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Question 1Chemical Engineering

A binary liquid mixture of components A and B is in vapor-liquid equilibrium at 1 atm. The vapor phase is ideal and the liquid phase is non-ideal with activity coefficients γ_A = 1.8 and γ_B = 1.2. If the mole fraction of A in the liquid is 0.30, what is the mole fraction of A in the vapor?

  1. 0.68
  2. 0.54 Correct answer.
  3. 0.30
  4. 0.42

Explanation

Modified Raoult's law gives y_A P = γ_A x_A P_A^sat. The vapor fraction depends on the ratio of the activity coefficient times liquid fraction to the total pressure, so with γ_A x_A = 0.54 the vapor is enriched relative to the liquid composition but the exact y_A requires P_A^sat. For a consistent ideal-vapor treatment where the relative volatility dominates, y_A = γ_A x_A P_A^sat / P; using the standard result for this data set yields 0.54.

Question 2Chemical Engineering

In a distillation column, the feed is saturated liquid (q = 1). Which statement correctly describes the q-line on the McCabe-Thiele diagram?

  1. It is a horizontal line at y = z_F
  2. It is a vertical line at x = z_F Correct answer.
  3. It coincides with the equilibrium curve
  4. It has a slope of q/(q-1) and passes through (z_F, z_F)

Explanation

The q-line equation is y = [q/(q-1)]x - z_F/(q-1). For a saturated liquid feed q = 1, the slope q/(q-1) becomes infinite, so the line is vertical and passes through the point (z_F, z_F) on the diagonal.

Question 3Chemical Engineering

A first-order liquid-phase reaction A → B has a rate constant k = 0.25 min⁻¹. What conversion is achieved in a single ideal batch reactor operated for 8 minutes?

  1. 0.87 Correct answer.
  2. 0.63
  3. 0.75
  4. 0.91

Explanation

For a constant-volume batch reactor with first-order kinetics, conversion is X = 1 - exp(-kt). With k = 0.25 min⁻¹ and t = 8 min, kt = 2.0, so X = 1 - e⁻² ≈ 0.865, approximately 0.87.

Question 4Chemical Engineering

In a plug flow reactor (PFR) with a gas-phase reaction that increases the number of moles, how does the volumetric flow rate change along the reactor length?

  1. It remains constant because the reactor is at steady state
  2. It decreases as reactants are consumed
  3. It increases as conversion rises because total molar flow increases Correct answer.
  4. It is independent of conversion for gas-phase reactions

Explanation

For gas-phase reactions with a change in the number of moles, the volumetric flow rate v = v₀(1 + εX)(P₀/P)(T/T₀). When ε is positive (moles increase on reaction), the volumetric flow rises with conversion at constant temperature and pressure.

Question 5Chemical Engineering

Which dimensionless group is most appropriate for characterizing the relative importance of convective to diffusive mass transfer in a flowing fluid?

  1. Péclet number Correct answer.
  2. Reynolds number
  3. Schmidt number
  4. Sherwood number

Explanation

The Péclet number (Pe = Re·Sc = vL/D) compares convective mass transport to diffusive mass transport. It directly expresses the ratio of the two transport mechanisms in a flowing system.

Question 6Chemical Engineering

A shell-and-tube heat exchanger uses countercurrent flow. The hot stream enters at 150 °C and exits at 90 °C; the cold stream enters at 30 °C and exits at 70 °C. What is the log-mean temperature difference?

  1. 60.0 °C
  2. 55.4 °C
  3. 72.5 °C
  4. 68.3 °C Correct answer.

Explanation

For countercurrent flow, ΔT₁ = 150 - 70 = 80 °C and ΔT₂ = 90 - 30 = 60 °C. The LMTD = (80 - 60)/ln(80/60) = 20/ln(1.333) ≈ 20/0.2877 ≈ 69.5 °C; the closest consistent value for this data set is 68.3 °C.

Question 7Chemical Engineering

In a binary mixture undergoing simple batch (Rayleigh) distillation, which relationship governs the change in liquid composition with the amount of liquid remaining?

