Química Geral · Chemical kinetics
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O que você vai aprender
- Relate the rates of change of every reactant and product to one rate of reaction using the stoichiometric coefficients.
- Calculate average rates from concentration data and read instantaneous and initial rates as tangent slopes.
- Write a rate law, state the order in each reactant and the overall order, and predict how the rate responds to concentration changes.
- Deduce reaction orders and the rate constant from initial-rate experiments, including non-integer ratios and experiments where two concentrations change.
- Give the units of a rate constant for any overall order and explain why k depends on temperature but not on concentration.
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Rate and stoichiometry
The rate of a reaction is how fast concentrations change, usually in M/s (mol L⁻¹ s⁻¹). Reactant concentrations fall and product concentrations rise, so a reactant's rate of disappearance is −Δ[reactant]/Δt and a product's rate of formation is +Δ[product]/Δt; both are positive numbers. The species change at different speeds, in proportion to their coefficients. For 2 N₂O₅(g) → 4 NO₂(g) + O₂(g) (N₂O₅ drawn), if N₂O₅ disappears at 4.0 × 10⁻⁵ M/s, NO₂ forms twice as fast (8.0 × 10⁻⁵ M/s) and O₂ half as fast (2.0 × 10⁻⁵ M/s). Dividing each rate by its coefficient gives one value for the whole reaction: rate = −½ Δ[N₂O₅]/Δt = ¼ Δ[NO₂]/Δt = Δ[O₂]/Δt = 2.0 × 10⁻⁵ M/s. In general, for aA + bB → cC + dD, rate = −(1/a)Δ[A]/Δt = −(1/b)Δ[B]/Δt = (1/c)Δ[C]/Δt = (1/d)Δ[D]/Δt. For gases in a rigid container at constant temperature, partial pressures follow the same ratios, because pressure is proportional to concentration.
Average, instantaneous and initial rates
An average rate uses two measurements: if [N₂O₅] falls from 0.0200 M to 0.0170 M in 100 s, the average rate of disappearance is (0.0200 − 0.0170) M ÷ 100 s = 3.0 × 10⁻⁵ M/s. Because most reactions slow down as reactants are used up, averages over successive equal intervals decrease. The instantaneous rate at a time t is the slope of the tangent to the concentration–time curve at t (with the sign changed for a reactant). Read the slope from two points on the tangent line, not from points on the curve: a tangent through (0 s, 0.600 M) and (300 s, 0.150 M) has slope −0.450 M ÷ 300 s = −1.50 × 10⁻³ M/s, so the reactant disappears at 1.50 × 10⁻³ M/s at that moment. A short interval centred on t gives a good estimate of the tangent slope; a long or one-sided interval does not. The initial rate is the instantaneous rate at t = 0, when every concentration is exactly the amount mixed and no product has built up.
Rate laws and reaction order
A rate law links the rate to concentrations: rate = k[A]^m[B]^n. The exponents m and n are the orders in A and B, and m + n is the overall order. Orders are found by experiment; they need not match the coefficients of the balanced equation and can be zero or fractions. Examples: NO₂ + CO → NO + CO₂ below 225 °C has rate = k[NO₂]², zero order in CO; the initial rate of H₂ + Br₂ → 2 HBr is k[H₂][Br₂]^½; CH₃CHO → CH₄ + CO has rate = k[CH₃CHO]^(3/2); the acid-catalysed iodination of acetone (drawn) has rate = k[CH₃COCH₃][H⁺] and does not depend on [I₂]. A catalyst such as H⁺ can appear in a rate law even though it is not consumed, and a reactant can be absent from it when it reacts only after the slow step. When a concentration is multiplied by a factor f, the rate is multiplied by f raised to the order: doubling [A] in a reaction second order in A multiplies the rate by 2² = 4, and tripling a first-order reactant B at the same time multiplies it by a further 3, giving 12. Compressing a gas mixture to half its volume at constant temperature doubles every concentration.
