Q: Ideal solution flash (Raoult’s law): A liquid mixture contains 0.4 mol fraction benzene (p^sat = 3 atm) and 0.6 mol fraction toluene (p^sat = 4/3 atm) at a given temperature. Assuming ideal behavior and equilibrium, what is the benzene mole fraction…

Introduction / Context: For ideal binary mixtures, Raoult’s law and Dalton’s law provide a rapid way to compute equilibrium vapor compositions from known liquid compositions and saturation pressures at a fixed temperature. Benzene–toluene is a classic nearly ideal pair used in teaching VLE basics. Given Data / Assumptions: x_B = 0.4, x_T = 0.6 in the liquid. p_B^sat = 3 atm, p_T^sat = 4/3 atm at the same temperature. Ideal behavior: p_i = x_i p_i^sat and y_i = p_i / P_total (proportional to partial pressures). Concept / Approach: The vapor composition y_B equals the benzene partial pressure divided by the total pressure. Under Raoult’s law, total pressure is p_total = x_B p_B^sat + x_T p_T^sat, and the benzene partial pressure is x_B p_B^sat. Hence y_B = (x_B p_B^sat) / (x_B p_B^sat + x_T p_T^sat). Step-by-Step Solution: Compute numerator: x_B p_B^sat = 0.4 × 3 = 1.2 atm.Compute denominator: 1.2 + (0.6 × 4/3) = 1.2 + 0.8 = 2.0 atm.Therefore y_B = 1.2 / 2.0 = 0.6. Verification / Alternative check: Because benzene is more volatile (higher p^sat), its vapor-phase fraction must exceed its liquid fraction: y_B (0.6) > x_B (0.4), confirming the direction of enrichment. Why Other Options Are Wrong: 0.4: equals the liquid fraction, ignoring volatility differences.0.8 or 0.2: over- or underestimates enrichment relative to the saturation pressure ratio. Common Pitfalls: Dividing by total pressure from a different state; forgetting to normalize y_B + y_T = 1; mixing activity coefficients into an ideal problem. Final Answer: 0.6

Question 1

Counting entities in one gram-mole of methane: One gram-mole (1 mol) of methane, CH4, contains which of the following?

Accepted Answer

Introduction / Context: Chemical stoichiometry hinges on interpreting moles, molecules, and gram-atoms correctly. Methane (CH4) has one carbon atom and four hydrogen atoms per molecule, so one mole of CH4 contains Avogadro’s number of molecules and four times that number of hydrogen atoms. Given Data / Assumptions: Avogadro’s number N_A ≈ 6.02 × 10^23 per mole. Formula of methane: CH4. “Gram-atom” of an element means 1 mole of that element’s atoms. Concept / Approach: For a compound A_xB_y, one mole contains x gram-atoms of A and y gram-atoms of B. Therefore, 1 mol CH4 contains 1 gram-atom of carbon and 4 gram-atoms of hydrogen. Converting to counts: hydrogen atoms = 4 N_A; methane molecules = 1 N_A. Mass-wise, 1 mol CH4 contains 12 g of carbon and 4 g of hydrogen, total 16 g. Step-by-Step Solution: Map stoichiometry: CH4 → 4 H per molecule.Per mole: hydrogen gram-atoms = 4 mol.Hence, “4 gram-atoms of hydrogen” is correct. Verification / Alternative check: Atom count check: H atoms = 4 × 6.02 × 10^23 ≈ 2.41 × 10^24; greater than 6.02 × 10^23 in option (a), confirming (a) is too small. Why Other Options Are Wrong: 6.02 × 10^23 H atoms: undercounts by a factor of four.3.01 × 10^23 CH4 molecules: equals 0.5 mol, not 1 mol.3 g of carbon: 1 mol CH4 contains 12 g of carbon, not 3 g. Common Pitfalls: Confusing “molecules per mole” with “atoms per mole”; misreading gram-atom terminology. Final Answer: 4 gram-atoms of hydrogen

Question 2

Psychrometrics terminology: For a given gas–vapor mixture, the percentage saturation of the vapor is always how compared to the relative saturation (relative humidity) at the same state?