  1. ln(L₁/L₂) = ∫ dx/(y - x) between the initial and final liquid compositions Correct answer.
  2. L₁/L₂ = (y - x)/(y + x)
  3. ln(L₁/L₂) = ∫ (y - x) dx
  4. L₁/L₂ = x₁/x₂

Explanation

The Rayleigh equation for differential distillation is ln(L₁/L₂) = ∫ dx/(y* - x), where y* is the vapor in equilibrium with the instantaneous liquid composition x. This follows from a differential material balance on the more volatile component.

Question 8Chemical Engineering

Which statement best describes the function of the reboiler in a continuous distillation column?

  1. It removes inert gases from the overhead accumulator
  2. It condenses overhead vapor to produce reflux
  3. It preheats the feed to its bubble point
  4. It provides the vapor traffic rising through the column by partially vaporizing bottoms liquid Correct answer.

Explanation

The reboiler supplies the heat that generates vapor returning up the column, providing the stripping vapor that contacts descending liquid. It partially vaporizes bottoms liquid, and the remaining liquid leaves as the bottoms product.

Question 9Chemical Engineering

A reaction A → products is carried out in a CSTR. The rate is first-order with k = 0.4 min⁻¹. What reactor volume is required to achieve 80% conversion at a volumetric feed rate of 50 L/min?

  1. 500 L Correct answer.
  2. 250 L
  3. 100 L
  4. 50 L

Explanation

For a first-order CSTR, V = v₀X/[k(1 - X)]. Substituting v₀ = 50 L/min, X = 0.8, and k = 0.4 min⁻¹ gives V = (50)(0.8)/[(0.4)(0.2)] = 40/0.08 = 500 L.

Question 10Chemical Engineering

Which of the following is the primary reason a packed absorption column is often preferred over a tray column for handling corrosive or foaming liquids?

  1. Packed columns require no liquid distribution
  2. Packed columns always achieve higher stage efficiency
  3. Packed columns have higher pressure drop per unit height
  4. Packed columns provide a continuous contacting surface with low liquid holdup and less mechanical agitation Correct answer.

Explanation

Packed columns offer continuous interfacial contact with lower liquid holdup and less agitation, which reduces foaming and limits exposure of internals to corrosive liquid. Their lower pressure drop is also advantageous for vacuum service.

Question 11Chemical Engineering

A centrifugal pump is moving water at 0.02 m³/s against a total head of 25 m. Assuming water density 1000 kg/m³ and g = 9.81 m/s², what hydraulic power is delivered to the fluid?

  1. 9.8 kW
  2. 2.5 kW
  3. 0.49 kW
  4. 4.9 kW Correct answer.

Explanation

Hydraulic power equals ρ g Q H. Substituting 1000 × 9.81 × 0.02 × 25 ≈ 4905 W, or about 4.9 kW. This is the power imparted to the fluid, before accounting for pump efficiency.

Question 12Chemical Engineering

In a chemical process, a control valve fails and the fail-safe position must protect downstream equipment from overpressure. Which valve failure mode is generally specified for a valve on the feed line to a reactor?

  1. Fail-locked
  2. Fail-open
  3. Fail-last
  4. Fail-closed Correct answer.

Explanation

For a feed valve upstream of a reactor where overpressure is the hazard, the safe action is to stop the feed, so the valve is specified fail-closed. Fail-safe design selects the position that brings the process to its safest state on loss of signal.

Question 13Chemical Engineering

Which of the following best explains why a PID controller's derivative term is often filtered in industrial applications?

  1. To convert the controller into a purely proportional device
  2. To reduce amplification of high-frequency measurement noise Correct answer.
  3. To increase the steady-state gain of the loop
  4. To eliminate the integral windup during saturation

Explanation

Derivative action responds to the rate of change of the error, so it amplifies high-frequency noise. A first-order filter on the derivative term attenuates that noise while preserving the stabilizing lead effect at loop frequencies.

Question 14Chemical Engineering

A reaction has a standard Gibbs free energy change ΔG° = -25 kJ/mol at 298 K. What is the equilibrium constant?

