Question 1

Pressure equivalence (reframed for uniqueness):\r Which of the following values is not approximately equal to 1 kgf/cm^2 (standard gravity, water at 4°C)?

Accepted Answer

Introduction: Engineering practice frequently interconverts legacy pressure units such as kgf/cm^2, bar, kPa, mmHg (torr), and water column. Recognizing near-equivalences helps in quick estimates and in reading older datasheets while avoiding significant errors. Given Data / Assumptions: Standard gravity g = 9.80665 m/s^2. 1 kgf = force exerted by 1 kg mass under standard gravity. Water density ρ ≈ 1000 kg/m^3 at 4°C for head equivalence. Concept / Approach: By definition, 1 kgf/cm^2 = 98,066.5 Pa = 98.07 kPa ≈ 0.967 bar. Hydrostatic equivalence gives about 10 m of water column. Converting to mmHg: 98,066.5 Pa ÷ 133.322 Pa/mmHg ≈ 735.6 mmHg. Therefore, values like 0.967 bar, 98.07 kPa, 10 m wc, and 735.6 mmHg are consistent with 1 kgf/cm^2, whereas exactly 1.000 bar (100 kPa) is slightly higher (~2% difference) and thus not equal. Step-by-Step Solution: Start from SI: 1 kgf/cm^2 = 98,066.5 Pa.Convert to bar: 98,066.5 Pa / 100,000 Pa/bar ≈ 0.967 bar.To kPa: 98.07 kPa (direct).To water head: P = ρ g h ⇒ h ≈ 10 m.To mmHg: 98,066.5 / 133.322 ≈ 735.6 mmHg. Verification / Alternative check: Cross-checks using multiple routes (e.g., bar and head) converge consistently, confirming the small mismatch with 1.000 bar. Why Other Options Are Wrong: 0.967 bar, 98.07 kPa, 10 m wc, 735.6 mmHg: All are established approximations for 1 kgf/cm^2. Common Pitfalls: Assuming 1 kgf/cm^2 equals exactly 1 bar or 100 kPa; the difference (~2%) can matter in precise calculations. Final Answer: 1.000 bar

Question 2

Steady-state material balance:\r In a steady-state system (no net accumulation with time), the rate of material __________ equals zero.

Accepted Answer

Introduction: Material balance is the foundation of process analysis. The general balance states: accumulation = input − output + generation − consumption. At steady state, system properties are time-invariant, simplifying many calculations in reactors, separators, and networks. Given Data / Assumptions: System is at steady state (d/dt of inventories = 0). Generation/consumption terms may exist (e.g., reaction), but are constant over time. Boundary flows (input/output) are constant in time. Concept / Approach: Steady state means no net change in the amount of material inside the system with time. Therefore, the accumulation term is zero, even though generation and consumption can be nonzero and must be balanced by appropriate differences between input and output. Confusing “generation” with “accumulation” is common; generation refers to formation within the system (e.g., reaction), while accumulation is the net time rate of increase of inventory. Step-by-Step Solution: Write general balance: accumulation = input − output + generation − consumption.At steady state: accumulation = 0 by definition.Conclude that only the accumulation term is guaranteed zero; others can be nonzero. Verification / Alternative check: In continuous stirred-tank reactors at steady state with reaction, generation is balanced by a higher output relative to input, keeping accumulation zero. Why Other Options Are Wrong: Production/generation may be nonzero due to reaction. Input is generally not zero in continuous operation. Consumption can be nonzero due to reaction or sorption. Common Pitfalls: Setting generation to zero at steady state; that only applies to nonreactive systems. Final Answer: accumulation

Question 3

Colligative properties check:\r Which of the following is not a colligative property of solutions?

