Heat & Calorimetry
A reaction flask feels cold because the reaction absorbs heat from its surroundings. Is the reaction endothermic or exothermic? Is ΔH positive or negative?
ANSWER: Endothermic; ΔH > 0.
WHY / SOLUTION: Heat flows into the system, so its enthalpy change is positive.
For a reaction, breaking chemical bonds takes in energy. Forming chemical bonds does what? Which of these steps has a positive energy contribution?
ANSWER: Bond formation releases energy; bond breaking requires energy (+).
WHY / SOLUTION: ΔH ≈ Σ(bonds broken) − Σ(bonds formed).
Which visible-light photon is more energetic: red light near 700 nm or violet light near 400 nm? Explain using wavelength and frequency.
ANSWER: Violet light is more energetic.
WHY / SOLUTION: Smaller λ means larger ν, and E = hν = hc/λ.
For an electron in a 3d subshell, what are n and l? How many orbital dashes should you draw?
ANSWER: n = 3; l = 2; five orbitals.
WHY / SOLUTION: d corresponds to l = 2. Allowed mₗ values: −2, −1, 0, +1, +2.
A student draws carbon’s 2p² as [↑↓][ ][ ]. What rule is violated, and how should the 2p diagram look?
ANSWER: Hund’s rule; [↑][↑][ ].
WHY / SOLUTION: Occupy equal-energy orbitals singly with parallel spins before pairing.
Which scientist gave the law that lets us combine enthalpy changes of reaction steps because ΔH is a state function?
ANSWER: Germain Hess — Hess’s law.
WHY / SOLUTION: The overall ΔH is the sum of step enthalpies and does not depend on the path.
How much heat warms 4.00 g of water by 8.00 °C? Use c = 4.184 J/(g·°C)?
ANSWER: 134 J absorbed (3 significant figures).
WHY / SOLUTION: q = mcΔT = (4.00 g)(4.184 J/g°C)(8.00°C) = 133.888 J.
Vaporizing 1 mol of water, H₂O(l) → H₂O(g), has ΔH = +44.0 kJ. What is ΔH when 1 mol of water vapor condenses?
ANSWER: −44.0 kJ.
WHY / SOLUTION: Reversing the reaction reverses the sign of ΔH.
A red laser has wavelength 650. nm. Find its frequency. Use c = 3.00 × 10⁸ m/s.
ANSWER: 4.62 × 10¹⁴ Hz.
WHY / SOLUTION: λ = 650 × 10⁻⁹ m; ν = c/λ = 3.00 × 10⁸ ÷ 6.50 × 10⁻⁷.
Given n = 4 and l = 2, name the subshell and list all allowed mₗ values.
ANSWER: 4d; mₗ = −2, −1, 0, +1, +2.
WHY / SOLUTION: l=2 means d; five distinct mₗ values mean five orbitals.
Which of these atoms have TWO unpaired electrons in their ground states: Mg, Si, or S? Choose all that apply.
ANSWER: Si and S.
WHY / SOLUTION: Mg 3s²: 0; Si 3p²: 2; S 3p⁴: 2 unpaired electrons.
Identify the law expressed by ΔE = q + w. What fundamental principle does it state?
ANSWER: The first law of thermodynamics: conservation of energy.
WHY / SOLUTION: A system’s internal-energy change equals heat transferred to it plus work done on it.
485 g of water absorbs 14.5 kJ. By how many °C does its temperature rise? Use c = 4.184 J/(g·°C).
ANSWER: 7.15 °C.
WHY / SOLUTION: ΔT = q/(mc) = 14,500 J ÷ (485 g × 4.184 J/g°C) = 7.15°C.
Melting 1 mol of ice requires +6.01 kJ. Vaporizing that water requires +44.0 kJ. Find ΔH for subliming 1 mol of ice directly to vapor.
ANSWER: +50.0 kJ/mol (to 3 sig. figs).
WHY / SOLUTION: Add the steps: ΔH = +6.01 + 44.0 = +50.01 ≈ +50.0 kJ/mol.
Mercury emits a violet line at 435.8 nm. What is the energy of one photon? Use h = 6.63 × 10⁻³⁴ J·s and c = 3.00 × 10⁸ m/s.
ANSWER: 4.56 × 10⁻¹⁹ J per photon.
WHY / SOLUTION: E = hc/λ = (6.63×10⁻³⁴)(3.00×10⁸)/(435.8×10⁻⁹) J.
Is (n=2, l=2, mₗ=0, mₛ=+½) an allowed set of quantum numbers? If not, repair it by changing only l.
ANSWER: Not allowed. Change l from 2 to 1 (or 0).
WHY / SOLUTION: For n=2, l can only be 0 or 1. mₗ=0 is valid for either choice.
Chromium and copper break the simple 4s² filling prediction. Give the ACTUAL ground-state shorthand configuration for BOTH neutral atoms.
ANSWER: Cr: [Ar] 4s¹ 3d⁵; Cu: [Ar] 4s¹ 3d¹⁰.
WHY / SOLUTION: The d⁵ and d¹⁰ arrangements are favored; use the experimentally observed configurations.