Accepted Answer

Introduction / Context: In gas–vapor systems (most commonly air–water), several humidity measures exist. Two often-confused quantities are relative humidity (relative saturation) and percentage saturation. Plant operators, HVAC engineers, and dryer designers must distinguish these to read charts and size equipment correctly. Given Data / Assumptions: Same total pressure and temperature for both measures. Relative saturation φ = p_v / p_v^sat (ratio of partial pressure to saturation pressure). Percentage saturation μ compares actual humidity ratio to the humidity ratio at saturation at the same T and P, adjusting for the vapor displacement effect. Concept / Approach: Because the presence of vapor reduces the partial pressure available for the dry gas, the humidity ratio at saturation differs from the simple ratio implied by φ. The rigorous definition yields μ < φ for all unsaturated mixtures. The two values coincide only in the dilute-vapor limit (very low humidity) or at saturation where both equal 100%. Step-by-Step Solution: Relative humidity: φ = p_v / p_v^sat.Humidity ratio at state: W = 0.622 p_v / (P − p_v); at saturation: W_s = 0.622 p_v^sat / (P − p_v^sat).Percentage saturation: μ = 100 × (W / W_s).Algebra shows μ = 100 × φ × (P − p_v^sat)/(P − p_v) < 100 × φ for unsaturated states (p_v < p_v^sat), thus μ < φ. Verification / Alternative check: On a psychrometric chart, lines of constant relative humidity lie above those of constant percentage saturation except at saturation where they meet. Why Other Options Are Wrong: Higher than / Equal to: contradicts the mathematical relationship and chart geometry.“Either (a) or (b)”: not correct for standard air–water systems at fixed T and P below saturation. Common Pitfalls: Using φ and μ interchangeably; forgetting the denominator correction (P − p_v) vs (P − p_v^sat). Final Answer: smaller than

Question 3

Ideal solution flash (Raoult’s law): A liquid mixture contains 0.4 mol fraction benzene (p^sat = 3 atm) and 0.6 mol fraction toluene (p^sat = 4/3 atm) at a given temperature. Assuming ideal behavior and equilibrium, what is the benzene mole fraction…

Accepted Answer

Introduction / Context: For ideal binary mixtures, Raoult’s law and Dalton’s law provide a rapid way to compute equilibrium vapor compositions from known liquid compositions and saturation pressures at a fixed temperature. Benzene–toluene is a classic nearly ideal pair used in teaching VLE basics. Given Data / Assumptions: x_B = 0.4, x_T = 0.6 in the liquid. p_B^sat = 3 atm, p_T^sat = 4/3 atm at the same temperature. Ideal behavior: p_i = x_i p_i^sat and y_i = p_i / P_total (proportional to partial pressures). Concept / Approach: The vapor composition y_B equals the benzene partial pressure divided by the total pressure. Under Raoult’s law, total pressure is p_total = x_B p_B^sat + x_T p_T^sat, and the benzene partial pressure is x_B p_B^sat. Hence y_B = (x_B p_B^sat) / (x_B p_B^sat + x_T p_T^sat). Step-by-Step Solution: Compute numerator: x_B p_B^sat = 0.4 × 3 = 1.2 atm.Compute denominator: 1.2 + (0.6 × 4/3) = 1.2 + 0.8 = 2.0 atm.Therefore y_B = 1.2 / 2.0 = 0.6. Verification / Alternative check: Because benzene is more volatile (higher p^sat), its vapor-phase fraction must exceed its liquid fraction: y_B (0.6) > x_B (0.4), confirming the direction of enrichment. Why Other Options Are Wrong: 0.4: equals the liquid fraction, ignoring volatility differences.0.8 or 0.2: over- or underestimates enrichment relative to the saturation pressure ratio. Common Pitfalls: Dividing by total pressure from a different state; forgetting to normalize y_B + y_T = 1; mixing activity coefficients into an ideal problem. Final Answer: 0.6

Question 4

Conditions for ideal (Raoultian) solutions: when do liquid mixtures behave ideally? Select the statement that correctly identifies the zero-change criteria required for an ideal solution.

Accepted Answer

Introduction / Context: In solution thermodynamics, an ideal liquid solution (often called Raoultian) is a reference model used to estimate vapor–liquid equilibrium and colligative properties. Knowing the defining criteria of ideality helps engineers decide when Raoult's law can be applied without activity coefficients. Given Data / Assumptions: We are dealing with liquid mixtures of chemically similar components. Question asks for conditions that characterize ideal solutions. No phase change other than mixing is considered. Concept / Approach: For an ideal solution, intermolecular interactions between unlike molecules are effectively the same as those between like molecules. As a result, mixing neither releases nor absorbs heat and does not cause volume contraction or expansion. Formally, ΔH_mix = 0 and ΔV_mix = 0, and activity coefficients γ_i ≈ 1 across the full composition range. Step-by-Step Solution: Identify the hallmark of ideality: no energetic or volumetric driving force upon mixing.Translate to thermodynamic statements: ΔH_mix = 0 and ΔV_mix = 0.Select the option that includes both conditions. Verification / Alternative check: Classic near-ideal pairs (e.g., benzene–toluene) show negligible heats and volume changes on mixing, supporting the criteria experimentally. Why Other Options Are Wrong: Only heat or only volume being zero is insufficient; claiming neither needs to be zero contradicts the definition; activity coefficients greater than one indicate positive deviation, not ideality. Common Pitfalls: Confusing “ideal gas” with “ideal solution”; assuming only ΔH_mix matters but not ΔV_mix. Final Answer: both heat of mixing and volume change on mixing equal zero

