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Química Geral · Exam review

Revisão de química nuclear e de coordenação

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O que você vai aprender

  • Balance nuclear equations, predict decay modes and count the α and β⁻ decays in a decay series.
  • Solve half-life, activity and radiometric-dating problems, including activity from a mass and ages from daughter-to-parent ratios.
  • Calculate mass defects, binding energies and reaction energies from atomic masses or binding energies per nucleon, per nucleus and per mole.
  • Read a coordination compound for its complex-ion charge, metal oxidation state, d-electron count, name, formula and isomers.
  • Use crystal field splitting, the spectrochemical series and pairing energy to predict spin state, unpaired electrons, magnetic moment, CFSE and colour.

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Nuclear equations and decay modes

Balance every nuclear equation twice: mass numbers (superscripts) and charges (subscripts) must each add up to the same total on both sides. α emission (⁴₂He, drawn) lowers A by 4 and Z by 2; β⁻ emission (⁰₋₁e) leaves A unchanged and raises Z by 1; positron emission (⁰₊₁e) and electron capture both lower Z by 1; γ emission changes neither. Example: ²³²₉₀Th →α ²²⁸₈₈Ra →β⁻ ²²⁸₈₉Ac →β⁻ ²²⁸₉₀Th, so one α and two β⁻ give an isotope of the starting element four mass units lighter. To count the steps in a series, only α changes A, so α = ΔA/4; then β⁻ = Z(final) − (Z(start) − 2 × α). For ²³²Th → ²⁰⁸Pb: α = 24/4 = 6, Z after six α = 90 − 12 = 78, so 82 − 78 = 4 β⁻. Predict the mode from the nuclide: Z ≥ 84 → α; mass number above the element's average atomic mass (neutron-rich) → β⁻; below it (proton-rich) → positron emission or electron capture. For bombardment reactions, solve for the unknown particle by subtracting A and Z.

Half-life, activity and dating

Decay is first order: k = ln 2/t½ = 0.693/t½, N = N₀(½)^(t/t½), and t = (t½/0.693) ln(N₀/N). Activity A = kN, in becquerels (decays per second) when k is in s⁻¹. Example: 1.00 µg of iodine-131 (t½ = 8.02 d, 130.9 g/mol) holds N = (1.00 × 10⁻⁶/130.9) × 6.022 × 10²³ = 4.60 × 10¹⁵ atoms; k = 0.693/(8.02 × 86 400 s) = 1.00 × 10⁻⁶ s⁻¹, so A = 4.60 × 10⁹ Bq. For equal numbers of atoms, activity is inversely proportional to half-life. If a mineral started with no daughter and none escaped, every lost parent atom became a daughter atom: after n half-lives P = (½)ⁿ of the original and D = 1 − (½)ⁿ, so D/P = 2ⁿ − 1 (3 after two half-lives, not 1/4). Radiocarbon: living carbon gives 15.3 disintegrations per minute per gram of carbon, so first divide a sample's count by its carbon mass. A 4.00 g sample counting 30.6 per minute gives 7.65 per minute per gram, half the living value, so it is one half-life (5730 yr) old. A decaying nuclide becomes its daughter: every tritium atom that decays gives one helium-3 atom.

Mass defect, binding energy and reaction energy

Use atomic masses with ¹H = 1.007825 u for each proton (the electrons then cancel) and n = 1.008665 u for each neutron. Mass defect Δm = Z(1.007825) + N(1.008665) − M(atom); binding energy = Δm × 931.5 MeV/u. For ¹²C: Δm = 6(1.007825) + 6(1.008665) − 12.000000 = 0.098940 u, so 92.16 MeV, or 7.68 MeV per nucleon. Binding energy per nucleon peaks near iron (about 8.8 MeV), so fusion of light nuclei and fission of heavy nuclei both release energy. For any reaction, energy released = (mass of reactants − mass of products) × 931.5 MeV/u: ³He + ³He → ⁴He + 2 ¹H releases (6.032058 − 6.018252) × 931.5 = 12.86 MeV. With binding energies instead, energy released = total binding energy of products − total binding energy of reactants; free neutrons and ¹H have none. Per mole, convert Δm in g/mol to kg and use E = Δm c² with c = 2.998 × 10⁸ m/s; 1 MeV per particle equals 9.649 × 10⁷ kJ/mol. The same relation applies to chemistry: a system that loses energy ΔU loses mass ΔU/c², but for chemical energies that is only nanograms per mole.

