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Química Geral · Thermochemistry

Energia, calor, trabalho e entalpia

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O que você vai aprender

  • Classify a system as open, closed or isolated and distinguish state functions (U, H, P, V, T) from path functions (q, w).
  • Apply the first law, ΔU = q + w, with the chemist's sign convention for heat and work.
  • Calculate pressure–volume work with w = −P_ext·ΔV, converting L·atm to joules, and with w = −Δn_gas·RT for reactions that make or consume gas.
  • Explain why ΔH equals the heat exchanged at constant pressure and convert between ΔH and ΔU with ΔH = ΔU + Δn_gas·RT.
  • Read thermochemical equations, including the sign of ΔH and the physical states, and use them to find the heat for given amounts of reactants or products.

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System, surroundings and energy

Thermochemistry divides the world into the system, the part we study (a reacting mixture, a gas in a cylinder), and the surroundings, everything else. An open system exchanges both matter and energy with its surroundings, a closed system exchanges energy but not matter (a sealed flask), and an isolated system exchanges neither (an ideal sealed, insulated, rigid container). Energy is the capacity to do work or transfer heat. It appears as kinetic energy (motion of molecules, which we sense as temperature) and potential energy (the arrangement of charges in atoms, molecules and bonds). The SI unit is the joule; 1 cal = 4.184 J exactly, 1 kcal = 4184 J, and the gas-work unit 1 L·atm = 101.325 J. The internal energy U of a system is the total kinetic and potential energy of its particles. Energy can be transferred and converted, but never created or destroyed.

State functions and path functions

A state function depends only on the present state of the system (its composition, temperature, pressure and volume), not on how it got there. U, H, P, V and T are state functions, so ΔU = U(final) − U(initial) is the same for every route between two states, and over any cycle that returns the system to its start ΔU = 0. Heat q and work w are not state functions: they describe how energy crosses the boundary along a particular route. Two routes between the same states can share out the energy differently, for example q = +600 J, w = −250 J along one route and q = +350 J, w = 0 along another, but the sum q + w = +350 J = ΔU must be the same. Altitude is a useful picture: the height gained between two points is fixed, but the distance walked depends on the trail.

The first law and its sign convention

The first law of thermodynamics is ΔU = q + w. Signs are always taken from the system's point of view. q > 0 when heat flows into the system and q < 0 when it flows out; w > 0 when the surroundings do work on the system (compression) and w < 0 when the system does work on the surroundings (expansion). Worked example: a gas absorbs 400 J of heat and does 150 J of work pushing a piston out. Then q = +400 J and w = −150 J, so ΔU = 400 − 150 = +250 J. For an ideal gas, U depends only on temperature: at constant temperature ΔU = 0 and q = −w. In a fast (adiabatic) compression no heat crosses the boundary, so ΔU = w > 0 and the gas warms up.

Pressure–volume work

When a gas expands or is compressed against a constant external pressure, the work done on the system is w = −P_ext·ΔV. Expansion (ΔV > 0) gives negative w; compression (ΔV < 0) gives positive w. With pressure in atm and volume in litres the product is in L·atm; multiply by 101.325 J per L·atm. Worked example: a gas expands from 1.00 L to 3.00 L against 1.00 atm, so w = −(1.00 atm)(2.00 L) = −2.00 L·atm = −2.00 × 101.325 J = −203 J. A gas expanding into a vacuum meets no external pressure and does no work (w = 0). For a reaction run at constant pressure, the volume change comes from the change in moles of gas, so w = −Δn_gas·RT, with Δn_gas = moles of gaseous products − moles of gaseous reactants and R = 8.314 J mol⁻¹ K⁻¹. At 25 °C (298.15 K), RT = 2479 J/mol = 2.479 kJ/mol.

Enthalpy: heat at constant pressure

Enthalpy is defined as H = U + PV. At constant pressure, with only expansion work, ΔH = ΔU + PΔV = (q − PΔV) + PΔV = q, so the heat exchanged in an open beaker equals ΔH. In a sealed rigid vessel no expansion work is possible (ΔV = 0), so the heat equals ΔU instead. For ideal gases PΔV = Δn_gas·RT, which gives ΔH = ΔU + Δn_gas·RT; solids, liquids and dissolved species are left out of Δn_gas because their volumes are tiny. Worked example: 2 H₂(g) + O₂(g) → 2 H₂O(l) (water drawn) has ΔH° = −571.6 kJ at 25 °C and Δn_gas = 0 − 3 = −3, so ΔU = ΔH − Δn_gas·RT = −571.6 − (−3)(2.479) = −571.6 + 7.4 = −564.2 kJ. When Δn_gas = 0, ΔH = ΔU; even when it is not, the difference is only a few kJ per mole, small next to most reaction enthalpies.

