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Química Geral · Exam review

Revisão de gases e termoquímica

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O que você vai aprender

  • Solve multi-step gas problems with PV = nRT, the combined gas law, gas density and reaction stoichiometry.
  • Use Dalton's law, mole fractions and the water-vapour correction, and follow pressures through a reaction in a closed vessel.
  • Apply kinetic molecular theory: average kinetic energy, rms speed and Graham's law of effusion.
  • Apply the first law with chemistry sign conventions, including PV work and the link between ΔH and ΔU.
  • Analyse coffee-cup and bomb calorimetry data, including heat exchange and calibration.
  • Calculate reaction enthalpies from Hess's law, standard enthalpies of formation and average bond enthalpies.

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One equation for ideal gases

PV = nRT with R = 0.08206 L·atm mol⁻¹ K⁻¹ (or 8.314 J mol⁻¹ K⁻¹ with pressure in Pa and volume in m³). Always use kelvin, T(K) = T(°C) + 273.15, and convert pressure first: 1 atm = 760 torr = 101.325 kPa. For one sample whose conditions change, P₁V₁/T₁ = P₂V₂/T₂ (n constant). Example: 2.50 g of CO₂ (drawn, 44.01 g/mol) in 1.50 L at 30.0 °C is 0.05680 mol, so P = 0.05680 × 0.08206 × 303.15 / 1.50 = 0.942 atm. Rearranging gives gas density d = PM/RT and molar mass M = dRT/P; CO₂ at 1.00 atm and 25 °C has d = 44.01/(0.08206 × 298.15) = 1.80 g/L. The molar volume of an ideal gas is 22.41 L/mol only at 0 °C and 1 atm; at 25 °C and 1 atm it is 24.47 L/mol. Trap: 22.4 L/mol used at room temperature.

Gas stoichiometry, mixtures and closed vessels

Route for gas stoichiometry: grams or litres → moles (n = m/M or n = PV/RT) → mole ratio from the balanced equation → moles of the wanted substance → grams or litres. At the same T and P, volumes of gases react in the same ratio as moles. In a mixture each gas has Pᵢ = nᵢRT/V = χᵢP_total, and the partial pressures add (Dalton's law); partial pressures follow moles, not masses. Example: 0.30 mol N₂ and 0.10 mol O₂ (drawn) at a total of 2.00 atm give χ(O₂) = 0.25 and P(O₂) = 0.500 atm. In a rigid vessel at constant temperature, pressure is proportional to moles, so a reaction can be tracked in atm: 0.40 atm CO and 0.30 atm O₂ react by 2 CO + O₂ → 2 CO₂ to leave 0.40 atm CO₂ and 0.10 atm O₂, total 0.50 atm. A gas collected over water is wet: subtract the vapour pressure of water (17.5 torr at 20 °C, 23.8 torr at 25 °C) from the barometric pressure before using n = PV/RT.

Kinetic molecular theory and effusion

Ideal-gas particles have negligible volume, do not attract one another and collide elastically. Their average translational kinetic energy depends only on absolute temperature: (3/2)RT per mole, so all gases at one temperature share the same average kinetic energy (6.24 kJ/mol at 500 K) whatever their mass, and the total kinetic energy of a sample is (3/2)nRT. Speed does depend on mass: u_rms = √(3RT/M) with M in kg/mol. Argon at 300 K: √(3 × 8.314 × 300 / 0.03995) = 433 m/s. Because kinetic energy goes as u², doubling the kelvin temperature doubles the kinetic energy but multiplies the speed by only √2. Graham's law: rate₁/rate₂ = √(M₂/M₁) at the same T and P, and the time for equal amounts to effuse is proportional to √M. Helium effuses √(16.04/4.003) = 2.00 times as fast as methane.

The first law and its signs

ΔU = q + w, with every sign taken from the system's point of view: q > 0 when heat flows into the system, w > 0 when the surroundings do work on the system. Expansion against a constant external pressure does work on the surroundings: w = −P_ext ΔV, and 1 L·atm = 101.325 J. Example: a gas absorbs 400. J while expanding from 1.00 L to 3.00 L against 1.50 atm; w = −3.00 L·atm = −304 J, so ΔU = +96 J. At constant pressure the heat equals the enthalpy change, q_p = ΔH; at constant volume it equals ΔU. For a reaction, ΔH = ΔU + Δn_gas RT, where Δn_gas counts moles of gaseous products minus gaseous reactants. For C₃H₈(g) + 5 O₂(g) → 3 CO₂(g) + 4 H₂O(l), Δn_gas = −3 and ΔH = −2220 kJ, so ΔU = −2220 + 3(8.314 × 10⁻³)(298.15) = −2213 kJ. When a liquid boils, ΔU = ΔH_vap − RT per mole of vapour formed.