Accepted Answer

Introduction: Colligative properties depend only on the number of solute particles in a solution, not their identity (within ideal approximations). Recognizing these properties is key in molecular weight determination, antifreeze design, and desalination studies. Given Data / Assumptions: Ideal or dilute solutions are assumed for the concept. Solute is nonvolatile and nonassociating unless noted. We identify which listed property is not colligative. Concept / Approach: The standard colligative properties are: lowering of vapor pressure, elevation of boiling point, depression of freezing point, and osmotic pressure. All four arise from the same thermodynamic basis—dilution of solvent chemical potential by solute particles—and scale with molality or molarity through proportionality constants (Kb, Kf, or van ’t Hoff factor for electrolytes). Therefore, options (a), (b), (c), and (e) are all genuine colligative properties. As the question asks for what is not a colligative property, the correct response is “none of these.” Step-by-Step Solution: List canonical colligative properties.Match each option to the list and confirm inclusion.Conclude that all provided are colligative; hence “none of these.” Verification / Alternative check: Textbook equations: ΔTb = Kb * m, ΔTf = Kf * m, π = i * M * R * T, and Raoult’s law for vapor pressure lowering all show dependency only on particle number (with i for electrolytes). Why Other Options Are Wrong: Each listed property (a), (b), (c), (e) is indeed colligative and thus not the correct “not” choice. Common Pitfalls: Confusing density or refractive index (not strictly colligative) with the classic four; these are not listed here. Final Answer: none of these.

Question 4

Calorific value unit conversions:\r Identify the WRONG conversion statement among the following energy-per-mass or energy-per-volume equivalences.

Accepted Answer

Introduction: Energy unit conversions appear everywhere from fuel specifications to dryer sizing. Small mistakes in unit factors can produce large design errors. This question asks you to spot the incorrect calorific value conversion among several commonly used relationships. Given Data / Assumptions: Exact factors: 1 kcal = 4.186 kJ; 1 BTU = 1.055 kJ; 1 m^3 = 35.3147 ft^3; 1 MJ = 10^3 kJ; 1 kcal ≈ 3.968 BTU. We assume standard conditions for volumetric conversions. Concept / Approach: Check each statement using base factors. For (a): 1 kcal/kg equals 3.968 BTU/lb and 4.186 kJ/kg—correct. For (b): 1 BTU/lb equals 1.055 kJ/kg which is 0.252 kcal/kg—rounded to 2.326 kJ/kg for 1 BTU/lb is incorrect unless a typo; the correct figure is about 2.326 kJ per kcal. We adopt the precise pairing 1 BTU/lb ≈ 2.326 kJ/kg = 0.252 kcal/kg as a consistent rounded set used in many handbooks. Step-by-Step Solution: Evaluate (c): 1 BTU/ft^3 × 35.3147 ft^3/m^3 × 1.055 kJ/BTU = 37.3 kJ/m^3 ≈ 0.038 MJ/m^3 ≈ 8.9 kcal/m^3 → correct.Evaluate (d): 1 kcal/m^3 in BTU/ft^3 = (3.968 BTU/kcal) / 35.3147 = 0.1124 BTU/ft^3, not 1.124 → WRONG.Evaluate (e): 1 MJ/kg ÷ 4.186 kJ/kcal = 238.9 kcal/kg → rounded 239 is fine. Verification / Alternative check: Independent recalculation with SI base units confirms that only statement (d) carries a factor-of-10 error. Why Other Options Are Wrong: Options (a), (b), (c), and (e) are consistent to typical handbook precision; (d) is the sole incorrect statement. Common Pitfalls: Dropping or misplacing the 35.3147 ft^3 per m^3 conversion factor often leads to 10× errors, as seen here. Final Answer: 1 kcal/m^3 = 1.124 BTU/ft^3.

Question 5

Recognizing pressure units:\r Which of the following is not a unit of pressure used in engineering or science?

Accepted Answer

Introduction: Pressure is expressed in many units: SI (pascal), derived (N/m^2), industrial (bar, ata), and head-based (mm H2O, mmHg). Recognizing legitimate pressure units prevents dimensional mistakes when reading datasheets or performing conversions. Given Data / Assumptions: We distinguish pressure units from those of length, time, or other quantities. Common pressure units include absolute and gauge variants. “Ata” denotes absolute atmospheres. Concept / Approach: Torr (mmHg) measures pressure; Newton per square meter is the pascal (SI). Bar and pascal (Pa), as well as “ata,” are established pressure units. Head units like mm H2O express pressure via equivalent fluid column. A parsec, however, is an astronomical unit of length (approximately 3.09 × 10^16 m) and is unrelated to pressure. Step-by-Step Solution: List pressure units: Pa (N/m^2), bar, ata, torr, mm H2O.Identify the outlier: parsec is a length unit.Select parsec as the only option that is not a pressure unit. Verification / Alternative check: Dimensional analysis confirms N/m^2 is M L^-1 T^-2, the correct pressure dimension; a parsec has dimension of length. Why Other Options Are Wrong: Torr and mm H2O: Traditional pressure measures (mercury and water columns). Newton/m^2: SI pressure unit (pascal). Ata, bar, pascal: All standard pressure units. Common Pitfalls: Confusing gauge vs absolute labeling; “bara” and “barg” indicate absolute and gauge, respectively, but both are still pressure units. Final Answer: Parsec

Question 6

Unit conversion in mechanics: In classical mechanics and SI–CGS conversions, one Newton (N) is equal to how many dynes?

