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Química Geral · Chemical equilibrium

Tabelas ICE e princípio de Le Châtelier

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O que você vai aprender

  • Build an ICE table with changes in the ratio of the coefficients and use it to find K from equilibrium data.
  • Find equilibrium concentrations from initial amounts and K, using the small-x approximation with a 5 % check or the exact quadratic.
  • Predict how an equilibrium responds to added or removed species, volume and pressure changes, inert gases, temperature and catalysts.
  • Calculate the new equilibrium composition after a disturbance by comparing Q with K and solving a second ICE table.

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Ler a aula gratuita (6 partes)

Setting up an ICE table

An ICE table has three rows under the balanced equation: Initial amounts, the Change needed to reach equilibrium, and the Equilibrium amounts (initial + change). Use mol/L for Kc and atm for Kp, never plain moles unless the moles of gas are the same on both sides. The change row always follows the coefficients: for N₂ + 3 H₂ ⇌ 2 NH₃ it is −x, −3x, +2x. When one equilibrium amount is measured, it fixes x and every other entry. Example: N₂O₄(g) ⇌ 2 NO₂(g) starts at [N₂O₄] = 0.0500 M with no NO₂, and at equilibrium [NO₂] = 0.0400 M. Then 2x = 0.0400, x = 0.0200, [N₂O₄] = 0.0500 − 0.0200 = 0.0300 M and Kc = (0.0400)²/0.0300 = 0.0533. K has the same value whatever the starting mixture, as long as the temperature is fixed. Pure solids and liquids are left out of K, so for NH₄HS(s) ⇌ NH₃(g) + H₂S(g) Kp = P(NH₃)·P(H₂S).

Solving for x: small-x approximation or quadratic

With K and the initial amounts known, write K in terms of x and solve. If K is small compared with the starting concentration, x is small and you may replace (c − x) by c. Always check: the approximation is accepted when x is below 5 % of c. Example: COCl₂(g) ⇌ CO(g) + Cl₂(g), Kc = 2.2 × 10⁻¹⁰ at 100 °C, [COCl₂]₀ = 0.100 M. x²/0.100 = 2.2 × 10⁻¹⁰ gives x = √(2.2 × 10⁻¹¹) = 4.7 × 10⁻⁶ M, far below 5 % of 0.100 M. For PCl₅(g) ⇌ PCl₃(g) + Cl₂(g) with Kc = 0.0400 and [PCl₅]₀ = 0.200 M the shortcut gives x = √0.00800 = 0.0894 M, 45 % of 0.200 M, so it fails. Solve x² + 0.0400x − 0.00800 = 0 instead: x = [−0.0400 + √(0.00160 + 0.0320)]/2 = 0.0717 M. Keep only the root that gives no negative concentration. When both sides are perfect squares (equal starting amounts with A + B ⇌ 2 C), take the square root first.

Le Châtelier: concentration, volume, pressure and inert gases

A disturbed equilibrium reacts in the direction that partly undoes the change; Q tells you which way. Adding a reactant or removing a product makes Q < K, so net reaction runs forward; adding a product makes Q > K. Pure solids and liquids are not in Q, so adding more of them changes nothing. Halving the volume of a gas mixture doubles every partial pressure and shifts the equilibrium toward the side with fewer moles of gas; if both sides have the same number of moles of gas, Q is unchanged and there is no shift. An inert gas added at constant volume leaves every partial pressure unchanged, so there is no shift; added at constant total pressure it expands the mixture, and the equilibrium shifts toward the side with more moles of gas (again, no shift if both sides have the same number). Diluting a solution equilibrium shifts it toward the side with more dissolved particles: for Fe³⁺ + SCN⁻ ⇌ FeSCN²⁺, doubling the volume makes Q = 2K, so some red FeSCN²⁺ breaks up. The shift only partly offsets the change: after O₂ is added to 2 SO₂ + O₂ ⇌ 2 SO₃, [O₂] at the new equilibrium is still higher than before.

