Química Geral · Thermochemistry
Entalpias de formação, lei de Hess e entalpias de ligação
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O que você vai aprender
- State what a standard state is, recognise formation reactions and explain why elements in their reference forms have ΔH°f = 0.
- Calculate ΔH°rxn from tabulated standard enthalpies of formation, and work backwards from a reaction enthalpy to an unknown ΔH°f.
- Combine thermochemical equations with Hess's law by reversing, scaling and adding them.
- Estimate reaction enthalpies from average bond enthalpies and explain why the estimates are approximate and apply to gases.
- Compare fuels by the energy they release per mole, per gram and per litre.
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Standard states and enthalpies of formation
The degree sign in ΔH° means every substance is in its standard state: the pure substance in a stated phase at 1 bar (solutes at 1 M), at a stated temperature, usually 25 °C. Older tables use 1 atm; the difference is negligible. The standard enthalpy of formation, ΔH°f, is the enthalpy change when one mole of a compound forms from its elements, each in its reference form (its most stable form at 1 bar and 25 °C). For liquid ethanol the formation reaction is 2 C(s, graphite) + 3 H₂(g) + ½ O₂(g) → C₂H₅OH(l), ΔH°f = −277.7 kJ/mol. Forming an element in its reference form from itself changes nothing, so ΔH°f = 0 for O₂(g), H₂(g), N₂(g), C(s, graphite), Br₂(l) and Fe(s). Other forms of an element are not zero: O₃(g) +142.7, C(s, diamond) +1.9, Br₂(g) +30.9 kJ/mol. A negative ΔH°f means the compound lies below its elements in enthalpy; a positive one, as for acetylene (+226.7 kJ/mol), means it lies above them. A positive ΔH°f does not mean a compound cannot exist: that is a question of rates.
ΔH°rxn from enthalpies of formation
Sign convention: ΔH is the heat gained by the system at constant pressure, so ΔH < 0 is exothermic (heat released) and ΔH > 0 is endothermic. Because enthalpy is a state function, any reaction can be imagined as taking the reactants apart into elements and building the products from them: ΔH°rxn = Σ n ΔH°f(products) − Σ n ΔH°f(reactants), where n are the coefficients of the balanced equation and the units are kJ for the reaction as written (kJ per mole of reaction). Check the phase of every species: ΔH°f of H₂O(l) is −285.8 and of H₂O(g) is −241.8 kJ/mol. Worked example, the combustion of liquid ethanol: C₂H₅OH(l) + 3 O₂(g) → 2 CO₂(g) + 3 H₂O(l). ΔH° = [2(−393.5) + 3(−285.8)] − [(−277.7) + 3(0)] = −1644.4 + 277.7 = −1366.7 kJ. The same equation can be solved for one unknown ΔH°f when ΔH°rxn and the other values are known.
Hess's law: reverse, scale, add
If equations add up to a target equation, their ΔH values add up to the target's ΔH. Three rules: reversing an equation changes the sign of ΔH; multiplying every coefficient by a factor multiplies ΔH by the same factor; species that appear on both sides cancel. Work from the target: find each target species in exactly one given equation, put it on the correct side and give it the correct coefficient. Worked example: find ΔH°f of ethene, 2 C(s, graphite) + 2 H₂(g) → C₂H₄(g), from (1) C(s, graphite) + O₂(g) → CO₂(g), −393.5 kJ; (2) H₂(g) + ½ O₂(g) → H₂O(l), −285.8 kJ; (3) C₂H₄(g) + 3 O₂(g) → 2 CO₂(g) + 2 H₂O(l), −1410.9 kJ. Take 2 × (1), 2 × (2) and the reverse of (3): ΔH = 2(−393.5) + 2(−285.8) + 1410.9 = −787.0 − 571.6 + 1410.9 = +52.3 kJ. The CO₂, H₂O and all three O₂ cancel.