Exothermic and endothermic processes

An exothermic process releases heat to the surroundings (ΔH < 0, q < 0 for the system): the products lie lower in enthalpy than the reactants. Combustion, freezing and condensation are exothermic. An endothermic process absorbs heat (ΔH > 0): melting, boiling and the dissolution of ammonium nitrate (drawn), ΔH ≈ +25.7 kJ/mol, which is why an instant cold pack feels cold. The heat the dissolving salt absorbs comes from the water and from your hand, so the surroundings cool down. The energy released by a reaction is chemical potential energy: breaking bonds always costs energy, and forming bonds releases it, so a reaction is exothermic when the bonds formed are stronger overall than the bonds broken.

Thermochemical equations and their stoichiometry

A thermochemical equation is a balanced equation with physical states and ΔH, for example C(s, graphite) + O₂(g) → CO₂(g), ΔH° = −393.5 kJ. ΔH refers to the amounts in moles written in the equation: here 393.5 kJ is released per mole of carbon burned or per mole of CO₂ formed. ΔH is extensive, so doubling the coefficients doubles ΔH, and reversing the equation changes its sign. States matter: forming liquid water instead of vapor releases an extra 44.0 kJ per mole of water at 25 °C, the heat of condensation. To find the heat for a given amount, convert to moles and scale by the ratio in the equation. Worked example: burning 6.00 g of graphite (12.01 g/mol) is 6.00 ÷ 12.01 = 0.4996 mol, which releases 0.4996 × 393.5 = 197 kJ. If two reactants are given, find the limiting reactant first; only it sets the heat released.

What to carry forward

Pick the system, keep every sign from its point of view, and write ΔU = q + w. Work against a constant pressure is −P_ext·ΔV (× 101.325 J per L·atm), or −Δn_gas·RT for a reaction at constant pressure. Heat at constant pressure is ΔH and heat at constant volume is ΔU, related by ΔH = ΔU + Δn_gas·RT. ΔH in a thermochemical equation belongs to the moles written, so convert to moles, use the limiting reactant and scale.

Problemas de prática (40)

Praticar é grátis com uma conta.

Preveja o produto 2

Heat, work and the first law

  • Work done by a gas expanding into a vacuumPredict that a gas expanding against zero external pressure does no work.

Enthalpy: ΔH versus ΔU

  • Open flask or sealed vessel: where is more heat released?Predict whether a gas-forming reaction releases more heat at constant pressure or at constant volume.

Classificar 3

System, surroundings and state functions

  • Spot the closed systemClassify a system as open, closed or isolated from what crosses its boundary.
  • Which quantity depends on the route?Distinguish work as a path function from state-function changes such as ΔU, ΔH and ΔT.

Heat, work and the first law

  • Signs of q and w during a compressionAssign the signs of q and w for a gas that is compressed while losing heat.

Comparar 4

System, surroundings and state functions

  • Rank energy units by sizeCompare common energy units (eV, J, cal, L·atm, kJ, kcal) by converting each to joules.

Thermochemical equations

  • Heat per mole of each species in ethane combustionUse the coefficients of a thermochemical equation to compare the heat released per mole of each reactant and product.

Enthalpy: ΔH versus ΔU

  • Rank reactions by ΔH − ΔURank reactions by ΔH − ΔU using the change in moles of gas.

Heat, work and the first law

  • Rank processes by ΔURank several processes by ΔU computed from signed heat and work values.