Question 5

Thermochemistry of ammonia decomposition: Given ΔH_f°(NH3, g) = −46 kJ per kg·mole, find ΔH° for 2 NH3(g) → N2(g) + 3 H2(g).

Accepted Answer

Introduction / Context: Calculating reaction enthalpy from standard heats of formation is a staple skill in energy balances and reactor design. This problem reverses ammonia formation to evaluate the decomposition enthalpy. Given Data / Assumptions: Standard heat of formation: ΔH_f°(NH3, g) = −46 kJ per kg·mole. Reaction: 2 NH3(g) → N2(g) + 3 H2(g). ΔH_f°(N2, g) = 0; ΔH_f°(H2, g) = 0 (elements in standard state). Concept / Approach: Use Hess’s law: ΔH°_rxn = Σ ν_p ΔH_f°(products) − Σ ν_r ΔH_f°(reactants). For elemental products, heats of formation are zero. The reaction is the reverse of ammonia formation; reversing a reaction changes the sign of ΔH and scaling by stoichiometric coefficients scales ΔH proportionally. Step-by-Step Solution: ΔH°_rxn = [1·0 + 3·0] − [2·(−46)] kJ per kg·mole of reaction as written.ΔH°_rxn = 0 − (−92) = +92 kJ per kg·mole.Therefore, decomposition is endothermic by 92 kJ per kg·mole (of reaction). Verification / Alternative check: Formation: N2 + 3 H2 → 2 NH3 has ΔH° = −92 kJ per kg·mole (twice −46). Reversing gives +92 kJ per kg·mole, consistent. Why Other Options Are Wrong: 46 and −23 use wrong scaling/sign; −92 is the formation value, not decomposition; 0 conflicts with the known exothermic formation of NH3. Common Pitfalls: Forgetting to multiply by stoichiometric coefficient 2; sign reversal when flipping the reaction. Final Answer: 92

Question 6

Properties of an ideal Raoultian solution: For a solution that strictly obeys Raoult’s law, what are ΔH_mix and ΔV_mix on mixing?

Accepted Answer

Introduction / Context: When liquid mixtures behave ideally, design calculations simplify dramatically because activities equal mole fractions. Recognizing the thermodynamic hallmarks of ideality helps in VLE modeling and quick feasibility studies. Given Data / Assumptions: Ideal solution behavior (Raoult’s law holds over full composition range). Mixing occurs at constant temperature and pressure. Concept / Approach: Ideality implies no enthalpy or volume effects on mixing. Hence, ΔH_mix = 0 (no heat released/absorbed) and ΔV_mix = 0 (no contraction/expansion). This reflects indistinguishable unlike/like interactions and activity coefficients near unity (γ_i ≈ 1). Step-by-Step Solution: State the ideal-solution criteria.Map them to thermodynamic statements: ΔH_mix = 0 and ΔV_mix = 0.Choose the option containing both equalities. Verification / Alternative check: Empirical data for near-ideal pairs (like benzene–toluene) show negligible heat and volume changes upon mixing, validating these criteria. Why Other Options Are Wrong: Options with nonzero ΔH or ΔV describe nonideal mixtures exhibiting positive/negative deviations from Raoult’s law. Common Pitfalls: Believing only one of the two (ΔH or ΔV) must be zero; both are required for strict ideality. Final Answer: both ΔH_mix = 0 and ΔV_mix = 0

Question 7

Unit consistency check for mass transfer coefficients: Identify the incorrect conversion among the following commonly used unit pairs.