Temperature and catalysts

Temperature is the only change that alters K. Treat heat as a product of an exothermic reaction and as a reactant of an endothermic one. For 2 SO₂ + O₂ ⇌ 2 SO₃ (ΔH° = −198 kJ) heating lowers K and shifts the mixture toward SO₂ and O₂. The cobalt(II) equilibrium [Co(H₂O)₆]²⁺ (pink) + 4 Cl⁻ ⇌ [CoCl₄]²⁻ (blue) + 6 H₂O turns blue when heated, so its forward reaction is endothermic. A catalyst lowers the activation energy of the forward and reverse reactions by the same amount. It speeds up both, so equilibrium is reached sooner, but K and the equilibrium composition do not change.

Re-equilibrating after a disturbance

To find the new equilibrium, start a second ICE table from the mixture just after the change, use Q to choose the direction, and solve with the same K (or the new K if the temperature changed). Example: butane ⇌ isobutane, Kc = 2.50, is at equilibrium with [butane] = 0.100 M and [isobutane] = 0.250 M. Isobutane is added, raising it to 0.400 M. Now Q = 0.400/0.100 = 4.00 > K, so the reaction runs backward by x: (0.400 − x)/(0.100 + x) = 2.50, 0.400 − x = 0.250 + 2.50x, x = 0.0429 M. The new equilibrium has [isobutane] = 0.357 M and [butane] = 0.143 M; the ratio is again 2.50. For a heterogeneous equilibrium such as CaCO₃(s) ⇌ CaO(s) + CO₂(g), Kp = P(CO₂), so after a volume change at constant temperature the pressure of CO₂ returns to the same value while some solid reacts, as long as both solids are still present.

What to carry forward

Write the balanced equation, fill in the ICE table with changes in the ratio of the coefficients, and use concentrations or partial pressures in K. Try the small-x approximation only when K is small compared with the starting concentrations, and check that x is under 5 %; otherwise solve the quadratic and keep the physical root. For a disturbance, compare Q with K: the system shifts to bring Q back to K and only partly offsets the change. Only temperature changes K, and a catalyst changes how fast equilibrium is reached, not where it lies.

Problemas de prática (40)

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Preveja o produto 7

Le Châtelier's principle

  • Adding argon at constant pressurePredict the effect of adding an inert gas at constant total pressure on an equilibrium with unequal moles of gas.
  • Compressing a reaction with equal moles of gasPredict the effect of compression on an equilibrium with the same number of moles of gas on both sides.
  • Heating an exothermic equilibriumPredict how heating changes K and the composition of an exothermic gas-phase equilibrium.
  • Pumping CO₂ over hot limestonePredict the final gas pressure when a heterogeneous equilibrium with a single gas is disturbed.
  • After adding oxygenPredict how each concentration at the new equilibrium compares with the original after one reactant is added.
  • Adding thiocyanate to the iron(III) equilibriumPredict the shift and colour change when a reactant ion is added to an aqueous equilibrium.
  • Diluting the iron(III) thiocyanate equilibriumPredict the shift caused by diluting a solution equilibrium from the change in Q.

Classificar 4

Le Châtelier's principle

  • Which equilibrium favours products when compressed?Classify equilibria by the direction a volume decrease shifts them, counting only gaseous species.
  • Which change alters K?Classify disturbances by whether they change the value of the equilibrium constant.

K from equilibrium data

  • The change row for ammonia synthesisWrite the change row of an ICE table in the ratio of the balanced-equation coefficients.

Solving ICE tables

  • When can x be neglected?Classify starting conditions by whether the small-x approximation will pass the 5 % check.

Comparar 1

  • Rank by fraction dissociatedCompare how the fraction of a reactant that dissociates depends on its starting concentration at a fixed K.

