamics, not on the catalyst.