Accepted Answer

Introduction / Context: Force units are frequently converted between the SI system (Newton, N) and the CGS system (dyne). Being comfortable with these conversions is essential in physics, chemical engineering calculations, and instrumentation where legacy CGS data may appear alongside modern SI data. Given Data / Assumptions: SI base: 1 N = 1 kg * m / s^2. CGS base: 1 dyne = 1 g * cm / s^2. Exact metric relations: 1 kg = 10^3 g; 1 m = 10^2 cm. Concept / Approach: Write both units in terms of base dimensions and convert systematically using the kilogram–gram and meter–centimeter relations. Avoid memorizing isolated numbers; derive once from first principles to reduce mistakes. Step-by-Step Solution: Start with 1 N = 1 kg * m / s^2.Convert kg to g: 1 kg = 10^3 g → 1 N = 10^3 g * m / s^2.Convert m to cm: 1 m = 10^2 cm → 1 N = 10^3 * 10^2 g * cm / s^2.Multiply powers of 10: 10^3 * 10^2 = 10^5.Therefore 1 N = 10^5 g * cm / s^2 = 10^5 dynes. Verification / Alternative check: The dyne is defined so that 1 dyne accelerates 1 g at 1 cm/s^2. Using dimensional analysis consistently always yields 10^5 as the factor between Newtons and dynes. Why Other Options Are Wrong: 10^2, 10^3, and 10^4 dynes underestimate the conversion because they miss one or both metric scale factors between kg↔g and m↔cm. Common Pitfalls: Converting only mass or only length but not both. Confusing dyne with pound-force; use consistent metric bases. Final Answer: 10^5 dynes

Question 7

Standard conditions in gas calculations: STP (standard temperature and pressure) corresponds to which of the following sets of conditions?

Accepted Answer

Introduction / Context: Standard states are reference conditions used to report and compare thermophysical data. In gas laws and stoichiometry, STP is a conventional benchmark that allows consistent molar volume and property comparisons across textbooks and problems. Given Data / Assumptions: Classical chemistry/physics convention for STP. 1 atm = 760 torr = 101.325 kPa. Temperature scales: 0°C = 273.15 K; 15.5°C = 288.65 K. Concept / Approach: Traditional STP used in many educational contexts is 1 atm pressure and 0°C temperature. Pressure is commonly expressed as 760 torr (or 760 mm Hg absolute), not gauge pressure. Recognize the distinction between absolute and gauge pressures: gauge excludes atmospheric baseline, absolute includes it. Step-by-Step Solution: Identify temperature: STP → 0°C (273.15 K).Identify pressure: STP → 1 atm absolute = 760 torr.Match the option that states both: '760 torr and 0°C'. Verification / Alternative check: Using the ideal gas law at STP gives classic molar volume values (about 22.414 L/mol under the older STP convention), reinforcing that STP is 1 atm and 0°C in many curricula. Why Other Options Are Wrong: Options with gauge pressure are incorrect reference states; 15.5°C corresponds to NTP-like conditions, not STP. Common Pitfalls: Confusing STP (0°C) with NTP or SATP (near 20–25°C). Using gauge instead of absolute pressure in gas calculations. Final Answer: 760 torr and 0°C

Question 8

Buffer action check: When 1 cm^3 of dilute hydrochloric acid (1% by volume) is added to 80 cm^3 of a buffer solution initially at pH = 4, what will be the resulting pH (qualitatively)?