Calcular 19

K from equilibrium data

  • Kp from a total pressure over a solidCalculate Kp for a solid that decomposes into two gases from the total equilibrium pressure.
  • K for methanol synthesis from one measurementUse one measured equilibrium concentration and the coefficient ratios of an ICE table to calculate Kc.
  • Kc for sulfur trioxide formationCalculate Kc from measured equilibrium concentrations, raising each to the power of its coefficient.
  • Kp with solid carbon presentCalculate Kp for a heterogeneous gas–solid equilibrium from partial pressures, leaving out the solid.
  • K from percent dissociationConvert a percent dissociation into equilibrium concentrations for a reaction with unequal coefficients and calculate Kc.
  • Kp from a rise in total pressureUse the rise in total pressure of a dissociating gas to set up an ICE table in partial pressures and calculate Kp.

Re-equilibrating after a disturbance

  • Adding butane to an isomerization equilibriumCalculate the new equilibrium concentration after a reactant is added to a one-to-one equilibrium.
  • More ethanol in an esterification equilibriumCalculate the new equilibrium amount of ester after excess alcohol is added to an esterification equilibrium.
  • Compressing CO₂ over limestoneCalculate how much gas is consumed when a single-gas heterogeneous equilibrium is compressed and its pressure returns to Kp.
  • Chlorine added to the PCl₅ equilibriumSolve a second ICE table after a product is added to find the new equilibrium concentration of the other product.
  • Doubling the volume of the PCl₅ equilibriumCalculate the new equilibrium concentrations after a volume increase shifts a gas equilibrium toward more moles of gas.
  • Q right after oxygen is injectedCalculate the reaction quotient immediately after a disturbance and use it to decide the direction of re-equilibration.

Solving ICE tables

  • Isomerization of but-2-eneSolve a one-to-one isomerization equilibrium for the product concentration with a linear ICE equation.
  • A small K with a cube to solveUse the small-x approximation when the equilibrium expression gives a cubic in x, and check the result.
  • Nitric oxide from air at high temperatureApply the small-x approximation to a reaction with two reactants and a doubled product, then check it.
  • Carbon monoxide from phosgeneUse the small-x approximation for a very small K to find a trace equilibrium concentration in µmol/L.
  • When the shortcut fails: sulfuryl chlorideSolve a dissociation equilibrium exactly with the quadratic formula when K is too large for the small-x approximation.
  • Dissociation with a product already presentSolve an ICE table exactly when one product is present at the start.
  • Choosing the physical rootSolve a two-reactant ICE table with the quadratic formula and reject the root that gives a negative concentration.

Encontre o erro 2

Solving ICE tables

  • Find the flaw in an iodine ICE tableDiagnose a small-x solution whose result fails the 5 % check.

K from equilibrium data

  • Find the error in a Kc calculationDiagnose a Kc calculation that uses moles instead of concentrations when the moles of gas change.

Interprete as evidências 3

Le Châtelier's principle

  • Reading ΔH from a colour changeInterpret a reversible colour change with temperature to deduce the sign of ΔH for a complex-ion equilibrium.

Re-equilibrating after a disturbance

  • Read the disturbance from a concentration plotInterpret a concentration–time record to identify the disturbance applied to a gas equilibrium.

K from equilibrium data

  • What stays the same in every flask?Interpret equilibrium data from several starting mixtures to identify the quantity that is constant at one temperature.

Trabalhe de trás para frente 1

  • Working back to the starting concentrationWork backwards from K and one equilibrium concentration to the initial concentration of a reactant.

Planeje uma síntese 1

  • Raising the yield of ethyl acetateChoose a change that raises the equilibrium conversion of a limiting reactant by applying Le Châtelier's principle.

Explique por quê 2

Le Châtelier's principle

  • Why a catalyst leaves the equilibrium aloneExplain why a catalyst changes the rate of approach to equilibrium but not the equilibrium composition.
  • What happens after H₂ is injectedExplain the response to an added reactant as an ordered sequence linking concentration, Q, net reaction and the restored equilibrium.

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