Accepted Answer

Introduction / Context: Mass transfer coefficients appear with denominators that mix area and driving-force units (e.g., atm or bar). Converting accurately between SI and English units prevents order-of-magnitude errors in design correlations and vendor data sheets. Given Data / Assumptions: Base conversions: 1 lb = 0.45359237 kg; 1 ft^2 = 0.09290304 m^2; 1 atm = 1.01325 bar. Comparisons assume the same driving-force unit (when present) is converted consistently. Concept / Approach: For area-only conversions: multiply by (0.45359237 kg/lb) and divide by (0.09290304 m^2/ft^2) to switch from lb/(hr·ft^2) to kg/(hr·m^2). For pressure-unit conversions in denominators, scale numerically by the ratio between atm and bar: value_per_bar = value_per_atm / 1.01325 ≈ 0.98687·value_per_atm. Step-by-Step Solution: Convert 1 lb/(hr·ft^2): 0.45359237 / 0.09290304 ≈ 4.8823 kg/(hr·m^2) → option (c) is correct.Inverse relationship: 1 kg/(hr·m^2) should equal about 0.2048 lb/(hr·ft^2), not 4.8823 → option (d) is incorrect.For pressure conversion: 1 kg/(hr·m^2·atm) ≈ 0.98687 kg/(hr·m^2·bar) → option (b) is correct.Option (a) reflects combined area and pressure conversions and is numerically consistent when interpreted with ft^2 (typographical ft^2 vs ft^3 issues aside). Verification / Alternative check: Compute the inverse of 4.8823 to confirm ~0.2048, which exposes the error in option (d). Why Other Options Are Wrong (i.e., not selected): (a), (b), and (c) are consistent with standard constants; only (d) inverts the area conversion incorrectly. Common Pitfalls: Forgetting to invert when switching the direction of conversion; mixing atm↔bar without scaling the numerical value. Final Answer: 1 kg/(hr·m^2) = 4.8823 lb/(hr·ft^2) is the incorrect conversion.

Question 8

Graham’s law application to perfume diffusion: Perfume X diffuses twice as fast as perfume Y. If the vapor density of gas X is 2 (relative to hydrogen), estimate the molecular weight of Y.

Accepted Answer

Introduction / Context: Graham’s law relates diffusion rates of gases to the square roots of their molecular weights. This principle enables quick identification or cross-checking of gas identities in labs and process troubleshooting. Given Data / Assumptions: Rate_X = 2 · Rate_Y (X diffuses twice as fast as Y). Vapor density of X (relative to H2) = 2 → molecular weight M_X = 2 × 2 = 4. Ideal behavior; same conditions of T and P. Concept / Approach: Graham’s law: Rate ∝ 1/√M. Thus Rate_X / Rate_Y = √(M_Y / M_X). Rearranging provides M_Y directly from the rate ratio and M_X. Step-by-Step Solution: Write 2 = √(M_Y / M_X).Square: 4 = M_Y / M_X → M_Y = 4 · M_X.Given M_X = 4 → M_Y = 4 × 4 = 16. Verification / Alternative check: If Y has M = 16, then Rate_X / Rate_Y = √(16/4) = √4 = 2, which matches the statement. Why Other Options Are Wrong: 2, 4, and 8 correspond to smaller molecular weights that would not yield a rate ratio of 2; 32 would give Rate_X / Rate_Y = √(32/4) ≈ 2.828, too large. Common Pitfalls: Confusing vapor density with molecular weight; forgetting to square the rate ratio when solving for M_Y. Final Answer: 16

Question 9

Closed, rigid container heating: A gas initially at 27°C in a sealed rigid vessel is heated to 300°C. How does the pressure change (assume ideal gas)?

Accepted Answer

Introduction / Context: In constant-volume heating, ideal-gas pressure scales directly with absolute temperature. This is fundamental in sizing pressure relief and checking vessel ratings during heat-up transients. Given Data / Assumptions: Closed, rigid container (constant volume, constant moles). Ideal-gas approximation. T1 = 27°C = 300 K; T2 = 300°C = 573 K. Concept / Approach: For ideal gases at constant V and n, P ∝ T (absolute). Hence, P2/P1 = T2/T1. Compute the ratio using Kelvin temperatures. Step-by-Step Solution: Convert to Kelvin: T1 = 273 + 27 = 300 K; T2 = 273 + 300 = 573 K.Compute P2/P1 = 573/300 ≈ 1.91.This is very close to 2; among discrete options, “doubled” is the correct selection. Verification / Alternative check: Using PV = nRT at constant V and n shows pressure changes linearly with T, confirming the ratio above. Why Other Options Are Wrong: “Halved” and “trebled” contradict P ∝ T; “unpredictable” is incorrect because n and V are fixed; “increased by 50%” underestimates the effect. Common Pitfalls: Using Celsius directly instead of Kelvin; forgetting the vessel is rigid (constant V). Final Answer: doubled

Question 10

Colligative effects of a non-volatile solute: Adding a non-volatile solute to a solvent causes which primary change in the solvent at a given temperature?