Calorimetry

q = mcΔT for a substance (c in J g⁻¹ °C⁻¹; a change of 1 °C equals a change of 1 K) and q = CΔT for an object of known heat capacity. In an insulated container the heats add to zero: Σq = 0, so heat lost by hot bodies equals heat gained by cold ones, and melting ice takes ΔH_fus before its water starts warming. The reaction's heat has the opposite sign to the calorimeter's: q_rxn = −(q_solution + q_cup). Example: a reaction in 100.0 g of solution raises its temperature by 5.20 °C, so q_solution = 100.0 × 4.184 × 5.20 = 2.18 kJ; if 0.0400 mol reacted, ΔH = −2.18 kJ / 0.0400 mol = −54.4 kJ/mol. A coffee cup is open, so it measures ΔH. A bomb is sealed and rigid, so it measures ΔU; its heat capacity C_cal is found first by burning a standard such as benzoic acid. With C_cal = 9.50 kJ/°C and ΔT = 2.40 °C, the sample released 22.8 kJ. Trap: dividing by the wrong number of moles; use the moles of the limiting reactant or of water formed, as the equation is written.

Hess's law, ΔH°f and bond enthalpies

Enthalpy is a state function, so equations can be added like algebra: reversing an equation changes the sign of ΔH, and multiplying it by a factor multiplies ΔH by the same factor. A standard enthalpy of formation, ΔH°f, is for forming one mole of a substance from its elements in their standard states (1 bar, usually 25 °C: O₂(g), C(s, graphite), Br₂(l)); for those elements ΔH°f = 0. Then ΔH°rxn = Σn ΔH°f(products) − Σn ΔH°f(reactants). Example: CH₄(g) + 2 O₂(g) → CO₂(g) + 2 H₂O(l) (drawn) has ΔH° = −393.5 + 2(−285.8) − (−74.8) = −890.3 kJ. Average bond enthalpies give an estimate for gas-phase reactions only: ΔH ≈ Σ(bonds broken) − Σ(bonds formed). For 2 H₂(g) + O₂(g) → 2 H₂O(g): 2(436) + 498 − 4(463) = −482 kJ, close to the measured −483.6 kJ. If a reactant or product is a liquid, add the enthalpy of the phase change separately.

What to carry forward

Gas problems: kelvin and atm first, then PV = nRT for moles, mole ratios for reactions, Pᵢ = χᵢP_total for mixtures (subtract water's vapour pressure for gas collected over water), (3/2)RT for kinetic energy and √(3RT/M) for speed. Energy problems: ΔU = q + w with system-based signs, w = −P_ext ΔV, q_p = ΔH and q_v = ΔU, ΔH = ΔU + Δn_gas RT, q = mcΔT with Σq = 0 in an insulated calorimeter, and ΔH°rxn from Hess's law, from ΔH°f (products minus reactants) or, approximately, from bond enthalpies (broken minus formed).

Problemas de prática (40)

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Preveja o produto 2

Mixtures and kinetic theory

  • Methane burns in a hot rigid vesselPredict partial and total pressures after a complete gas-phase combustion in a rigid vessel at constant temperature.

First law and calorimetry

  • Final temperature when NaOH dissolvesPredict the final temperature of a coffee-cup calorimeter from a known enthalpy of solution.

Classificar 3

Hess's law, ΔH°f and bond enthalpies

  • The formation equation of calcium carbonateIdentify the thermochemical equation whose ΔH° is the standard enthalpy of formation of a compound.

First law and calorimetry

  • Which exam statement is true?Pick the one correct statement among common gas and thermochemistry claims, using Gay-Lussac's law, standard states, sign conventions and calorimeter types.
  • Which process has q < 0 and w < 0?Classify processes by the signs of q and w using the chemistry convention that both are measured from the system's point of view.

Comparar 5

First law and calorimetry

  • Hot copper or hot aluminium: which water ends warmer?Compare final temperatures in two heat-exchange experiments using the specific heats of the metals.

Gas laws and gas stoichiometry

  • Two 1.0 L flasks at the same T and PUse Avogadro's law to decide which property two equal gas volumes at the same temperature and pressure share.
  • Rank gas densities at different conditionsRank gas samples held at different pressures and temperatures by density using d = PM/RT.

Hess's law, ΔH°f and bond enthalpies

  • Rank fuels by heat released per mole of O₂Rank fuels by heat released per mole of oxygen consumed, using balanced combustion equations and given enthalpies of combustion.

Mixtures and kinetic theory

  • Rank samples by total translational kinetic energyRank gas samples by total translational kinetic energy using (3/2)nRT, independent of molar mass.