Reading a coordination compound

Work from the outside in. Counter-ions fix the charge of the complex ion; ligand charges then fix the metal's oxidation state; and d count = group number − oxidation state, because the 4s (or 5s, 6s) electrons leave first. Neutral ligands: H₂O, NH₃, CO, en (ethylenediamine, drawn). Anionic ligands: halides, OH⁻, CN⁻ and NO₂⁻ (−1), oxalate (−2). Example: in Na₃[Co(NO₂)₆] the complex is 3−, so x − 6 = −3, cobalt is +3 and, in group 9, d⁶. Chloride inside the brackets is a ligand and still counts −1. Coordination number counts donor atoms, so each en or oxalate counts 2. Werner's tests count ions outside the brackets: a salt of a complex cation that gives three ions per formula unit has two free anions per cation, and only free halide precipitates with Ag⁺. Names: cation first, ligands in alphabetical order (ignoring di-, tri-), then the metal with its oxidation state; an anionic complex ends in -ate: [Pt(NH₃)₄]Cl₂ is tetraammineplatinum(II) chloride and K₂[PtCl₄] is potassium tetrachloridoplatinate(II). Isomers: octahedral [MA₄B₂] has cis and trans forms, [MA₃B₃] has fac and mer forms, chelates can make a complex chiral, and ionization isomers swap a ligand with a counter-ion, so they release different free ions.

Crystal field splitting, spin and magnetism

In an octahedron the d orbitals split into a lower t2g set and an upper eg set separated by Δo. Δo follows the ligand (spectrochemical series I⁻ < Br⁻ < Cl⁻ < F⁻ < OH⁻ < oxalate < H₂O < NH₃ < en < NO₂⁻ < CN⁻ < CO) and the metal: it grows with oxidation state ([Co(NH₃)₆]²⁺ about 10 200 cm⁻¹, [Co(NH₃)₆]³⁺ about 22 900 cm⁻¹) and down a group ([Rh(NH₃)₆]³⁺ about 34 100 cm⁻¹). Only d⁴ to d⁷ ions have a choice: if Δo is smaller than the pairing energy P, the ion is high spin; if larger, low spin. Fe³⁺ (d⁵) with H₂O is t2g³eg², 5 unpaired; with CN⁻ (drawn) it is t2g⁵, 1 unpaired. d¹–d³ and d⁸–d¹⁰ have one arrangement each. Tetrahedral splitting is small (Δt ≈ 4/9 Δo, order e below t2), so tetrahedral complexes are high spin. d⁸ ions with a large splitting (Pd²⁺, Pt²⁺, Au³⁺, Ni²⁺ with CN⁻) prefer square planar and are diamagnetic. Spin-only moment μ = √(n(n + 2)) μB: 1.73, 2.83, 3.87, 4.90 and 5.92 μB for n = 1 to 5. CFSE = (−0.4 × t2g electrons + 0.6 × eg electrons) Δo: d³ gives −1.2Δo.