Bond enthalpies and their limits
A bond enthalpy is the enthalpy needed to break one mole of a given bond in gaseous molecules into gaseous fragments; it is always positive. Breaking bonds costs energy and forming bonds releases it, so ΔH ≈ Σ(bond enthalpies of bonds broken) − Σ(bond enthalpies of bonds formed). Example, the chlorination of methane in the gas phase, CH₄ + Cl₂ → CH₃Cl + HCl, with C–H 413, Cl–Cl 243, C–Cl 328 and H–Cl 431 kJ/mol: broken 413 + 243 = 656 kJ, formed 328 + 431 = 759 kJ, ΔH ≈ 656 − 759 = −103 kJ. Bonds that survive unchanged can be left out. Two limits matter. Tabulated values are averages over many molecules (the C–H bond is not identical in methane, ethanol and chloroform), so estimates are usually within a few tens of kJ. They describe gases only: a reaction that makes liquid water releases about 44 kJ more per mole of water than the bond-enthalpy estimate, the enthalpy of condensation. Bond order matters: C–O ≈ 358, C=O ≈ 745 and C≡O ≈ 1072 kJ/mol.
Fuels and energy per gram
A fuel's value depends on what you carry. Per mole, a large hydrocarbon wins; per gram, fuels rich in hydrogen win, because hydrogen is light and forming the strong O–H bonds of water releases a lot of energy. Divide the heat released per mole by the molar mass: propane, ΔH°c = −2219.9 kJ/mol (to liquid water) and M = 44.10 g/mol, releases 2219.9 ÷ 44.10 = 50.3 kJ/g. Fuels that already contain oxygen, such as methanol and ethanol, are partly oxidized, so they release less per gram than hydrocarbons. The phase of the water product matters: values quoted with liquid water (the higher heating value) exceed those with water vapour (the lower heating value) by about 44 kJ per mole of water formed. For gases, compare per litre as well: equal volumes hold equal numbers of moles, so hydrogen, the best fuel per gram, carries much less energy per litre than methane or propane, whose molar combustion enthalpies are far larger.
What to carry forward
Use ΔH°rxn = Σ n ΔH°f(products) − Σ n ΔH°f(reactants) with elements in their reference forms at zero and every phase checked. For Hess's law, reverse (change the sign), scale (multiply ΔH) and add until the target equation appears. Bond enthalpies give ΔH ≈ bonds broken − bonds formed, an estimate for gases built from average values. Compare fuels per gram by dividing the heat released per mole by the molar mass.
Problemas de prática (40)
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Preveja o produto 2
Standard states and ΔH°f
- Formation reaction of ethanolWrite the formation reaction whose ΔH° equals ΔH°f of a compound.
Hess's law
- Reverse and scale the peroxide equationPredict ΔH for an equation that is the reverse of a given equation multiplied by a fractional factor.
Classificar 2
Bond enthalpies
- What a bond enthalpy isClassify statements about bond enthalpies as correct or incorrect from the definition.
Standard states and ΔH°f
- Which substance has ΔH°f = 0?Identify which form of an element is its reference form, with a standard enthalpy of formation of zero.
Comparar 4
Bond enthalpies
- Rank carbon–oxygen bonds by strengthRank carbon–oxygen bonds by bond enthalpy using bond order.
Fuels and energy per gram
- Acetylene or methane: per mole and per gramCompare two fuels per mole and per gram and recognise that the rankings can differ.
- Hydrogen and methane per gram and per litreCompare two gaseous fuels per gram and per litre using molar volume.
- Rank fuels by energy per gramRank fuels by energy released per gram from molar combustion enthalpies and molar masses.
Calcular 21
Reaction enthalpies from ΔH°f
- Oxidizing ammonia to nitric oxideCalculate ΔH°rxn from enthalpies of formation with large coefficients and a mix of signs.
- Decomposing ammonium nitrateCalculate ΔH°rxn for a decomposition in which one product has a positive enthalpy of formation.
- Dimerizing nitrogen dioxideApply products-minus-reactants when both species have positive enthalpies of formation.
- Oxidizing sulfur dioxideCalculate ΔH°rxn from enthalpies of formation for a reaction with coefficients of two.