Calcular 17

Enthalpy: ΔH versus ΔU

  • ΔU for burning carbon monoxideConvert a reaction enthalpy to an internal energy change for a reaction that consumes gas.
  • Δn_gas for burning ethanolCount the change in moles of gas for a combustion equation, leaving out liquids.
  • ΔH of octane combustion from bomb dataConvert a constant-volume combustion energy to ΔH, counting only gaseous species in Δn_gas.
  • Work done when propane burns at constant pressureDetermine the sign and size of the work for a combustion at constant pressure in which the moles of gas decrease.
  • Internal energy of vaporization of waterFind ΔU of vaporization from ΔH_vap, using the work done by the vapor pushing back the atmosphere.
  • Work done by hydrogen from zinc and acidCalculate the expansion work of a gas-forming reaction at constant pressure from w = −Δn_gas·RT.

Heat, work and the first law

  • ΔU for a gas compressed while it coolsFind ΔU for a compression with positive work and negative heat.
  • ΔU for a gas that is heated as it expandsCombine heat in kilojoules with pressure–volume work in L·atm to find ΔU in joules.
  • Expansion work in joulesCalculate expansion work against a constant external pressure and convert L·atm to joules.
  • ΔU from heat absorbed and work doneApply ΔU = q + w with the correct signs when a gas absorbs heat and does work.
  • Heat absorbed in an isothermal expansionUse ΔU = 0 for an ideal gas at constant temperature to find the heat absorbed during an expansion.

Thermochemical equations

  • Heat from burning 10.0 g of hydrogenConvert a mass of reactant to moles and use the equation's mole ratio to find the heat released.
  • ΔU for burning 8.00 g of methaneCombine thermochemical stoichiometry with the ΔH-to-ΔU conversion for a given mass of fuel.
  • Heat absorbed in forming 15.0 g of NOUse the coefficient of a product to find the heat absorbed when a given mass of it forms.
  • Heat from burning 0.250 mol of propaneScale the ΔH of a thermochemical equation to a given number of moles of fuel.
  • Heat from a thermite mixtureIdentify the limiting reactant and use it to find the heat released by a thermochemical equation.

System, surroundings and state functions

  • Same states, two routesUse the route-independence of ΔU to find the work along a second route between the same two states.

Encontre o erro 3

Enthalpy: ΔH versus ΔU

  • Find the error in a ΔU calculationDiagnose a J-versus-kJ mismatch when converting ΔH to ΔU with Δn_gas·RT.

System, surroundings and state functions

  • Do two routes share the same heat and work?Diagnose the error of treating heat and work as state functions.

Heat, work and the first law

  • Find the error in a work calculationDiagnose a missing L·atm-to-joule conversion in a pressure–volume work calculation.

Interprete as evidências 3

System, surroundings and state functions

  • Which way does heat flow in a cold pack?Interpret a temperature drop in the surroundings as evidence of an endothermic process with q > 0 for the system.
  • Heat in the last step of a cycleUse ΔU = 0 for a complete cycle to find the missing heat in one step from tabulated q and w values.

Thermochemical equations

  • Reading a thermochemical equationInterpret the sign of ΔH and the amounts of substance to which it refers in a thermochemical equation.

Trabalhe de trás para frente 2

Heat, work and the first law

  • Initial volume from the work of compressionWork backwards from the work done on a gas and the external pressure to its initial volume.

Thermochemical equations

  • Mass of methane needed for 1000 kJWork backwards from a required amount of heat to the mass of fuel that must burn.

Planeje uma síntese 1

  • How much ammonium nitrate for a cold pack?Plan the amount of a reagent needed to absorb a target amount of heat using its ΔH of dissolution.

Explique por quê 5

System, surroundings and state functions

  • Why does a bicycle pump get warm?Explain the temperature rise of a gas in an adiabatic compression with ΔU = w.
  • Where does the heat of burning hydrogen come from?Explain the heat released by a reaction as a drop in chemical potential energy when stronger bonds form than are broken.

Enthalpy: ΔH versus ΔU

  • Why heat at constant pressure equals ΔHExplain from H = U + PV and the first law why the heat exchanged at constant pressure equals ΔH.
  • Why ΔH ≈ ΔU for a neutralizationExplain why ΔH and ΔU are practically equal for reactions without gases.

Thermochemical equations

  • Why the state of water changes ΔHExplain why the physical state of a product changes the ΔH of a thermochemical equation.

Travou em energia, calor, trabalho e entalpia? Escaneie o problema.

Tire uma foto da reação da sua lista ou do livro e desenhe o mecanismo com cada seta corrigida. 1 scan grátis agora, sem cadastro; mais 1 com uma conta gratuita.

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