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Química Geral · Chemical equilibrium

Constantes de equilíbrio e Q

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O que você vai aprender

  • Describe chemical equilibrium as a dynamic state in which the forward and reverse rates are equal and the composition is constant.
  • Write Kc and Kp expressions for homogeneous and heterogeneous equilibria, leaving out pure solids and pure liquids.
  • Convert between Kc and Kp with Kp = Kc(RT)^Δn, counting only gaseous species in Δn.
  • Find K for a reversed, scaled or combined equation from the K values of the given equations.
  • Interpret the magnitude of K and compare the reaction quotient Q with K to predict the direction of net reaction.

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Equilibrium is dynamic

In a closed flask, colourless N₂O₄ (drawn) dissociates into brown NO₂, and NO₂ molecules recombine into N₂O₄. At first the forward rate is the larger, so NO₂ builds up; as N₂O₄ is used up the forward rate falls and the reverse rate rises. When the two rates become equal the concentrations stop changing: the system is at equilibrium. Both reactions keep running at the same rate, so individual molecules still react; only the net change is zero. Equilibrium does not mean equal concentrations of reactants and products. The same equilibrium mixture is reached whether you start from N₂O₄, from the equivalent amount of NO₂ or from a matching mixture of them, provided the temperature, the volume and the total amount of nitrogen and oxygen are the same.

Writing the equilibrium-constant expression

For aA + bB ⇌ cC + dD, the law of mass action gives Kc = [C]^c[D]^d / ([A]^a[B]^b): products over reactants, each concentration at equilibrium raised to its coefficient in the balanced equation. For N₂(g) + 3 H₂(g) ⇌ 2 NH₃(g), Kc = [NH₃]²/([N₂][H₂]³). A homogeneous equilibrium has every species in one phase; a heterogeneous one involves more than one phase. Pure solids and pure liquids are left out of the expression because their activity is 1 and does not change with how much is present. For NH₄HS(s) ⇌ NH₃(g) + H₂S(g) (ions drawn), Kc = [NH₃][H₂S]; for Br₂(l) + Cl₂(g) ⇌ 2 BrCl(g), Kc = [BrCl]²/[Cl₂]. Water as a gas (steam) does appear in K; liquid water as a reactant or as the solvent does not. Each K belongs to the equation exactly as written and to one temperature.

Kc and Kp

For gases, K can be written with partial pressures in atm: Kp = (P_C)^c(P_D)^d / ((P_A)^a(P_B)^b). Because P = (n/V)RT = [X]RT for an ideal gas, Kp = Kc(RT)^Δn, where Δn = (moles of gaseous products) − (moles of gaseous reactants) and R = 0.08206 L·atm/(mol·K), the value that matches concentrations in mol/L and pressures in atm. Solids and liquids do not count in Δn. Example: 2 SO₂(g) + O₂(g) ⇌ 2 SO₃(g) has Kc = 2.8 × 10² at 1000 K and Δn = 2 − 3 = −1, so Kp = 280 × (0.08206 × 1000)^−1 = 280/82.06 = 3.41. When Δn = 0, as for H₂(g) + I₂(g) ⇌ 2 HI(g), Kp = Kc. Equilibrium constants are reported without units because each concentration or pressure is strictly divided by its standard value (1 mol/L or 1 atm).

Manipulating K

Three rules follow from the expression itself. Reversing an equation inverts K: H₂(g) + I₂(g) ⇌ 2 HI(g) has Kc = 50.0 at 448 °C, so 2 HI(g) ⇌ H₂(g) + I₂(g) has Kc = 1/50.0 = 0.0200. Multiplying every coefficient by n raises K to the power n: doubling gives 50.0² = 2500, and halving, ½ H₂ + ½ I₂ ⇌ HI, gives 50.0^½ = 7.07. Adding equations multiplies their K values, because the expression of the sum is the product of the two expressions (shared species cancel). Example: 2 NO(g) ⇌ N₂(g) + O₂(g) (K₁) plus N₂(g) + 2 O₂(g) ⇌ 2 NO₂(g) (K₂) gives 2 NO(g) + O₂(g) ⇌ 2 NO₂(g) with K = K₁ × K₂. These rules mirror Hess's law: where ΔH values add or change sign, K values multiply or invert, because ln K = −ΔG°/RT. All the K values combined must refer to the same temperature.

What the size of K tells you

A very large K (roughly above 10³) means the equilibrium mixture is mostly products; a very small K (roughly below 10⁻³) means it is mostly reactants; values in between leave significant amounts of both. K says nothing about how fast equilibrium is reached. A mixture of H₂ and O₂ has an enormous K for forming water yet survives for years at room temperature until a spark or catalyst lowers the barrier. K changes only with temperature, not with the starting amounts, the pressure or a catalyst.

The reaction quotient Q

Q has exactly the same form as K but uses the concentrations (or pressures) present at any moment, not necessarily at equilibrium. Compare Q with K: if Q < K there are too few products, so the net reaction runs forward; if Q > K there are too many products, so it runs in reverse; if Q = K the mixture is at equilibrium. Example: for N₂O₄(g) ⇌ 2 NO₂(g), Kc = 4.6 × 10⁻³ at 25 °C. A mixture with [N₂O₄] = 0.020 M and [NO₂] = 0.020 M has Q = 0.020²/0.020 = 0.020, which is larger than K, so NO₂ combines to N₂O₄ until Q falls to 4.6 × 10⁻³. Always apply the exponents and leave out pure solids and liquids when calculating Q, just as for K.