Colour and the size of Δo

A d–d transition absorbs light of energy about Δo, and the solution shows the complementary colour (red–green, orange–blue, yellow–violet). Per mole, Δo = NA·hc/λ = (6.022 × 10²³)(6.626 × 10⁻³⁴ J s)(2.998 × 10⁸ m/s)/λ = 0.11963 J m mol⁻¹/λ, so with λ in nm, Δo in kJ/mol = 1.1963 × 10⁵/λ. [Ti(H₂O)₆]³⁺ absorbs at 493 nm: Δo = 1.1963 × 10⁵/493 = 243 kJ/mol, and it looks purple. A larger Δo means a shorter absorbed wavelength, so swapping water for a stronger-field ligand shifts the absorption toward blue and changes the colour seen. d⁰ and d¹⁰ ions have no d–d transition, so complexes such as [Zn(H₂O)₆]²⁺ are colourless; when a d⁰ or d¹⁰ species is coloured, as in purple MnO₄⁻, the absorption is charge transfer, not d–d.

Exam traps

β⁻ raises Z; positron emission and electron capture lower it; β particles carry no mass number. In a nuclear equation, count every emitted neutron. Half-life does not depend on the amount, temperature or chemical form, but activity is proportional to the number of atoms. Convert years to seconds before computing becquerels. Use ln, not log, in t = (t½/0.693) ln(N₀/N). Use the ¹H atom mass, not the bare proton mass, with atomic masses. In a decay series, count α steps from the change in A before counting β⁻ steps from Z. In coordination compounds, chloride inside the brackets still counts −1, oxalate is −2, and the d count is group minus oxidation state. A violet solution absorbs yellow light, not violet light.

What to carry forward

Nuclear problems: balance A and Z, use Z ≥ 84 → α, neutron-rich → β⁻, proton-rich → β⁺ or electron capture; decay is first order with A = kN and t = (t½/0.693) ln(N₀/N); energy is Δm × 931.5 MeV/u or Δm c². Coordination problems: counter-ions give the complex charge, ligands give the oxidation state, group number minus oxidation state gives the d count, then Δo against P gives the spin state, unpaired electrons, μ = √(n(n + 2)) μB, CFSE and, through Δo = NA·hc/λ, the colour.

Problemas de prática (40)

Praticar é grátis com uma conta.

Preveja o produto 4

Nuclear equations and decay

  • The particle from boron-10 neutron captureIdentify the missing particle in a neutron-induced reaction by balancing mass number and charge.
  • How does caesium-137 decay?Use a nuclide's neutron excess relative to the stable isotope to choose its decay equation.
  • The PET nuclide fluorine-18Predict the daughter of a positron emitter by lowering Z by one at constant mass number.
  • Four steps down the uranium-238 seriesTrack A and Z through a sequence of α and β⁻ decays to identify the final nuclide.

Classificar 5

Coordination compounds and d counts

  • Name Magnus's green saltName a salt in which both the cation and the anion are complex ions.

Nuclear equations and decay

  • Match three nuclides to their decay modesAssign β⁻, positron and α decay to three nuclides from their mass numbers and atomic numbers.

Half-life, activity and dating

  • Two samples of phosphorus-32Distinguish how the amount of a radionuclide affects its activity but not its half-life.

Binding energy and nuclear energy

  • Which equation shows fusion?Classify nuclear equations as fusion, fission or radioactive decay.

Crystal fields, colour and magnetism

  • Which ion can be high spin or low spin?Identify which d-electron counts allow distinct high-spin and low-spin octahedral configurations.

Comparar 2

Half-life, activity and dating

  • Equal numbers of atoms, different activitiesRank radionuclides by activity for equal numbers of atoms from their half-lives.

Crystal fields, colour and magnetism

  • Rank six complexes by spin-only momentRank octahedral complexes by spin-only magnetic moment after working out each metal's d count and spin state.

Calcular 17

Half-life, activity and dating

  • Radiocarbon age of a charcoal sampleDate a sample by radiocarbon after converting its total count rate into a count rate per gram of carbon.
  • Activity of a 1 mg cobalt-60 sourceCalculate the activity of a radioactive sample from its mass, molar mass and half-life using A = kN.
  • Half-life from two count ratesDetermine a half-life from two activity measurements separated by a known time.
  • Lead-to-uranium ratio after three half-livesFind the daughter-to-parent atom ratio in a mineral of known age expressed in half-lives.
  • Helium-3 growing in a tritium lightCalculate how much stable daughter accumulates from a radioactive parent after a time that is not a whole number of half-lives.