Accepted Answer

Introduction / Context: Buffers resist changes in pH when small amounts of acid or base are added. This robustness is central in biochemical assays, fermentations, and analytical chemistry where stable hydrogen ion activity is critical. Given Data / Assumptions: Buffer volume: 80 cm^3 at pH 4. Added acid: 1 cm^3 of 1% HCl (very small, dilute addition). Assume buffer capacity is adequate; temperature effects negligible. Concept / Approach: The Henderson–Hasselbalch relation shows that pH depends on the ratio base/acid forms. Small additions cause minimal ratio changes if the buffer capacity is not exhausted. A tiny acid addition to a relatively large buffer volume will not significantly shift pH. Step-by-Step Solution: Estimate moles of added H^+ (very small due to 1% and tiny volume).Compare to moles of buffer components (much larger).Conclude the ratio changes insignificantly; pH remains approximately 4.Hence, select pH = 4. Verification / Alternative check: Quantitative buffer capacity calculations (β) confirm millimole-level buffering can neutralize micromole additions with negligible pH change. Why Other Options Are Wrong: pH 1 or 2 implies overwhelming acid addition; pH 8 implies base addition, contrary to the scenario. Common Pitfalls: Forgetting that buffer capacity is finite; here, however, the addition is very small. Assuming any acid addition drastically changes pH regardless of buffer volume. Final Answer: pH = 4

Question 9

Stoichiometry from oxide reduction: A metal oxide is fully reduced by hydrogen. From 3.15 g of the oxide, 1.05 g of metal is obtained (2.10 g is oxygen). What can be inferred about the metal's equivalent or atomic weight?

Accepted Answer

Introduction / Context: Gravimetric data from oxide reduction provide ratios of metal to oxygen that can reveal atomic or equivalent weights. This classic approach predates modern spectroscopy and still trains intuition about formula masses and valency. Given Data / Assumptions: Mass of oxide: 3.15 g → yields metal: 1.05 g; oxygen removed: 2.10 g. Atomic mass of oxygen = 16 g/mol. Assume the metal forms a simple oxide (commonly MO for divalent metals). Concept / Approach: The oxygen-to-metal mass ratio is 2.10 / 1.05 = 2. For an oxide MO, the ratio by mass equals 16 / A_M (A_M = atomic weight of metal). Setting 16 / A_M = 2 gives A_M = 8. While no stable metal has atomic weight 8, the question asks what can be inferred: if the metal were divalent, the equivalent weight E = A_M / valency = 8 / 2 = 4, which matches a valid inference from the data alone (without assigning an element identity). Step-by-Step Solution: Compute mass ratio O:M = 2.10 / 1.05 = 2.Assume MO: 16 / A_M = 2 → A_M = 8.For a divalent metal, equivalent weight E = A_M / 2 = 4.Therefore, from the data, we can infer the equivalent weight is 4. Verification / Alternative check: If the oxide formula were M2O or M2O3, the inferred atomic weight would differ; however, the simplest consistent interpretation for the provided options is MO leading to E = 4. Why Other Options Are Wrong: Atomic weights 4 or 2 conflict with the observed mass ratio; equivalent weight 8 does not follow from MO with valency 2. Common Pitfalls: Confusing atomic with equivalent weight; remember E = A / valency. Ignoring valency assumptions embedded in oxide stoichiometry. Final Answer: Equivalent weight of the metal is 4

Question 10

Baumé gravity scale (heavy liquids): Which expression defines degrees Baumé (°Bé) for liquids heavier than water in terms of specific gravity G (at the reference temperature)?

Accepted Answer

Introduction / Context: The Baumé scale is a hydrometer scale historically used in chemical processing to express the density of liquids. Different formulas exist for liquids lighter or heavier than water. Correctly identifying the relation prevents miscalculation of concentrations, especially in legacy specifications and plant procedures. Given Data / Assumptions: G denotes specific gravity (dimensionless) at the reference temperature. We require the expression applicable to heavy liquids (G > 1). Standard Baumé convention is assumed. Concept / Approach: For liquids heavier than water, the Baumé degrees decrease as specific gravity increases. The conventional formula is °Bé = 145 − 145/G (at 60°F reference in common U.S. practice). For liquids lighter than water, a different formula is used. Note that API gravity and other scales have different constants and should not be confused with Baumé. Step-by-Step Solution: Identify the correct heavy-liquid relation: °Bé = 145 − (145 / G).Verify dimensionality: G is unitless; °Bé is by definition in degrees Baumé.Reject alternate constants that belong to other scales (e.g., API). Verification / Alternative check: Handbooks list the complementary light-liquid formula as °Bé = 140/G − 130, emphasizing that constants differ by convention and reference temperature. Why Other Options Are Wrong: (141.5/G) − 131.5: that is the API gravity relationship, not Baumé. 200(G − 1) and (400/G) − 400: not standard Baumé definitions. 100(1 − 1/G): an ad hoc expression lacking Baumé foundations. Common Pitfalls: Using the light-liquid formula for heavy liquids; always check whether G is above or below 1 and apply the corresponding equation. Final Answer: 145 - (145 / G).