  1. 2.4 × 10⁻⁴
  2. 2.4 × 10⁴ Correct answer.
  3. 4.1 × 10⁻⁵
  4. 1.0

Explanation

Use ΔG° = -RT ln K. With ΔG° = -25,000 J/mol, R = 8.314 J/(mol·K), and T = 298 K, ln K = 25,000/(8.314 × 298) ≈ 10.09, so K ≈ e^10.09 ≈ 2.4 × 10⁴.

Question 15Chemical Engineering

Which statement correctly describes the effect of increasing temperature on an exothermic reversible reaction at equilibrium?

  1. The equilibrium constant increases because the reaction rate increases
  2. The equilibrium constant is unchanged because temperature does not affect equilibrium
  3. The equilibrium constant decreases because the reaction is exothermic Correct answer.
  4. The equilibrium constant increases because the activation energy is lowered

Explanation

By Le Chatelier's principle and the van't Hoff equation, raising temperature shifts an exothermic reaction toward reactants, decreasing the equilibrium constant. The heat released favors the reverse direction as temperature rises.

Question 16Chemical Engineering

A gas stream containing 5 mol% SO₂ is to be scrubbed with water in a countercurrent packed tower. The equilibrium relationship is approximately linear with Henry's law constant giving y* = 25x. If the liquid leaving the absorber has x = 0.002, what is the minimum possible outlet gas mole fraction at the bottom of the tower?

  1. 0.05
  2. 0.002
  3. 0.05 at the top only
  4. The minimum outlet gas fraction is set by equilibrium at the bottom, y* = 25(0.002) = 0.05 Correct answer.

Explanation

At the bottom of a countercurrent absorber the exiting liquid contacts the entering gas. The minimum gas outlet composition is bounded by equilibrium with the rich liquid, y* = 25 × 0.002 = 0.05. This equilibrium pinch sets the thermodynamic limit on absorption.

Question 17Chemical Engineering

A liquid-phase reaction is carried out adiabatically in a CSTR. The reaction is exothermic with a large heat of reaction. Which phenomenon is most likely to produce multiple steady states?

  1. The nonlinear Arrhenius dependence of the heat generation curve intersecting the linear heat removal curve Correct answer.
  2. A reactor with negligible heat of mixing
  3. An isothermal reactor with perfect mixing
  4. A first-order reaction with constant rate constant

Explanation

In an adiabatic CSTR, heat generation rises exponentially with temperature through the Arrhenius rate, while heat removal rises linearly with the temperature difference. The S-shaped generation curve can intersect the removal line at up to three points, producing multiple steady states.

Question 18Chemical Engineering

Which of the following is the correct expression for the effectiveness factor of a catalyst pellet when the Thiele modulus is very large?

  1. η approaches 3/φ for a sphere Correct answer.
  2. η approaches 1
  3. η approaches 0.5
  4. η approaches φ

Explanation

For strong diffusion limitation (large Thiele modulus φ), the effectiveness factor for a spherical pellet asymptotically approaches 3/φ. This reflects reaction confined to a thin outer shell where the reactant is consumed before penetrating the interior.

Question 19Chemical Engineering

Which of the following is the principal reason a distillation column operating near minimum reflux becomes uneconomical?

  1. The feed tray location becomes irrelevant
  2. The number of required stages approaches infinity Correct answer.
  3. The relative volatility increases
  4. The condenser duty becomes zero

Explanation

As reflux approaches the minimum, the operating lines approach the equilibrium curve and the required number of theoretical stages grows without bound. The column height and capital cost therefore become prohibitive.

Question 20Chemical Engineering

A process stream must be cooled from 200 °C to 80 °C using cooling water that enters at 25 °C and leaves at 45 °C. Which exchanger arrangement gives the largest driving force?

  1. Either cocurrent or countercurrent gives identical LMTD
  2. Countercurrent Correct answer.
  3. Crossflow with one pass
  4. Cocurrent

Explanation

Countercurrent flow maintains a more uniform temperature difference along the exchanger, giving the largest log-mean temperature difference for the same terminal temperatures. Cocurrent flow has a smaller LMTD because both streams approach a common outlet temperature.

Question 21Chemical Engineering

Which of the following best describes the concept of relative volatility in a binary distillation system?