Crystal fields, colour and magnetism

  • CFSE of [Cr(H₂O)₆]³⁺ from its absorptionCalculate Δo from an absorption wavelength and use it to find the crystal field stabilization energy of a d³ complex.
  • Unpaired electrons in potassium ferrioxalateFind the unpaired electrons of a metal in a chelate complex by combining the ligand charge, the d count and the ligand field strength.
  • Unpaired electrons in K₄[Mn(CN)₆]Combine charge balance, d-electron count and ligand field strength to find the unpaired electrons in a low-spin complex.

Coordination compounds and d counts

  • Stereoisomers of [Co(en)(NH₃)₂Cl₂]⁺Count all stereoisomers, including enantiomers, of an octahedral complex with one chelating ligand and two pairs of monodentate ligands.
  • Isomers of [Cr(NH₃)₃Cl₃]Count the stereoisomers of an octahedral MA₃B₃ complex.
  • d electrons in a ruthenium ammineFind the d-electron count of a metal in a complex that has a halide both inside and outside the coordination sphere.

Binding energy and nuclear energy

  • Mass defect of lithium-7Calculate the mass defect of a nuclide from its atomic mass and the masses of hydrogen atoms and neutrons.
  • Splitting lithium-7 with a protonCalculate the energy released by a nuclear reaction from the atomic masses of reactants and products.
  • Does burning methane lose mass?Apply E = Δm c² to a chemical reaction to show why chemical mass changes are unmeasurable.
  • Binding energy per nucleon of oxygen-16Calculate the binding energy per nucleon of a nucleus from its atomic mass.
  • Energy from a gram of polonium-210Convert the mass defect of a decay into the energy released by one gram of the radionuclide.

Nuclear equations and decay

  • β⁻ steps in the neptunium seriesCount the β⁻ decays in a decay series from the changes in mass number and atomic number.

Encontre o erro 2

Coordination compounds and d counts

  • Find the error: chromium in [Cr(NH₃)₄Cl₂]ClDiagnose an oxidation-state error caused by ignoring anionic ligands inside the coordination sphere.

Nuclear equations and decay

  • Spot the unbalanced nuclear equationCheck mass-number and charge balance across several nuclear equations to find the one that fails.

Interprete as evidências 3

Crystal fields, colour and magnetism

  • Which chromium(III) solution is the ammine?Assign two complexes of the same metal ion to their ligands from their absorption wavelengths and colours.
  • What does 4.9 μB say about K₃[MnF₆]?Use a measured magnetic moment to assign the spin state and electron configuration of an octahedral complex.

Binding energy and nuclear energy

  • Fission energy from binding energies per nucleonUse a table of binding energies per nucleon to calculate the energy released by a fission reaction.

Trabalhe de trás para frente 4

Binding energy and nuclear energy

  • Atomic mass of calcium-40 from its binding energyWork backwards from a binding energy per nucleon to the atomic mass of the nuclide.

Nuclear equations and decay

  • The beam that made oganessonWork backwards from a balanced bombardment equation to identify the projectile nucleus.

Coordination compounds and d counts

  • A platinum ammine that gives three ionsDeduce the formula and metal oxidation state of a Werner complex from the number of ions it gives in solution.
  • Formula of potassium tetracyanidonickelate(II)Write the formula of a salt containing a complex anion from its systematic name.

Planeje uma síntese 2

Half-life, activity and dating

  • Choose a radionuclide for medical imagingChoose a radionuclide for diagnostic imaging from its type of radiation and half-life.

Coordination compounds and d counts

  • Tell two ionization isomers apartChoose a precipitation test that distinguishes ionization isomers by the ion each releases.

Explique por quê 1

  • Same ligand, same group, different magnetismExplain why two d⁸ tetrachlorido complexes of the same group differ in geometry and magnetism.

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