Question 11

Solution concentration terms: The number of gram-equivalents of solute dissolved per litre of solution defines which concentration unit?

Accepted Answer

Introduction / Context: Several concentration units are used in chemistry and process calculations. Selecting the correct unit is essential for stoichiometry, titration, reaction engineering, and quality control. Normality is particularly common in acid-base and redox titrations where equivalents are more convenient than moles. Given Data / Assumptions: Definition required: gram-equivalents of solute per litre of solution. Applies to reactions defined by equivalent weight (e.g., H+ or e− transfer). Volume basis is the total solution volume. Concept / Approach: Normality (N) is defined as equivalents per litre (eq/L). By contrast, molarity (M) is moles per litre, molality (m) is moles per kilogram of solvent, and formality is moles of solute formula units per litre when dissociation is considered. Mole fraction is dimensionless. Thus, the definition given directly maps to normality. Step-by-Step Solution: Identify keyword: “gram-equivalents per litre”.Map to unit: Normality = eq/L.Confirm others do not match the given definition. Verification / Alternative check: Analytical chemistry protocols for titration calculate normality from standardization using equivalents; example: 1 N HCl contains 1 equivalent H+ per litre. Why Other Options Are Wrong: Molarity: uses moles, not equivalents. Molality: uses mass of solvent, not volume of solution. Formality: similar to molarity but for dissociating solutes; still moles per litre. Mole fraction: ratio of moles; dimensionless. Common Pitfalls: Using normality interchangeably with molarity; they coincide only when the reaction equivalent equals the mole (e.g., monoprotic acids in simple acid-base reactions). Final Answer: Normality.

Question 12

Pressure units equivalence: One torr is, by definition, equal to which of the following pressure units under standard laboratory conventions?

Accepted Answer

Introduction / Context: Pressure units appear in vacuum systems, distillation design, and physical measurements. Converting among units avoids errors in design calculations and instrument interpretation. The torr is widely used in vacuum technology and historically ties to the height of a mercury column. Given Data / Assumptions: 1 torr is historically defined as 1 mm of mercury at standard gravity and temperature. Modern SI relations: 1 atm ≈ 760 torr ≈ 101325 Pa. Concept / Approach: By definition, 1 torr = 1 mm Hg (exact in many practical contexts; minor corrections exist for temperature/gravity and the adoption of the pascal). This clear mapping helps in quick mental conversions between vacuum gauge readings and SI units. Step-by-Step Solution: Recall: 760 torr = 1 atm ≈ 101325 Pa.Therefore, 1 torr ≈ 133.322 Pa and equals 1 mm Hg by definition.Select the precise equivalence in the options. Verification / Alternative check: Instrument manuals for vacuum gauges list torr and mm Hg interchangeably; conversion charts confirm the relation. Why Other Options Are Wrong: 1 Pa: much smaller; 1 torr ≈ 133.322 Pa. 1 ata: equals 1 kgf/cm2; not equivalent to 1 torr. 1 mm wc: water column unit; ≈ 9.80665 Pa. 1 bar: 10^5 Pa; vastly larger than 1 torr. Common Pitfalls: Confusing torr with “Torricelli” in flow; remember torr is a pressure unit directly tied to mm Hg. Final Answer: 1 mm Hg (millimetre of mercury).

Question 13

Identify the incorrect statements: Which of the following statements are wrong regarding colligative properties and concentration definitions?

Accepted Answer

Introduction / Context: This question probes understanding of molarity changes upon evaporation and the effects of dissolved salts on freezing and boiling points, as well as the distinction between mass fraction and mole fraction. Careful reasoning about definitions and colligative properties is essential in solution chemistry and process calculations. Given Data / Assumptions: Glucose is nonvolatile and non-dissociating in water. Sea water contains salts (e.g., NaCl, MgSO4) increasing total solute concentration. Liquids X and Y are different substances with generally different molar masses. Concept / Approach: For statement (a): Molarity = moles of solute per litre of solution. Evaporation removes solvent, decreasing solution volume while moles of solute remain constant; hence molarity increases. For statement (b): Dissolved salts lower freezing point and raise boiling point relative to pure water; therefore, sea water has a lower freezing point and a higher boiling point, not both higher. For statement (c): Equal masses do not generally imply equal moles unless molar masses are identical; therefore, mole fractions are generally unequal. Step-by-Step Solution: Check (a): Volume decreases on evaporation; molarity increases → (a) is correct.Check (b): Freezing point depression makes T_f lower; boiling point elevation makes T_b higher → (b) is wrong.Check (c): n = m/M; equal masses with different M give different moles → (c) is wrong.Therefore, the wrong statements are (b) and (c). Verification / Alternative check: Colligative property formulas: ΔT_b = K_b * m and ΔT_f = K_f * m confirm qualitative trends for electrolytes in sea water. Why Other Options Are Wrong: Option (a): correctly states molarity increases. Option (e): not all statements are wrong; (a) is correct. Common Pitfalls: Confusing molarity (volume-based) with molality (mass of solvent-based). Evaporation does not change molality when only solvent is lost, but it does increase molarity. Final Answer: Statements (b) and (c) are wrong.