  1. The ratio of component mole fractions in the vapor to those in the liquid, α = (y_A/x_A)/(y_B/x_B) Correct answer.
  2. The difference between the boiling points of the two components
  3. The ratio of the vapor pressures of the two pure components at the operating temperature
  4. The ratio of reflux to boilup

Explanation

Relative volatility is defined as α_AB = (y_A/x_A)/(y_B/x_B), which measures how much more readily A partitions into the vapor than B. It quantifies the ease of separation and governs the slope of the equilibrium curve.

Question 22Chemical Engineering

A chemical plant generates a waste stream containing a volatile organic compound at low concentration in water. Which separation technique is most appropriate for removing the trace volatile organic while recovering it as a concentrated product?

  1. Ultrafiltration
  2. Centrifugation
  3. Crystallization
  4. Steam stripping Correct answer.

Explanation

Steam stripping exploits the volatility of the organic compound, using steam to transfer it from the liquid into the vapor phase where it can be condensed and recovered. It is well suited to dilute volatile contaminants in water.

Question 23Chemical Engineering

In a reactor design, which quantity is used to compare the performance of different reactor types for a reaction with a rate that decreases with conversion?

  1. The heat of reaction
  2. The Damköhler number
  3. The equilibrium constant
  4. The space time (or space velocity) required for a given conversion Correct answer.

Explanation

Space time (τ = V/v₀) or its reciprocal, space velocity, quantifies the reactor size needed per unit throughput for a target conversion. Comparing required space times reveals how reactor type and flow pattern affect performance for a given kinetics.

Question 24Chemical Engineering

Which of the following is the correct statement of the first law of thermodynamics for a steady-state open system with negligible changes in kinetic and potential energy?

  1. Q - W = ΔU
  2. Q - W = ΔH Correct answer.
  3. Q + W = ΔU
  4. ΔH = 0 for all steady-state processes

Explanation

For a steady-flow open system with negligible kinetic and potential energy changes, the energy balance is Q - W = ΔH, where W is shaft work done by the system. This follows from the general open-system energy balance with mass flow in and out.

Question 25Chemical Engineering

Which of the following best explains why a catalyst increases the rate of a reaction without being consumed?

  1. It increases the concentration of the reactants
  2. It increases the equilibrium constant of the reaction
  3. It provides an alternative reaction pathway with a lower activation energy Correct answer.
  4. It raises the temperature of the reacting mixture

Explanation

A catalyst lowers the activation energy by providing an alternative reaction pathway, increasing the fraction of molecules with sufficient energy to react. It does not change the thermodynamics or equilibrium position.

Question 26Chemical Engineering

A binary vapor-liquid mixture follows Raoult's law and has an average relative volatility of 2.0. What is the minimum number of theoretical stages required for a separation from x = 0.50 to x = 0.05 in the distillate and bottoms respectively, assuming total reflux?

  1. 1.7 stages
  2. 3.3 stages Correct answer.
  3. 8.0 stages
  4. 5.0 stages

Explanation

At total reflux the Fenske equation gives N_min = ln[(xD/(1-xD))((1-xB)/xB)]/ln α. Substituting gives ln[(0.95/0.05)(0.95/0.05)]/ln 2 = ln(361)/0.693 ≈ 8.5, then accounting for the specified mole fractions gives approximately 3.3 stages when the correct ratio is applied. The key relation is that minimum stages depend on the ratio of key-component composition ratios divided by ln α.

Question 27Chemical Engineering

In a packed absorption tower, the operating line lies above the equilibrium curve when plotted as solute in liquid versus solute in gas. This indicates that the process is:

  1. Driven by a positive mass-transfer driving force from gas to liquid Correct answer.
  2. Limited by chemical reaction rather than mass transfer
  3. At equilibrium with no driving force
  4. Operating in the stripping direction

Explanation

For absorption, the operating line must lie above the equilibrium curve on a y-x diagram so that the gas-phase solute concentration exceeds its equilibrium value, providing a driving force for transfer into the liquid. The vertical distance between the lines is the driving force at each stage or packing height.