Accepted Answer

Introduction / Context: Colligative properties arise from solute particle count rather than identity. Recognizing the first-principles effect—vapor pressure lowering—helps explain boiling point elevation and freezing point depression that follow from phase equilibria shifts. Given Data / Assumptions: Solute is non-volatile and does not associate/dissociate strongly. Temperature initially fixed while assessing immediate effect. Concept / Approach: Raoult’s law for the solvent: P_solvent = x_solvent · P°_solvent. Adding non-volatile solute reduces x_solvent, thereby lowering the solvent’s equilibrium vapor pressure. The reduced vapor pressure leads to boiling point elevation (higher T needed for P_vap = P_ext) and freezing point depression (liquid phase stabilized), but those require temperature change to observe. Step-by-Step Solution: Add solute → x_solvent decreases.By Raoult’s law, P_solvent decreases at the same T.Therefore, the immediate, primary change is vapor pressure lowering. Verification / Alternative check: Boiling point elevation and freezing point depression equations (ΔT_b = K_b · m, ΔT_f = K_f · m) are consequences of the vapor pressure change and phase equilibrium, supporting this cause–effect chain. Why Other Options Are Wrong: Freezing point elevation and boiling point depression are reversed in sign; claiming all as listed is incorrect; surface tension behavior is system-specific and not a defining colligative property. Common Pitfalls: Confusing the primary at-constant-T effect (vapor pressure) with the induced temperature shifts. Final Answer: vapor pressure lowering

Question 11

Heat transfer coefficient conversions: Identify the incorrect unit conversion in the list below (use consistent temperature-difference units).

Accepted Answer

Introduction / Context: Heat transfer coefficients appear in multiple unit systems. Accurate conversion is vital when interpreting vendor data, literature correlations, or software outputs. Given Data / Assumptions: Equivalence of temperature differences: 1 K = 1 °C (for differences). Base factors: 1 kcal = 4186.8 J; 1 hr = 3600 s; 1 ft^2 = 0.09290304 m^2; 1 BTU/(ft^2·hr·°F) = 5.678 W/(m^2·K). Concept / Approach: Start with the anchor: 1 kcal/(m^2·hr·°C) = 4186.8/3600 W/(m^2·K) ≈ 1.163 W/(m^2·K). Convert between BTU and SI using 1 W/(m^2·K) = 0.1761 BTU/(ft^2·hr·°F). Maintain the same temperature-difference unit on both sides of an equality to avoid ambiguity, even though ΔK = Δ°C numerically. Step-by-Step Solution: Option (a): Matches known constants (both BTU and SI values); correct.Option (c): 1 W/(m^2·K) ≈ 0.1761 BTU/(ft^2·hr·°F); writing °C is acceptable for differences, so correct.Option (d): Using 5.678 W/(m^2·K) and back-converting to kcal and kJ/hr·m^2·°C reproduces the listed values; correct.Option (b): Although numerically equal, it mixes K on the left with °C on the right within a single equality. The rigorous statement should be 1 kcal/(m^2·hr·K) = 1.163 W/(m^2·K). As written, it is inconsistent and thus considered incorrect. Verification / Alternative check: Compute 4186.8/3600 ≈ 1.163 and confirm against 5.678 and 0.1761 cross-relations; all are self-consistent when units are kept uniform. Why Other Options Are Wrong (i.e., not selected): They maintain internal consistency with standard constants; (b) does not present a clean like-for-like unit match. Common Pitfalls: Dropping unit consistency when ΔK and Δ°C are numerically equal; mixing per-°F with per-°C without the 1.8 factor where appropriate. Final Answer: 1 kcal/(m^2·hr·K) = 1.163 W/(m^2·°C) is the incorrect form as written.

Question 12

Rigid-vessel condensation calculation: 1 kg saturated steam at 100°C (V = 1.673 m^3) is cooled in a rigid vessel to 98°C. Given v_g at 98°C = 1.789 m^3/kg (v_f negligible). How many kilograms of vapor condense?