Question 14

Boiling point elevation: The rise in boiling point (ΔT_b) of a dilute solution is directly proportional to which concentration measure?

Accepted Answer

Introduction / Context: Boiling point elevation and freezing point depression are classic colligative properties used to determine molar masses and to design antifreeze and coolant formulations. The appropriate concentration basis matters because temperature changes depend on solute amount relative to solvent mass, not solution volume. Given Data / Assumptions: Dilute, non-electrolyte solutions (van’t Hoff factor ~ 1) for simplicity. Constant pressure conditions (typically 1 atm). Concept / Approach: The empirical relationship is ΔT_b = K_b * m * i, where K_b is the ebullioscopic constant, m is molality (moles solute per kilogram of solvent), and i is the van’t Hoff factor. Thus, ΔT_b is directly proportional to molality for a given solvent and solute dissociation factor. Molarity varies with temperature and volume changes; normality depends on reaction equivalents, not colligative behavior. Step-by-Step Solution: Recall formula: ΔT_b ∝ m (for constant i and K_b).Identify correct concentration unit: molality = moles solute / kg solvent.Select option (a) as the direct proportionality. Verification / Alternative check: Freezing point depression similarly follows ΔT_f = K_f * m, reinforcing that solvent-mass-based concentration controls colligative effects. Why Other Options Are Wrong: 1/m, N, M: not the correct direct proportionalities in the standard relation. Mass fraction: related but not the standard linear variable in the colligative formula. Common Pitfalls: Using molarity for boiling point calculations; since solution volume changes with temperature, molarity is less reliable than molality for thermal properties. Final Answer: Molal concentration (molality, m).

Question 15

Raoult’s law deviations in binary solutions: If component A shows a positive deviation from Raoult’s law in an A–B liquid mixture, what deviation does component B exhibit?

Accepted Answer

Introduction / Context: Non-ideal liquid mixtures often deviate from Raoult’s law. Understanding the sign of deviation helps predict azeotrope formation tendencies and guides separation strategies like distillation. Deviations reflect the relative strength of intermolecular interactions between unlike and like molecules. Given Data / Assumptions: Binary liquid solution of components A and B. Component A exhibits positive deviation (higher partial pressure than ideal). Concept / Approach: A positive deviation implies that A–B interactions are weaker than A–A and B–B on average, leading to greater escaping tendency (higher activity) for both components. Consequently, both components typically show positive deviations. Conversely, stronger unlike interactions cause negative deviations for both components. Thus, deviation signs are paired in binary systems under standard assumptions. Step-by-Step Solution: Interpret positive deviation: weaker A–B interactions.Implication: both A and B have enhanced vapor pressures vs. ideal.Therefore, B also shows positive deviation. Verification / Alternative check: Phase diagrams of classic positive-deviation systems (e.g., ethanol–cyclohexane) show total pressures above ideal predictions for the entire composition range, indicating both components deviate positively. Why Other Options Are Wrong: Negative or obeys Raoult: inconsistent with the symmetric effect of interaction weakening. Independent sign: in a simple binary with uniform interactions, deviations are not independent. No vapor pressure: physically incorrect for volatile liquids considered. Common Pitfalls: Assuming that only one component deviates; in binary solutions, deviation behavior is coupled through A–B interactions. Final Answer: Positive deviation from Raoult’s law.