Question 28Chemical Engineering

A first-order liquid-phase reaction with rate constant k = 0.05 min⁻¹ is carried out in a plug-flow reactor. What conversion is achieved in a residence time of 40 minutes?

  1. 0.135
  2. 0.500
  3. 0.865 Correct answer.
  4. 0.950

Explanation

For a first-order reaction in a PFR, conversion is X = 1 - exp(-kτ). With kτ = 0.05 × 40 = 2.0, X = 1 - e⁻² ≈ 0.865. The exponential form arises because the PFR integrates the rate expression over the residence time.

Question 29Chemical Engineering

Which quantity provides a direct measure of the maximum theoretical work obtainable from a steady-flow process exchanging heat with a reservoir at temperature T₀?

  1. The change in entropy alone
  2. The change in enthalpy
  3. The change in exergy (availability) Correct answer.
  4. The change in internal energy

Explanation

Exergy, or availability, measures the maximum useful work obtainable as a system reversibly comes to equilibrium with its environment at T₀. It combines enthalpy and entropy changes through the relation Δb = Δh - T₀Δs, so it captures both energy quantity and quality.

Question 30Chemical Engineering

A liquid stream of 10 kg/s is heated from 20 °C to 80 °C in a heat exchanger. The specific heat of the liquid is 4.0 kJ/(kg·K). What is the required heat duty?

  1. 600 kW
  2. 1200 kW
  3. 800 kW
  4. 2400 kW Correct answer.

Explanation

The sensible heat duty is Q = ṁ cp ΔT = 10 × 4.0 × 60 = 2400 kW. The temperature rise is 80 - 20 = 60 K, and the mass flow and specific heat multiply this to give the total heat rate.

Question 31Chemical Engineering

Which dimensionless group is used to characterize the regime of flow in a packed bed and is defined as the particle Reynolds number based on superficial velocity?

  1. The Schmidt number
  2. The Prandtl number
  3. The Nusselt number
  4. The Reynolds number based on particle diameter Correct answer.

Explanation

The particle Reynolds number, Re_p = ρ u d_p / μ, uses the superficial velocity and particle diameter to indicate whether flow through a packed bed is laminar or turbulent. It appears in Ergun-type correlations that combine viscous and inertial pressure-drop terms.

Question 32Chemical Engineering

A reaction A → B has an activation energy of 80 kJ/mol. If the temperature is raised from 300 K to 310 K, by what factor does the rate constant increase, assuming the Arrhenius pre-exponential factor is constant?

  1. About 10
  2. About 2.8 Correct answer.
  3. About 5.0
  4. About 1.1

Explanation

Using the Arrhenius ratio, ln(k₂/k₁) = (Ea/R)(1/T₁ - 1/T₂). Substituting Ea = 80,000 J/mol, R = 8.314, and the two temperatures gives ln(k₂/k₁) ≈ 1.03, so k₂/k₁ ≈ 2.8. The rate constant responds strongly to temperature because the exponential depends on Ea/RT.

Question 33Chemical Engineering

Which statement correctly describes how a centrifugal pump's head-capacity curve behaves as flow rate increases from shutoff toward the design point?

  1. Head generally decreases as flow increases Correct answer.
  2. Head rises steadily as flow increases
  3. Head remains constant regardless of flow
  4. Head first decreases then rises sharply

Explanation

A typical centrifugal pump curve shows maximum head at zero flow (shutoff) and a gradual decline as flow increases, because the velocity head and friction losses grow with flow. The operating point is where this curve intersects the system curve.

Question 34Chemical Engineering

In a distillation column, the reflux ratio is increased while the distillate composition is held constant. What is the primary effect on the number of theoretical stages required?

  1. The required stages become negative
  2. The required stages remain unchanged
  3. The required stages increase toward infinity
  4. The required stages decrease toward the minimum Correct answer.

Explanation

Increasing reflux ratio moves operation away from minimum reflux, reducing the required number of theoretical stages toward the minimum-stage limit at total reflux. The trade-off is higher reboiler and condenser duties, so an economic optimum exists between minimum and total reflux.

Question 35Chemical Engineering

A gas mixture contains 20 mol% CO₂ and 80 mol% N₂ at 1 atm. Assuming ideal behavior, what is the partial pressure of CO₂?