What to carry forward

Write K as products over reactants with each concentration or pressure raised to its coefficient, and leave out pure solids and liquids. Convert with Kp = Kc(RT)^Δn using only gas moles. Reverse an equation and K inverts; multiply by n and K is raised to the n; add equations and K values multiply. Large K favours products, small K favours reactants, and neither says anything about speed. Compare Q with K: Q < K runs forward, Q > K runs in reverse.

Problemas de prática (40)

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Preveja o produto 7

Magnitude of K and the reaction quotient

  • Carbon, CO and CO₂Predict the direction of a heterogeneous reaction from Qp and Kp, leaving out the solid.
  • Which way will it go?Predict the direction of net reaction when Q is greater than K.

Manipulating and combining K

  • Doubling the equationPredict how K changes when every coefficient of an equation is doubled.

Dynamic equilibrium and K expressions

  • Iron and steamWrite Kc for a heterogeneous equilibrium that contains two pure solids and two gases.
  • Kc for the Deacon processWrite Kc for a homogeneous gas-phase equilibrium with coefficients as exponents.
  • Following a radioactive labelUse an isotope-labelling experiment to show that reactions continue at equilibrium.

Kc and Kp

  • Kp for steam reformingWrite a Kp expression in partial pressures for a gas-phase equilibrium.

Classificar 2

Dynamic equilibrium and K expressions

  • Spot the heterogeneous equilibriumClassify an equilibrium as homogeneous or heterogeneous from the phases of its species.

Kc and Kp

  • When does Kp equal Kc?Classify equilibria by whether Kp equals Kc, using the change in moles of gas.

Comparar 3

Kc and Kp

  • Is Kp larger or smaller than Kc?Compare the sizes of Kp and Kc from the sign of Δn and the value of RT.

Magnitude of K and the reaction quotient

  • Rank mixtures by QRank non-equilibrium mixtures by reaction quotient when one concentration is squared, and relate each to K.

Manipulating and combining K

  • Rank K for rewritten equationsRank the equilibrium constants of an equation that has been reversed, halved and doubled.

Calcular 18

Manipulating and combining K

  • Add two equationsCombine two equations that add directly to the target by multiplying their K values.
  • Combine with a reversed equationCombine one equation as written with the reverse of another, dividing their K values.
  • K per mole of NOFind K for an equation whose coefficients are halved by taking the square root.
  • Three manipulations at onceReverse, halve and add equations to find K for forming a compound from its elements.
  • Kp for phosgene formationReverse an equation and convert the resulting Kc to Kp, keeping track of the sign of Δn.
  • K for the reverse reactionFind K for a reversed equation by taking the reciprocal.

Magnitude of K and the reaction quotient

  • Q right after compressionCalculate how Q changes relative to K when every concentration of a gas-phase equilibrium is doubled.
  • Q for an H₂/I₂/HI mixtureCalculate a reaction quotient from non-equilibrium concentrations.
  • Q for methanol synthesisCalculate a reaction quotient from partial pressures and use it to judge the direction of reaction.
  • Where does the net direction switch?Find the concentration at which Q equals K, the boundary between forward and reverse net reaction.

Kc and Kp

  • Δn for a gas-phase equilibriumCalculate Δn, the change in moles of gas, used to convert between Kc and Kp.
  • Kc for ammonia synthesis from KpConvert Kp to Kc when the moles of gas decrease by two.
  • Kp for a solid that decomposes into two gasesConvert Kc to Kp for a heterogeneous equilibrium, counting only gases in Δn.
  • Kp for N₂O₄ ⇌ 2 NO₂Convert Kc to Kp for a dissociation in which the moles of gas increase.
  • Kp from partial pressuresCalculate Kp from equilibrium partial pressures with squared terms.
  • Pressure above solid NH₄HSUse a heterogeneous Kp and the 1:1 stoichiometry of the gases to find the total equilibrium pressure.

Dynamic equilibrium and K expressions

  • Kc from moles in a 2.00 L flaskConvert equilibrium amounts to molar concentrations before calculating Kc for a reaction whose gas moles change.
  • Kc for nickel tetracarbonyl formationCalculate Kc from equilibrium concentrations when a solid is omitted and a coefficient of 4 becomes an exponent.

Encontre o erro 3

Kc and Kp

  • A Δn errorDiagnose a Kc-to-Kp conversion that counts a liquid product in Δn.

Magnitude of K and the reaction quotient

  • Huge K, no reaction?Diagnose the error of using the size of K to predict how fast a reaction occurs.

Dynamic equilibrium and K expressions

  • Find the error in a K expressionDiagnose a heterogeneous K expression that wrongly includes a pure solid and a pure liquid.

Interprete as evidências 2

Magnitude of K and the reaction quotient

  • Reading Q over timeInterpret a series of reaction-quotient values to deduce the starting composition, the net direction and when equilibrium is reached.
  • A very small KInterpret a very small equilibrium constant in terms of the composition of the equilibrium mixture.

Trabalhe de trás para frente 1

  • Which equation fits this Kc?Work back from a Kc expression to the balanced equation, including phases and coefficients.

Planeje uma síntese 1

  • Plan a combination of equationsChoose how to reverse, scale and add two equations to reach a target, and the K that results.

Explique por quê 3

Dynamic equilibrium and K expressions

  • What stays equal at equilibrium?Identify the defining feature of a dynamic chemical equilibrium.
  • Adding more liquid waterExplain why adding more of a pure liquid does not change the equilibrium pressure of its vapour.

Manipulating and combining K

  • Why multiply, not add?Explain why the K values of added equations multiply while their ΔH values add.

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