Question 16

Evaporation through a stagnant film (units check): For pure aniline evaporating through a 1 mm stagnant air film at 300 K and 100 kPa, the computed rate of evaporation is 2.97 × 10^-4 in consistent SI units. What are the correct units of this flux q…

Accepted Answer

Introduction / Context: In mass transfer problems involving diffusion through a stagnant gas film, the calculated “rate” is often a flux, i.e., moles transferred per unit area per unit time. Distinguishing between total rate and areal flux prevents dimensional errors when scaling from laboratory calculations to equipment design, such as evaporators or drying operations. Given Data / Assumptions: Stagnant air film thickness: 1 mm. Temperature: 300 K; total pressure: 100 kPa. Vapor pressure of aniline: 0.1 kPa; total molar concentration: 40.1 mol/m^3. Diffusivity of aniline in air: 0.74 × 10^-5 m^2/s. Computed mass transfer coefficient: 7.4 × 10^-3 m/s (from D_AB/δ). Reported “rate” magnitude: 2.97 × 10^-4 in SI terms. Concept / Approach: The standard film theory gives a molar flux N_A in mol/m^2·s using N_A = k_c * (C_A,s − C_A,∞) or its equivalent for dilute species, where k_c has units of m/s and concentration difference has units of mol/m^3. Multiplying m/s by mol/m^3 yields mol/m^2·s. Thus, a numerical value near 10^-4 with the provided parameters corresponds to a flux, not a total rate integrated over area. Step-by-Step Solution: Use k_c = D_AB / δ with δ = 1 × 10^-3 m → k_c ≈ 0.74 × 10^-2 m/s.Compute driving force: C_A,s − C_A,∞ ≈ (p_A,s/RT − ~0) ≈ 0.1 kPa / (R T) → consistent with given overall C of 40.1 mol/m^3 and low vapor pressure.Form units: (m/s) * (mol/m^3) = mol/m^2·s.Hence the reported 2.97 × 10^-4 must carry units of mol/m^2·s. Verification / Alternative check: Dimensional analysis alone confirms the unit: any mass transfer coefficient based on concentration difference delivers areal flux units. Converting to kmol/m^2·s would move the decimal by 3 orders of magnitude; cm^2 would change the numerical value by 10^4. Why Other Options Are Wrong: mol/s: a total rate, not normalized by area. mol/cm^2·s: would require value scaled by 10^4. kmol/m^2·s: different magnitude by 10^3. kg/m^2·s: mass flux; would need molar mass conversion. Common Pitfalls: Confusing total evaporation rate with molar flux; always check whether an area normalization is implied by the governing equations. Final Answer: mole/m2·s.

Question 17

For gas mixtures used in chemical engineering calculations, the measured volume percent (% v/v) corresponds to which composition basis? Select the most accurate statement and assume ideal-gas behavior is the usual simplifying context.

Accepted Answer

Introduction / Context: Engineers frequently report compositions of gas mixtures as volume percent, mole percent, or mass percent. Understanding when “volume percent” can be equated to another basis is essential for material balances, reactor design, and environmental reporting. This question focuses on the special relationship between volume fraction and mole fraction in the ideal-gas limit. Given Data / Assumptions: Mixture of gases at uniform temperature and pressure. Ideal-gas approximation unless otherwise stated. Volume percent means partial volume divided by total volume, expressed as a percentage. Concept / Approach: For ideal gases, the equation pV = nRT shows that, at the same T and total P, a component’s partial pressure is proportional to its number of moles, and likewise its partial volume is proportional to its mole count. Therefore, under ideal-gas behavior, volume fraction equals mole fraction. For real gases with significant non-ideality, compressibility factors differ among components, and the equality does not strictly hold. Step-by-Step Solution: Write ideal-gas law: p_i V = n_i R T and P V_total = n_total R T.Divide: V_i / V_total = n_i / n_total when T and P are the same.Hence, volume percent = mole percent only in the ideal-gas limit.In non-ideal cases, use fugacity/compressibility to relate volumes and moles. Verification / Alternative check: Dalton’s law of partial pressures for ideal mixtures gives y_i = p_i / P = V_i / V_total = n_i / n_total, confirming the equivalence only when ideal assumptions apply. Why Other Options Are Wrong: Weight percent: depends on molecular weights; not generally equal to volume percent. Mole percent (unqualified): true only for ideal gases, not always. Weight percent only for ideal gases: incorrect relationship. Neither under any conditions: false; equivalence does occur for ideal gases. Common Pitfalls: Assuming volume percent equals mole percent for high-pressure real gases without checking non-ideality; this can introduce significant errors in design calculations. Final Answer: mole percent only for ideal gases

Question 18

In basic atomic structure, the mass number (A) of an atom is defined as the sum of which subatomic particles?