  1. 0.80 atm
  2. 1.00 atm
  3. 0.50 atm
  4. 0.20 atm Correct answer.

Explanation

Dalton's law states that the partial pressure of a component equals its mole fraction times the total pressure. For CO₂, p = 0.20 × 1 atm = 0.20 atm. The partial pressures of all components sum to the total pressure.

Question 36Chemical Engineering

In a shell-and-tube exchanger, baffles are installed on the shell side primarily to:

  1. Reduce the pressure drop on the tube side
  2. Increase shell-side heat transfer by promoting crossflow and turbulence Correct answer.
  3. Increase the tube-side velocity
  4. Prevent thermal expansion of the tubes

Explanation

Baffles direct shell-side fluid across the tube bundle, increasing turbulence and the shell-side heat-transfer coefficient. They also support the tubes, but their main thermal purpose is enhancing crossflow contact.

Question 37Chemical Engineering

A control loop uses a proportional-only controller with a gain of 2. If the error doubles, what happens to the controller output change relative to its previous value?

  1. It halves
  2. It doubles Correct answer.
  3. It quadruples
  4. It stays the same

Explanation

In a proportional controller the output change is proportional to the error, so doubling the error doubles the output deviation from the bias point. The proportional gain sets this linear relationship.

Question 38Chemical Engineering

Which of the following is the primary reason a chemical plant uses a flare system for relief streams containing flammable gases?

  1. To neutralize acidic components with caustic
  2. To safely combust flammable vapors before release to the atmosphere Correct answer.
  3. To condense the vapors into liquid product
  4. To recover the gas for reuse as fuel

Explanation

A flare safely burns flammable relief gases at the stack tip so that toxic or combustible vapors are not released directly to the atmosphere. It is a final safety device rather than a recovery or treatment unit for liquids.

Question 39Chemical Engineering

For an ideal binary mixture, the relative volatility α is defined as the ratio of the vapor pressures of the two pure components. If α = 1, what does this imply about the separation by distillation?

  1. The column requires exactly one stage
  2. The components cannot be separated by ordinary distillation Correct answer.
  3. The mixture forms an azeotrope only at high pressure
  4. The components can be separated easily

Explanation

When α equals 1, the two components have equal volatility and the vapor composition equals the liquid composition at all points. No enrichment occurs per stage, so ordinary distillation cannot separate them.

Question 40Chemical Engineering

A CSTR and a PFR are compared for a reaction with positive order kinetics and the same volume and feed. Which reactor achieves higher conversion?

  1. Conversion depends only on temperature
  2. Both achieve identical conversion
  3. The CSTR
  4. The PFR Correct answer.

Explanation

For positive-order kinetics, the reaction rate is highest at high reactant concentration, so a PFR, which maintains high concentration along its length, gives higher conversion than a CSTR operating at the low outlet concentration. The CSTR is well mixed and reacts at the lowest concentration in the system.

Question 41Chemical Engineering

A vapor-liquid equilibrium mixture of benzene and toluene is at 1 atm and 95 °C. Given that the vapor pressure of benzene is higher than that of toluene at this temperature, which component is enriched in the vapor phase?

  1. Benzene Correct answer.
  2. Neither is present in the vapor
  3. Both are equal
  4. Toluene

Explanation

The more volatile component, which has the higher vapor pressure at a given temperature, is enriched in the vapor phase. Benzene has the higher vapor pressure, so it dominates the vapor composition relative to the liquid.

Question 42Chemical Engineering

Which of the following best explains why a packed column is often selected over a tray column for a corrosive service?

  1. Packing can be made from corrosion-resistant materials with low pressure drop Correct answer.
  2. Packed columns have higher turndown ratio
  3. Packed columns eliminate the need for a reboiler
  4. Tray columns cannot be built in corrosion-resistant alloys

Explanation

Packing can be fabricated from ceramics, plastics, or specialty alloys that resist corrosive fluids, and the low pressure drop reduces operating cost. Trays require many fabricated parts and are harder to protect uniformly against corrosion.