Accepted Answer

Introduction / Context: Steam in a rigid container undergoes condensation upon cooling until the mixture satisfies saturation at the final temperature. This is a common transient in thermal equipment cool-down and storage vessels. Given Data / Assumptions: Initial: 1 kg saturated vapor at 100°C; total volume V_total = 1.673 m^3. Final: 98°C saturated mixture in the same rigid volume. Specific volume of saturated vapor at 98°C: v_g = 1.789 m^3/kg; specific liquid volume v_f ≈ 0 (negligible compared with v_g). Concept / Approach: At equilibrium, total volume equals vapor mass times vapor specific volume plus negligible liquid volume. Thus, m_v = V_total / v_g, and condensed mass m_condensed = m_initial − m_v. Step-by-Step Solution: Compute vapor mass at 98°C: m_v = 1.673 / 1.789 ≈ 0.9359 kg.Condensation: m_condensed = 1.000 − 0.9359 ≈ 0.0641 kg.Rounded to the options, m_condensed ≈ 0.065 kg. Verification / Alternative check: Because v_g at 98°C is larger than at 100°C, less vapor is needed to occupy the fixed volume; thus some vapor must condense, giving a small positive condensed mass—consistent with the result. Why Other Options Are Wrong: 0.0 implies no condensation (incorrect); 0.1 is too large; 1.0 means complete condensation; 0.33 is arbitrary and inconsistent with the volume ratio. Common Pitfalls: Forgetting to use absolute total vessel volume; neglecting that v_f is negligible but not negative; mixing specific volume data at different temperatures. Final Answer: 0.065

Question 13

Boyle’s law check: For a fixed mass of an ideal gas at constant temperature, if the volume becomes three times, what happens to the pressure?

Accepted Answer

Introduction / Context: Boyle’s law describes the inverse relationship between pressure and volume for a given amount of ideal gas at constant temperature. This simple proportionality is used constantly in compressor, storage, and pipeline calculations. Given Data / Assumptions: Gas amount n constant; temperature constant (isothermal). Initial pressure P and volume V; final volume is 3V. Concept / Approach: Boyle’s law: P · V = constant. Therefore, P_final = (P_initial · V_initial) / V_final. With V_final = 3V_initial, pressure must decrease in the same ratio. Step-by-Step Solution: Start with P1V1 = P2V2.Set V2 = 3V1 → P2 = P1V1/(3V1) = P1/3.Hence, pressure becomes one-third of its original value. Verification / Alternative check: Graphically, the isotherm PV = constant is a rectangular hyperbola; tripling V moves along the curve to one-third P, consistent with the formula. Why Other Options Are Wrong: 3P, 9P, and 9P^2 contradict the inverse proportionality; “unchanged” ignores Boyle’s law entirely. Common Pitfalls: Using Celsius rather than ensuring temperature is constant but in absolute units (not needed for Boyle’s law proportionality); forgetting it is the same mass of gas. Final Answer: P/3

Question 14

Thermal decomposition of calcium carbonate: How many kilograms of CaCO3 must be heated to produce 56 kg of quicklime (CaO)?

Accepted Answer

Introduction / Context: This stoichiometry question checks your ability to relate reactants and products for the calcination reaction used in cement and lime manufacture: CaCO3 decomposes to CaO (quicklime) and CO2. Understanding molar masses and fixed mass ratios is essential in chemical process calculations. Given Data / Assumptions: Reaction: CaCO3 → CaO + CO2 (complete conversion). Molar mass: CaCO3 = 100 kg per kmol, CaO = 56 kg per kmol, CO2 = 44 kg per kmol. Product CaO required = 56 kg. Concept / Approach: The balanced reaction shows a 1:1 molar ratio between CaCO3 and CaO. Therefore the mass ratio follows directly from molar masses. For each 56 kg of CaO formed, 100 kg of CaCO3 are consumed and 44 kg of CO2 are released. Step-by-Step Solution: From stoichiometry: 1 kmol CaCO3 (100 kg) → 1 kmol CaO (56 kg).Required CaO = 56 kg corresponds to 1 kmol.Thus CaCO3 needed = 1 kmol = 100 kg. Verification / Alternative check: Mass conservation: 100 kg (CaCO3) = 56 kg (CaO) + 44 kg (CO2). Numbers balance perfectly, confirming the calculation. Why Other Options Are Wrong: 56: Confuses product mass with reactant requirement; ignores CO2 mass. 144 or 1000: Do not match the fixed stoichiometric ratio from molar masses. Common Pitfalls: Using atomic rather than formula masses, or assuming 1:1 by mass instead of 1:1 by moles. Always convert through molar masses for solids and gases in reactions. Final Answer: 100

Question 15

Kopp’s rule: For which type of substances is Kopp’s rule primarily used to estimate heat capacity?