Which scientist explained the photoelectric effect using packets of light energy called photons?
ANSWER: Albert Einstein.
WHY / SOLUTION: Einstein’s photoelectric explanation supported the particle-like behavior of light.
30.0 g of water begins at 26.5 °C and absorbs 1.506 kJ from a reaction. What is its final temperature? Use c = 4.184 J/(g·°C).
ANSWER: 38.5 °C.
WHY / SOLUTION: ΔT = 1506 J / (30.0 g × 4.184 J/g°C) = 12.0°C; Tfinal = 26.5 + 12.0 = 38.5°C.
CH₄ + 2O₂ → CO₂ + 2H₂O(g) has ΔH = −802 kJ. Vaporization H₂O(l) → H₂O(g) has ΔH = +44 kJ/mol. Find ΔH when methane burns to form liquid water.
ANSWER: −890 kJ (per reaction as written).
WHY / SOLUTION: Reverse vaporization twice (2 × −44 = −88 kJ); combine with −802 kJ → −890 kJ.
A lithium atom emits a photon with energy 2.961 × 10⁻¹⁹ J. Find its wavelength. Use h = 6.63 × 10⁻³⁴ J·s and c = 3.00 × 10⁸ m/s.
ANSWER: 6.72 × 10⁻⁷ m (about 672 nm).
WHY / SOLUTION: λ = hc/E = (6.63×10⁻³⁴)(3.00×10⁸)/(2.961×10⁻¹⁹) ≈ 6.72×10⁻⁷ m.
A 3p orbital diagram has three boxes labeled mₗ = −1, 0, +1. What are all four quantum numbers for the DOWN arrow in the MIDDLE box?
ANSWER: (3, 1, 0, −½).
WHY / SOLUTION: 3p gives n=3, l=1; center dash mₗ=0; ↓ means mₛ=−½.
Start with neutral chromium’s actual configuration, then form Cr²⁺. Give its final configuration, number of unpaired electrons, and magnetic classification.
ANSWER: Cr²⁺: [Ar] 3d⁴; 4 unpaired; paramagnetic.
WHY / SOLUTION: Neutral Cr = [Ar] 4s¹ 3d⁵. Remove the 4s electron first, then one 3d electron.
Whose hydrogen-atom model uses allowed energy levels? In that model, an electron moves from n=3 to n=2. Is light absorbed or emitted?
ANSWER: Niels Bohr; light is emitted.
WHY / SOLUTION: Moving to a lower allowed level releases a photon (relaxation).
Mix 50.0 mL of 1.00 M HCl with 50.0 mL of 1.00 M NaOH. The solution warms by 6.50 °C. Assume density 1.00 g/mL and c = 4.184 J/(g·°C). Find q for the reaction, then ΔH per mole of water formed.
ANSWER: qreaction = −2.72 kJ; ΔH ≈ −54.4 kJ/mol.
WHY / SOLUTION: qsolution = 100.0 × 4.184 × 6.50 = +2719.6 J;
qreaction = −2.72 kJ.
Reaction makes 0.0500 mol H2O, so −2.7196/0.0500 = −54.4 kJ/mol.
Estimate ΔH for H₂(g) + Cl₂(g) → 2HCl(g) using bond enthalpies (kJ/mol): H–H 436, Cl–Cl 243, H–Cl 431.
ANSWER: Approximately −183 kJ per reaction.
WHY / SOLUTION: Broken: 436 + 243 = 679. Formed: 2 × 431 = 862. ΔH ≈ 679 − 862 = −183 kJ.
Find the energy of exactly 1 mole of photons from radio waves with frequency 1.002 × 10⁸ Hz. Use h = 6.63 × 10⁻³⁴ J·s; Nₐ = 6.022 × 10²³ mol⁻¹.
ANSWER: 4.00 × 10⁻² J per mole of photons.
WHY / SOLUTION: E = hνNₐ = (6.63×10⁻³⁴)(1.002×10⁸)(6.022×10²³) = 0.0400 J.
ANSWER: Not allowed. Change l from 2 to 1 (or 0).
WHY / SOLUTION: For n=2, l can only be 0 or 1. mₗ=0 is valid for either choice.
ANSWER: One valid answer: (4, 1, −1, −½).
WHY / SOLUTION: The fourth electron pairs in the leftmost 4p box under this stated filling convention. Different degenerate-orbital labels can also be physically valid.
Fe²⁺ and Zn²⁺ both have even electron counts. Which one is paramagnetic? Give each ion’s 3d configuration and unpaired-electron count.
ANSWER: Fe²⁺: [Ar] 3d⁶, 4 unpaired, PARAMAGNETIC. Zn²⁺: [Ar] 3d¹⁰, 0 unpaired, DIAMAGNETIC.
WHY / SOLUTION: Remove 4s before 3d. Even electron count does not guarantee all electrons are paired.
Name the THREE orbital-filling principles: (1) lowest-energy orbitals fill first; (2) two electrons in one orbital have opposite spins; (3) degenerate orbitals fill singly before pairing.
ANSWER: (1) Aufbau principle; (2) Pauli exclusion principle; (3) Hund’s rule.