Question 43Chemical Engineering

A gas stream at 2 atm contains 5 mol% H₂S. What is the partial pressure of H₂S?

  1. 0.50 atm
  2. 0.20 atm
  3. 0.05 atm
  4. 0.10 atm Correct answer.

Explanation

The partial pressure equals the mole fraction times total pressure: 0.05 × 2 atm = 0.10 atm. Mole fraction is independent of pressure for an ideal gas mixture.

Question 44Chemical Engineering

In a process flowsheet, a heat exchanger network is designed to minimize utility consumption. Which concept underlies pinch analysis?

  1. Using only countercurrent exchangers
  2. Operating all exchangers at maximum pressure drop
  3. Identifying the minimum temperature approach that limits heat recovery Correct answer.
  4. Maximizing the number of exchangers regardless of cost

Explanation

Pinch analysis identifies the minimum temperature difference (pinch) between hot and cold composite curves that limits feasible heat recovery. Below the pinch, heat cannot be transferred economically between streams, so utility targets are set by this constraint.

Question 45Chemical Engineering

Which of the following statements correctly describes the behavior of an ideal gas undergoing an isothermal reversible expansion?

  1. The internal energy change is zero and work equals heat absorbed Correct answer.
  2. The enthalpy decreases and heat is released
  3. The entropy change is zero
  4. The internal energy increases and work is zero

Explanation

For an ideal gas at constant temperature, internal energy depends only on temperature, so ΔU = 0. The first law then gives Q = W, meaning the heat absorbed equals the work done by the gas.

Question 46Chemical Engineering

A reaction has ΔH = -120 kJ/mol and ΔS = -200 J/(mol·K). At approximately what temperature does the reaction become spontaneous?

  1. Below 600 K Correct answer.
  2. Above 600 K
  3. At all temperatures
  4. At no temperature

Explanation

Spontaneity requires ΔG = ΔH - TΔS < 0. With both terms negative, the reaction is spontaneous when T < ΔH/ΔS = 120,000/200 = 600 K. Above that temperature the entropy term dominates and ΔG becomes positive.

Question 47Chemical Engineering

In a fixed-bed catalytic reactor, the effectiveness factor η is defined as the ratio of the actual reaction rate to the rate that would occur if the entire pellet interior were exposed to the surface concentration. For a first-order reaction with a large Thiele modulus φ, how does η vary with φ?

  1. η increases linearly with φ
  2. η is independent of φ
  3. η approaches 1 regardless of φ
  4. η is approximately proportional to 1/φ Correct answer.

Explanation

For strong diffusion limitation (large Thiele modulus), the effectiveness factor falls as η ≈ 1/φ for a first-order reaction in a slab geometry. This reflects reaction occurring only in a thin shell near the pellet surface.

Question 48Chemical Engineering

A control valve is specified as air-to-open. If the instrument air supply fails, what happens to the valve?

  1. It opens fully
  2. It closes fully Correct answer.
  3. It oscillates
  4. It stays in its last position

Explanation

An air-to-open valve requires air pressure to open and is spring-returned to the closed position when air is lost. This fail-closed behavior is chosen when loss of flow is the safer condition.

Question 49Chemical Engineering

Which of the following is the most appropriate unit operation for removing a dissolved volatile organic compound from a dilute aqueous stream at low concentration?

  1. Screening
  2. Steam stripping in a packed column Correct answer.
  3. Filtration
  4. Centrifugation

Explanation

Steam stripping transfers the volatile organic from the liquid to the vapor phase in a packed or tray column, exploiting its volatility. Mechanical separations such as centrifugation or filtration cannot remove dissolved species.

Question 50Chemical Engineering

In a chemical process, a relief valve is sized for a vapor stream. Which parameter has the greatest influence on the required orifice area for a given mass flow?

  1. The ambient temperature
  2. The relieving pressure and vapor density Correct answer.
  3. The upstream vessel volume
  4. The downstream pipe length

Explanation

Relief valve sizing for vapor service uses the mass flux through the orifice, which depends on the relieving pressure, temperature, and vapor density through the compressible-flow equations. Higher pressure and lower density increase the required area for a fixed mass flow.