Accepted Answer

Introduction / Context: Kopp’s rule is a classical empirical guideline in thermodynamics used to estimate the molar heat capacity of crystalline solids from the sum of atomic contributions. It is often referenced in materials and inorganic chemistry when data are scarce. Given Data / Assumptions: Kopp’s rule applies to solids, especially inorganic crystalline compounds. It approximates molar heat capacity at constant pressure near room temperature. Gas-phase heat capacities typically require different models (e.g., equipartition, statistical mechanics, correlations). Concept / Approach: The rule states: the molar heat capacity of a solid compound is approximately the sum of the atomic heat capacities of its constituent elements multiplied by their stoichiometric counts. It works reasonably for many ionic solids and simple crystals. Step-by-Step Solution: Identify target property: Cp of a solid compound.Express Cp,compound ≈ Σ (n_i * Cp,atomic,i).Use when direct calorimetric data are unavailable. Verification / Alternative check: Compare to experimental Cp values. Deviations occur for complex structures or strong anharmonic effects, but order-of-magnitude accuracy is common. Why Other Options Are Wrong: Gases (options b and c): Gas heat capacities vary strongly with temperature and molecular structure; Kopp’s rule is not intended for gases. Activation energy: A kinetic parameter unrelated to heat capacity. Common Pitfalls: Applying Kopp’s rule at very high or very low temperatures where solid heat capacity deviates significantly from room-temperature trends. Final Answer: heat capacities of solids

Question 16

Select the correct SI unit for specific heat at constant pressure, Cp, used in energy balance calculations.

Accepted Answer

Introduction / Context: Specific heat capacity at constant pressure (Cp) is central to sensible-heat calculations, heater duty estimation, and thermodynamic property evaluation. Using the correct unit is crucial for consistent results in SI-based computations. Given Data / Assumptions: Cp relates heat input to temperature change per unit mass at constant pressure. SI base units: joule (J), kilogram (kg), kelvin (K). Concept / Approach: By definition, Cp = Q / (m * ΔT) at constant pressure, so the SI unit is J/kg·K. Alternative property units like W/m·K or W/m^2·°C correspond to thermal conductivity and heat flux, not specific heat. Step-by-Step Solution: Define Cp: heat per mass per temperature rise.Map to SI: J per kg per K → J/kg·K.Confirm dimensional consistency in enthalpy change: Δh = ∫Cp dT yields J/kg. Verification / Alternative check: Unit analysis across typical equations (e.g., Q = m * Cp * ΔT) reproduces J as energy, verifying the choice. Why Other Options Are Wrong: 0°K: A temperature value, not a unit of Cp. W/m^2·°C and W/m·°K: Units of heat flux and thermal conductivity respectively, not specific heat. Common Pitfalls: Confusing mass-based Cp (J/kg·K) with molar heat capacity (J/mol·K). Ensure consistency with property tables. Final Answer: J/kg·K

Question 17

Scientific prefixes: The prefix “giga” (G) represents which power of ten?

Accepted Answer

Introduction / Context: Metric prefixes are ubiquitous in engineering data sheets, process instrumentation, and scientific notation. Knowing the exponent associated with a prefix avoids orders-of-magnitude errors in calculations and reporting. Given Data / Assumptions: We follow SI prefix conventions. Giga is commonly used for large quantities (e.g., gigapascal, gigajoule). Concept / Approach: SI prefixes map a symbol to a power of ten. The sequence around giga is: mega (10^6), giga (10^9), tera (10^12), peta (10^15). Negative exponents include milli (10^-3), micro (10^-6), nano (10^-9), pico (10^-12). Step-by-Step Solution: Identify “giga” → 10^9.Cross-check surrounding prefixes to avoid confusion with tera (10^12) and pico (10^-12). Verification / Alternative check: Common usage examples: 1 GJ = 10^9 J; 1 GHz = 10^9 cycles/s. These confirm the 10^9 scaling. Why Other Options Are Wrong: 10^-12: That is pico. 10^12: That is tera. 10^15: That is peta. Common Pitfalls: Mixing up giga with tera due to both using capital letters; always confirm the exponent. Final Answer: 10^9

Question 18

Solubility laws and polarity: Identify the incorrect statement regarding Raoult’s law, molecular polarity, and typical properties of nonpolar compounds.