- Energy per gram of thermite mixtureCombine a ΔH°f calculation with molar masses to find the energy released per gram of a reacting mixture.
- The thermite reactionCalculate ΔH°rxn from enthalpies of formation when several species are elements with ΔH°f = 0.
Bond enthalpies
- Hydrogen chloride from bond enthalpiesEstimate ΔH for a gas-phase reaction from bonds broken and bonds formed, counting every bond formed.
- Average C–H bond enthalpy from atomizationDerive an average bond enthalpy from the atomization enthalpy calculated with enthalpies of formation of gaseous atoms.
- Methanol vapour combustion from bond enthalpiesEstimate a combustion enthalpy from bond enthalpies, including a fractional coefficient on O₂.
Fuels and energy per gram
- Energy per gram of glucoseCalculate the energy released per gram when a food molecule is fully oxidized, from enthalpies of formation.
- Energy per gram of hydrogenConvert a molar combustion enthalpy into energy released per gram of fuel.
- Methane burned with water vapour in the exhaustChoose the correct phase of water when computing a fuel's energy per gram under real conditions.
- Energy per gram of octane from ΔH°fCalculate a fuel's energy content per gram from enthalpies of formation and its molar mass.
Hess's law
- ΔH°f of acetylene from three equationsCombine three thermochemical equations, using doubling, reversing and halving, to find an enthalpy of formation.
- Burning ammonia to nitrogenFind a reaction enthalpy by reversing one equation and scaling two equations by different factors.
- Hydration of ethene from combustion dataDerive the enthalpy of a reaction between two organic compounds from their combustion enthalpies.
- Graphite to diamond by Hess's lawUse two combustion enthalpies to find the enthalpy of a transformation that cannot be measured directly.
- ΔH°f of NO₂ by Hess's lawAdd two thermochemical equations and scale the sum to one mole of product.
- The water–gas shift reactionCombine two thermochemical equations, reversing one, to obtain the enthalpy of a target reaction.
Standard states and ΔH°f
- ΔH°f of ozoneObtain a standard enthalpy of formation by scaling an equation to one mole of product.
- Vaporizing water from ΔH°f valuesUse enthalpies of formation of two phases of one compound to find a phase-change enthalpy.
Encontre o erro 3
Bond enthalpies
- Find the error: bond enthalpies and liquid waterDiagnose why a bond-enthalpy estimate misses the enthalpy of a reaction that forms a liquid.
Reaction enthalpies from ΔH°f
- Find the error: ethane combustionDiagnose a reversed products-minus-reactants subtraction in a ΔH°f calculation.
Standard states and ΔH°f
- Find the error: ΔH°f of water vapourDiagnose a ΔH°f error caused by an equation that forms more than one mole of product.
Interprete as evidências 1
- What a positive ΔH°f meansInterpret the sign and meaning of a positive standard enthalpy of formation.
Trabalhe de trás para frente 2
Bond enthalpies
- H–F bond enthalpy from a reaction enthalpyWork backwards from a reaction enthalpy to an unknown bond enthalpy.
Reaction enthalpies from ΔH°f
- ΔH°f of propane from its combustion enthalpyWork backwards from a measured combustion enthalpy to an unknown enthalpy of formation.
Planeje uma síntese 1
- Plan a Hess's law route to ΔH°f of ethaneChoose the combination of combustion equations that produces a target formation reaction.
Explique por quê 4
Bond enthalpies
- Why the bond-enthalpy estimate is offExplain why a bond-enthalpy estimate differs from the value obtained from enthalpies of formation for an all-gas reaction.
Standard states and ΔH°f
- Why Br₂(g) is not zeroExplain why a gaseous diatomic element can have a nonzero standard enthalpy of formation.
- What the degree sign meansExplain the conditions that the degree sign in ΔH° specifies.
Fuels and energy per gram
- Why ethanol gives less energy per gramExplain why an oxygen-containing fuel releases less energy per gram than a hydrocarbon.
Travou em entalpias de formação, lei de Hess e entalpias de ligação? Escaneie o problema.
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Depois, Scan Standard: /mês