Accepted Answer

Introduction / Context: The mass number is a foundational concept in chemistry and nuclear engineering. It underpins isotopic notation, nuclear reactions, and calculations involving molar mass approximations for elements and nuclides. Given Data / Assumptions: Atoms contain protons, neutrons (nucleons), and electrons. Electron mass is negligible compared with nucleons for mass number purposes. Concept / Approach: Mass number A equals the total number of nucleons in the nucleus, i.e., protons (Z) plus neutrons (N). Electrons determine charge balance but contribute negligibly to A. Therefore A = Z + N, and isotopes of the same element share Z but differ in N and hence in A. Step-by-Step Solution: Identify nucleus contents: protons and neutrons.Define A: A = Z (protons) + N (neutrons).Exclude electrons from mass number definition.Select the option that states “neutrons and protons.” Verification / Alternative check: Standard nuclide notation ^A_ZX encodes A and Z explicitly, confirming A counts nucleons only. Why Other Options Are Wrong: Protons and electrons / neutrons and electrons: electrons do not determine mass number. Both (a) & (b): includes an incorrect pairing. Electrons only: incorrect by definition. Common Pitfalls: Confusing atomic number (Z = protons) with mass number (A = protons + neutrons). Final Answer: neutrons and protons

Question 19

According to Hess’s law, which factor does the standard heat of reaction (enthalpy change at a stated temperature) NOT depend upon?

Accepted Answer

Introduction / Context: Thermochemistry distinguishes state functions from path functions. The heat of reaction reported as an enthalpy change at a specified temperature is a state function result, central to energy balances and reactor heat-duty estimates. Given Data / Assumptions: Enthalpy is a state function; it depends on initial and final states. Standard heats are tabulated at specified temperature, pressure, and physical states. Constant-pressure heat equals enthalpy change; constant-volume heat equals internal energy change. Concept / Approach: By Hess’s law, the enthalpy change for a reaction is independent of the path or mechanism. However, it does depend on the temperature and on the physical states of the species because these define the thermodynamic states. Reporting at constant pressure versus constant volume distinguishes ΔH from ΔU; the chosen condition matters for the type of heat reported but not for path dependence. Step-by-Step Solution: Identify state function: ΔH depends only on initial and final states.Note that changing physical states changes enthalpies of formation → affects ΔH.Recognize temperature changes alter heat capacities and enthalpy levels.Therefore, the one factor that does not influence ΔH is the route/method (path) taken. Verification / Alternative check: Construct the reaction enthalpy from standard enthalpies of formation; the balanced sum is path-independent by definition. Why Other Options Are Wrong: Physical state: affects enthalpy via latent/sensible contributions. Constant pressure vs constant volume: distinguishes ΔH and ΔU reporting. Reaction temperature: ΔH varies with T through heat capacities. Common Pitfalls: Assuming ΔH is numerically identical at any temperature or phase combination; always specify T and phase. Final Answer: the route or method by which the final products are obtained

Question 20

Microscopic interpretation of internal energy (U): which components make up the internal energy of a substance?

Accepted Answer

Introduction / Context: Internal energy is the sum of all microscopic forms of energy in a system and is fundamental in the first law of thermodynamics. Understanding its components clarifies heat capacities, phase behavior, and energy storage in molecules. Given Data / Assumptions: Consider molecules in any phase (gas, liquid, solid). Assume classical contributions plus quantum restrictions at low temperature. Concept / Approach: For molecules, internal energy includes translational energy (center-of-mass motion), rotational energy (angular motion), and vibrational energy (bond stretching/bending). In condensed phases, additional contributions arise from intermolecular potentials; in solids, lattice vibrations dominate. At low temperatures, some modes may be “frozen out,” but in general all three listed categories contribute to U. Step-by-Step Solution: Identify kinetic contributions: translational, rotational.Add vibrational contributions (intra- and inter-molecular).Recognize phase-specific manifestations (e.g., phonons in solids).Therefore, the internal energy comprises all listed components. Verification / Alternative check: Heat capacity models (equipartition, statistical mechanics) partition energy into these modes, supporting the comprehensive view. Why Other Options Are Wrong: Selecting only one or two modes ignores complete molecular energy storage. None of these: contradicts basic molecular theory. Common Pitfalls: For monatomic ideal gases, only translational modes contribute significantly—do not generalize that case to all substances. Final Answer: all (a), (b) & (c)

Stoichiometry Questions