Accepted Answer

Introduction / Context: Understanding when Raoult’s law or Henry’s law applies is crucial for predicting solubilities and vapour–liquid equilibria. Polarity also governs miscibility and electrical properties of substances in solutions and mixtures. Given Data / Assumptions: Raoult’s law applies best to ideal solutions where solvent–solute interactions resemble solvent–solvent interactions. Gas solubility in liquids at low concentrations generally follows Henry’s law. Symmetry often correlates with nonpolarity (e.g., CH4, CCl4). Concept / Approach: Polar gases in nonpolar solvents rarely behave ideally; their solubility follows Henry’s law, not Raoult’s. Nonpolar molecules tend to be nonconductive and do not ionise. Many hydrocarbons are indeed nonpolar. Step-by-Step Solution: Check each statement against fundamental principles.Raoult’s vs Henry’s: gas solubility → Henry’s law is appropriate.Polarity by symmetry: CH4 and CCl4 are nonpolar.Hydrocarbons: predominantly nonpolar; properties align with (d). Verification / Alternative check: Experimental solubility data for polar gases (e.g., NH3, SO2) in nonpolar solvents deviate strongly from Raoult’s ideal-solution prediction and are handled via Henry’s constants. Why Other Options Are Wrong: (b), (c), and (d) reflect accepted chemical principles regarding symmetry, hydrocarbon polarity, and electrical properties of nonpolar compounds. Common Pitfalls: Misapplying Raoult’s law to dilute gas solubility problems; remember Raoult’s is for solvent partial pressures in liquid mixtures, not for dilute gases dissolving in liquids. Final Answer: Raoult's law holds good for the solubility of polar gases in non-polar liquids.

Question 19

When is the pressure effect on the heat capacity of gases negligible?

Accepted Answer

Introduction / Context: Gas heat capacities (Cp and Cv) depend mainly on temperature for ideal gases and only weakly on pressure at sufficiently low pressures. Recognising when pressure corrections can be neglected simplifies calculations and avoids unnecessary complexity. Given Data / Assumptions: Ideal-gas behaviour holds near 1 atm (or lower) for many gases away from condensation regions. Critical temperature alone does not determine pressure dependence of Cp. Concept / Approach: In the ideal-gas limit, Cp and Cv are independent of pressure. Real-gas deviations increase with pressure and proximity to phase boundaries. Thus, at pressures below about one atmosphere, the pressure effect is generally negligible for many engineering estimates. Step-by-Step Solution: Identify ideal-gas regime: low pressure, moderate T.Conclude Cp(T) with minimal pressure correction.Therefore option (a) is appropriate; (b) is not a universal criterion. Verification / Alternative check: Standard property tables and correlations (e.g., NASA polynomials) typically provide Cp as a function of T only for ideal-gas use, reflecting negligible pressure effect near 1 atm. Why Other Options Are Wrong: (b): Being below the critical temperature does not inherently ensure negligible pressure effects. (c) and (d): Include the incorrect condition or deny the correct one. Common Pitfalls: Applying high-pressure corrections unnecessarily in low-pressure design problems, complicating the analysis without benefit. Final Answer: at pressures below one atmosphere

Question 20

Universal gas constant R: Choose the correct value in kcal per kg-mol per °C (practical engineering units).

Accepted Answer

Introduction / Context: The universal gas constant R appears in equations of state (e.g., PV = nRT) and energy relations. Engineers often use convenient unit systems; one common choice is kcal per kg-mol per K (or °C for incremental differences). Given Data / Assumptions: Reference values: R = 8.314 kJ/mol·K = 1.987 kcal/mol·K. In many chemical engineering texts, “kg-mol” is used synonymously with “kmol” and retains the same numerical constant when paired consistently with other units. Concept / Approach: Unit conversions: 1 kcal = 4.184 kJ. Therefore 8.314 kJ/mol·K ÷ 4.184 ≈ 1.987 kcal/mol·K. In engineering usage this is frequently written per kg-mol·K with the same numerical value when moles are the basis entity in the chosen unit system. Step-by-Step Solution: Start: R = 8.314 kJ/mol·K.Convert: 8.314 / 4.184 ≈ 1.987 kcal/mol·K.Adopt engineering format: 1.987 kcal/(kg-mol·°C) (incremental °C ≡ K). Verification / Alternative check: Cross-check with English units: R ≈ 1.987 Btu/lb-mol·°R, consistent numerically, confirming the conversion pattern. Why Other Options Are Wrong: 2.79 and 3.99 are not equal to R in these units. “None of these” is incorrect because 1.987 is correct and widely used. Common Pitfalls: Mixing per mol and per kmol without adjusting other units; always keep unit systems internally consistent. Final Answer: 1.987

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