Derive an expression for the time dependence of the degree of polymerization for the stepwise polymerization of a hydroxyacid HO−R−COOH for which the rate law is d[A]/dt = −kr[A]2[OH], where A denotes the carboxylic acid group.
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Derive an expression for the time dependence of the degree of
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- The degradation of the antibiotic clindamycin stored at 343 K in aqueous solution at pH 4 is found to be first order with a rate constant of 2.49 x 10−7 s −1. Over the temperature range 320 K to 360 K theactivation energy was found to be 123.3 kJ mol−1. (a) Calculate the rate constant at 325 K.(b) The threshold for product safety is 1% degradation. At 295 K the time taken for 1% of the antibiotic to degrade is found to be close to 0.01/ k. Comment on the shelf-life of the drug.In general for the reaction: cC + dD ➡️ aA + bB, write the rate law expression for reaction.Derive the integrated form of a third-order rate law v = kr[A]2[B] in which the stoichiometry is 2 A + B → P and the reactants are initially present in (a) their stoichiometric proportions ([B]0 = 12[A]0); (b) with B present initially in twice that amount ([B]0 = [A]0). Express your rate law in terms of [A]0, [B]0, and x, where [A] = [A]0 − 2x.
- The rate law for the oxidation reaction 2CO(g) + O2(g) → 2CO2(g) assuming that the reaction occurs by the Langmuir -Hinshelwood mechanism. The over-all rate law for this mechanism is Rate = k3θCOθO2 ΘO2 = (KO2 [O2])1/2 and ΘCO = KCO [CO] --------------------------------- --------------------------------- 1+ (KO2[O2])1/2 + KCO[CO] 1+ (KO2[O2])1/2 + KCO[CO]In the hydrogenation of ethylene using a nickel catalyst, the initial concentration of ethylene is 1.70 mol⋅L^−1 and its rate constant (k) is 0.0010 mol⋅L^−1⋅s^−1 . Determine the rate of reaction if it follows a zero-order reaction mechanism.Derive the integrated form of a third-order rate law v = kr[A]2[B] in which the stoichiometry is 2 A +B −−→ P and the reactants are initially present in (a) their stoichiometric proportions, (b) with Bpresent initially in twice the amount.
- The rate constant for the reaction 2NO2 → 2NO + O2 is experimentally determined to be 0.153 mol−1 dm3 s −1 at 300°C and 0.993 mol−1 dm3 s −1 at 350°C. Estimate the effective radius of an NO2 molecule. The steric factor for this reaction is 0.05.Calculate the magnitude of the diffusion-controlled rate constant at 320 K for the recombination of two atoms in water, for which η = 0.89 cP. Assuming the concentration of the reacting species is 1.5 mmol dm−3 initially, how long does it take for the concentration of the atoms to fall to half that value? Assume the reaction is elementary.2. Derive an expression for the time dependence of the degree of polymerization for the stepwise polymerization of a hydroxyacid HO – R- COOH for which the rate law is dA = -k,[A]²[0H] ,where A denotes the carboxylic acid group.
- Rate law experiments don’t always give data in the form of a rate in molesper second. Some of them give an amount of time necessary for areaction to proceed to a given point. The faster the rate, the less timenecessary. For the following data, assume that the time recorded for eachexperiment is the time required to consume 0.10 M of A in a hypotheticalreaction A + B yields C Time taken (s) [A]0 [B]0 36.8 0.20 0.40 25.0 0.20 0.60 10.0 0.50 0.60 Determine the rate law and the rate constant for the reactionThe rate constant of the reaction H2O2(aq) + I−(aq) + H+(aq) → H2O(l) + HIO(aq) is sensitive to the ionic strength of the aqueous solution in which the reaction occurs. At 25 °C, kr = 12.2 dm6 mol−2 min−1 at an ionic strength of 0.0525. Use the Debye–Hückel limiting law to estimate the rate constant at zero ionic strength.An elementary reaction is generally expressed as: dC, = -kC," dt where A is the species being depleted as the reaction progresses, k is the rate constant, and n is the order of reaction, usually referred to as the stoichiometric coefficient of the resulting product. For a polymerization reaction A> 3B, find the initial amount if after 30 seconds, A species is reduced to 5 moles/L within 3 minutes. Take the rate constant as 0.314 L'/(moP-min).