Calcular 20

Mixtures and kinetic theory

  • Opening the valve between NH₃ and HClFind the final pressure when two gases in connected flasks react to form a solid, using PV as a measure of moles.
  • Effusion time of N₂ from that of kryptonUse Graham's law to convert an effusion time for one gas into the time for another gas.
  • Partial pressure of N₂ in a CH₄–N₂ mixtureFind a partial pressure in a gas mixture given by masses, using moles rather than mass fractions.

Hess's law, ΔH°f and bond enthalpies

  • Reducing iron ore with carbon monoxideCalculate a reaction enthalpy from standard enthalpies of formation, applying coefficients and ΔH°f = 0 for elements.
  • ΔH°f of carbon disulfide by Hess's lawObtain a formation enthalpy by reversing a combustion equation and scaling the formation equations of its products.
  • ΔH°f of diborane from four equationsCombine four thermochemical equations, reversing and scaling them as needed, to obtain a formation enthalpy.
  • Heat from burning 10.0 g of hydrazineCombine ΔH°rxn from enthalpies of formation with a mass-to-mole conversion to find the heat released by a sample.
  • Bond enthalpies when the water is liquidEstimate a reaction enthalpy from bond enthalpies when a product is a liquid, adding the phase change separately.
  • Chlorinating methane: a bond-enthalpy estimateEstimate a gas-phase reaction enthalpy from average bond enthalpies, counting only the bonds that change.

First law and calorimetry

  • ΔU for boiling 10.0 g of ethanolFind ΔU for a vaporization from ΔH and the expansion work of the vapour formed.
  • ΔU when heat leaves and work is done on the systemApply ΔU = q + w with correct signs and consistent units when heat leaves a system and work is done on it.
  • How much ice cools hot tea to 10 °C?Find the mass of ice needed to reach a target temperature, including both melting and warming of the meltwater.
  • Hot lead shot in a cup that absorbs heatFind the final temperature of a metal–water mixture when the calorimeter's own heat capacity is included.
  • Methane needed to heat a kettle on a stoveChain calorimetry, a thermochemical equation with an efficiency and the ideal gas law to find a fuel volume.
  • Calibrate a bomb, then burn sucroseCalibrate a bomb calorimeter with a standard and use it to find the molar internal energy of combustion of a sample.

Gas laws and gas stoichiometry

  • How many balloons from one gas cylinder?Use Boyle's law to count how many containers a high-pressure cylinder can fill, allowing for the gas that must stay in the cylinder.
  • Pressure after sparking H₂ and O₂ in a hot flaskFind the pressure in a rigid vessel after a gas reaction by working out the limiting reactant and the moles of every gas left.
  • Oxygen needed to burn 5.00 g of ethanolCombine mass-to-mole conversion, a mole ratio and the ideal gas law to find the volume of a reacting gas.
  • Potassium superoxide for a breathing apparatusFind the mass of a solid reagent needed to absorb a measured volume of gas, using PV = nRT and a 2:1 mole ratio.
  • Correct a syringe volume to STPConvert a gas volume measured at room conditions to STP with the combined gas law, converting torr and °C first.

Encontre o erro 3

Gas laws and gas stoichiometry

  • Find the error: 22.4 L/mol at room temperatureIdentify the misuse of the 0 °C molar volume for a gas at room temperature and give the corrected amount.

First law and calorimetry

  • Find the error: a neutralization enthalpy half too smallFind the error in a coffee-cup neutralization calculation that divides by the wrong number of moles.

Mixtures and kinetic theory

  • Find the error: doubling T doubles the speedCorrect the misconception that doubling the absolute temperature doubles molecular speed.

Interprete as evidências 2

Gas laws and gas stoichiometry

  • Molecular formula from composition and vapour dataCombine an empirical formula from mass percentages with a molar mass from vapour data to find a molecular formula.

Hess's law, ΔH°f and bond enthalpies

  • ΔH°f of MgO from two coffee-cup runsCombine two measured reaction enthalpies with a tabulated one to find a formation enthalpy that cannot be measured directly.

Trabalhe de trás para frente 3

Hess's law, ΔH°f and bond enthalpies

  • ΔH°f of acetone from its combustion enthalpyWork backwards from a measured combustion enthalpy to the standard enthalpy of formation of the fuel.

Mixtures and kinetic theory

  • Temperature for a given rms speed of CO₂Rearrange the rms-speed equation to find the temperature at which a gas reaches a given speed.
  • Mass of peroxide from oxygen collected over waterWork back from a volume of gas collected over water to the mass of reactant that produced it.

Planeje uma síntese 1

  • Plan a Hess route to ΔH°f of N₂O₅Choose the combination of given equations whose sum is the formation reaction of one mole of a compound.

Explique por quê 1

  • Why heavy krypton does not push harderExplain with kinetic theory why equal moles of a light and a heavy gas exert equal partial pressures.

Travou em revisão de gases e termoquímica? 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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