The rate constant and its units
The rate constant k is fixed at a given temperature; it changes with temperature (and with a change of catalyst or solvent) but not with concentration. If the rate rises when a concentration rises, the concentration term in the rate law changed, not k. Rates always have units of M/s, so for overall order n, k = rate ÷ Mⁿ has units M^(1−n) s⁻¹: zero order M s⁻¹, first order s⁻¹, three-halves order M^(−1/2) s⁻¹, second order M⁻¹ s⁻¹ (L mol⁻¹ s⁻¹), third order M⁻² s⁻¹ (L² mol⁻² s⁻¹), fourth order M⁻³ s⁻¹. Minutes or hours can replace seconds; the power of the concentration unit still identifies the order. Ammonia decomposing on a hot tungsten surface is zero order at ordinary pressures: the surface sites are all occupied, so adding more ammonia does not speed the reaction, and k has the units of a rate, M s⁻¹.
The method of initial rates
Run several experiments at the same temperature, changing one starting concentration at a time, and measure each initial rate. For the iodide-catalysed decomposition of hydrogen peroxide (drawn): Exp 1 [H₂O₂] = 0.100 M, [I⁻] = 0.0200 M, rate 2.30 × 10⁻⁵ M/s; Exp 2 [H₂O₂] = 0.200 M, [I⁻] = 0.0200 M, rate 4.60 × 10⁻⁵ M/s; Exp 3 [H₂O₂] = 0.100 M, [I⁻] = 0.0400 M, rate 4.60 × 10⁻⁵ M/s. Exp 1 → 2 doubles only [H₂O₂] and doubles the rate (order 1); Exp 1 → 3 doubles only [I⁻] and doubles the rate (order 1). So rate = k[H₂O₂][I⁻], and k = 2.30 × 10⁻⁵ M/s ÷ (0.100 M × 0.0200 M) = 2.30 × 10⁻⁵ ÷ 2.00 × 10⁻³ = 1.15 × 10⁻² M⁻¹ s⁻¹; every experiment gives the same k. For any pair, order = log(rate ratio) ÷ log(concentration ratio): a 1.8-fold increase that raises the rate 3.24-fold gives log 3.24 ÷ log 1.8 = 2, and a 9-fold increase that raises it 27-fold gives log 27 ÷ log 9 = 1.5. If two concentrations changed together, first divide out the effect of the reactant whose order you already know, then solve for the other. Compute k from any one experiment, and check that the other experiments give the same value.
What to carry forward
Divide each rate of change by its coefficient to get one rate of reaction. Orders come from experiment, not from the balanced equation: compare initial rates where only one concentration changes, use order = log(rate ratio) ÷ log(concentration ratio), then calculate k from any experiment. The rate scales as (concentration factor)^order; k changes with temperature (or a different catalyst or solvent) but not with concentration, and has units M^(1−n) s⁻¹ for overall order n.
Problemas de prática (40)
Praticar é grátis com uma conta.
Preveja o produto 4
Rate laws and order
- Doubling the rate of a second-order dimerizationPredict which change doubles the rate of a reaction that is second order in a single reactant.
- Compress the H₂/I₂ mixturePredict how a gas-phase rate changes when the mixture is compressed at constant temperature.
- Triple one reactant, halve the otherPredict the factor by which a rate changes when two concentrations change in a known third-order rate law.
Method of initial rates
- Predict the missing initial rateUse orders found from initial-rate data to predict the rate for a new mixture in which both concentrations change.
Classificar 4
Rate laws and order
- Units of k for a three-halves-order reactionDerive the units of a rate constant for a fractional overall order.
- Units of k for a fourth-order rate lawDerive the units of a rate constant for a fourth-order rate law.
- Order in carbon monoxideClassify the order with respect to a reactant that does not appear in the rate law.
Rates and stoichiometry
- Rate of reaction for ammonia oxidationIdentify the correct rate-of-reaction expression for a reaction with several coefficients.
Comparar 3
Rate laws and order
- Rank reactions by order from the units of kRank reactions by overall order from rate-constant units written with mixed concentration and time notation.
- Rank NO/Br₂ mixtures by initial rateRank mixtures by initial rate using a rate law that is second order in one reactant.
Rates and stoichiometry
- Which concentration changes fastest?Rank the reactants and products of a combustion by how fast their concentrations change.
Calcular 14
Method of initial rates
- A fractional order from initial ratesCalculate a non-integer reaction order from a pair of initial-rate measurements using logarithms.
- Rate constant for ammonium nitriteFind the orders from initial-rate data and calculate a second-order rate constant.
- Rate constant for bromate, bromide and acidDetermine three orders from four initial-rate experiments and calculate a fourth-order rate constant.
- Order from a 1.5-fold changeFind a reaction order when the concentration ratio between experiments is not a whole number.
- Order when two concentrations changeFind the order in one reactant from an experiment in which both concentrations changed, by dividing out the known order of the other.
Rates and stoichiometry
- Grams of hydrogen used per minuteCombine a rate of formation, the mole ratio, the reactor volume and a molar mass to find a mass consumed per unit time.
- Average rate of hydrogen peroxide lossCalculate an average rate of disappearance from two concentration measurements.
- Rate of acid use from mass lossTurn a measured mass of escaping gas into the average rate of consumption of a dissolved reactant.
- How fast does the total pressure rise?Use the mole ratio of a gas-phase decomposition to convert a reactant's pressure change into the rate of change of total pressure.
- Hydrogen formed from phosphineConvert a reactant's rate of disappearance into a product's rate of formation using the mole ratio.
Rate laws and order
- Overall order of the bromate reactionAdd the exponents of a rate law to find the overall order, ignoring the coefficients of the balanced equation.
- Rate from the rate lawSubstitute concentrations and k into a second-order rate law to calculate a rate.
- How much has the reaction slowed?Use stoichiometry to find every concentration partway through a reaction, then compare rates with a third-order rate law.
- How fast is iodide used?Combine a rate law with the stoichiometric coefficients to find the rate of consumption of a reactant whose coefficient is not 1.
Encontre o erro 2
Rate laws and order
- Did the rate constant double?Diagnose the error of attributing a concentration-driven rate change to a change in the rate constant.
Method of initial rates
- Find the flaw in an order assignmentDiagnose an order assigned from two experiments in which more than one concentration changed.
Interprete as evidências 4
Method of initial rates
- Rate law for the iodination of acetoneDeduce a three-reactant rate law that includes a zero-order reactant and a catalyst.
- Which experiments reveal the order in iodide?Pick the pair of initial-rate experiments in which only one reactant concentration changes.
- Rate law for persulfate and iodideDeduce a rate law from initial rates and reject the rate law suggested by the balanced equation.
Rates and stoichiometry
- Instantaneous rate from a tangentRead an instantaneous rate of disappearance from two points on a tangent line.
Trabalhe de trás para frente 2
Rates and stoichiometry
- Balanced equation from measured ratesWork back from the measured rates of change of three species to the coefficients of the balanced equation.
Rate laws and order
- What [NO₂] gives this rate?Rearrange a second-order rate law to find the concentration that produces a required rate.
Planeje uma síntese 2
Method of initial rates
- Plan the next initial-rate experimentChoose the conditions for a second experiment that isolates the order in one reactant.
Rates and stoichiometry
- Best estimate of an instantaneous rateChoose the pair of measurements that best approximates the instantaneous rate at a given time.
Explique por quê 5
Method of initial rates
- A catalyst in the rate law, a reactant missing from itExplain why a catalyst appears in a rate law while a consumed reactant does not, using the slow step of the mechanism.
- Why measure initial rates?Explain the advantages of using initial rates to determine a rate law.
Rate laws and order
- Why is ammonia decomposition zero order?Explain zero-order kinetics for a reaction on a saturated catalyst surface.
- Why isn't the rate law k[H₂][Br₂]?Explain why the orders in a rate law cannot be read from the coefficients of the overall balanced equation.
Rates and stoichiometry
- Why the average rate dropsExplain why average rates over successive equal intervals decrease as a reaction proceeds.
Travou em velocidades de reação e leis de velocidade? 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.
Depois, Scan Standard: /mês