The catalyzed decomposition of ethanol at 327^∘ C has a rate constant of 4.00 ×10^-5 mol L^-1

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The catalyzed decomposition of ethanol at 327^∘ C has a rate...

The catalyzed decomposition of ethanol at $327^{\circ} \mathrm{C}$ has a rate constant of $4.00 \times 10^{-5} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$. The plot of concentration of ethanol versus time gives a straight line. The balanced equation for this reaction is $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})$ If the initial concentration of ethanol is $0.020 \mathrm{~mol} \mathrm{~L}^{-1}$ how long will it take for the pressure to reach $1.4 \mathrm{~atm}$ at $327^{\circ} \mathrm{C} ?$

Key Concepts

Integration of Kinetic and Pressure Data

Integrating kinetic information with pressure data involves using the rate law to determine the change in concentration of gaseous reactants and the corresponding change in the total number of moles in the system. Through stoichiometry and the ideal gas law, one can correlate the decrease in reactant concentration and the increase in product concentrations with the observed pressure change over time.

Ideal Gas Law Application

The ideal gas law, PV = nRT, relates the pressure of a gas to its number of moles, the volume, and the temperature. In reactions that occur in the gas phase at constant volume and temperature, any change in the number of moles of gas due to the reaction will result in a proportional change in the pressure, allowing kinetic data to be linked to pressure measurements.

Reaction Stoichiometry in Gas-phase Systems

Stoichiometry in a chemical reaction provides the quantitative relationships between reactants and products. In gas-phase reactions, the stoichiometric coefficients indicate how many moles of product gases are generated per mole of reactant consumed, which directly affects the total number of moles in the system and, consequently, the pressure when using the ideal gas law.

Rate Constant Units and Meaning

The rate constant, k, quantifies the speed of a reaction under given conditions. For a zero order reaction, k is expressed in units of mol L?¹ s?¹, reflecting the fact that the rate of reaction does not depend on the instantaneous concentration of the reactant, but only on the value of k and time.

Zero Order Kinetics

Zero order kinetics describe reactions in which the rate is constant and independent of the concentration of the reactants. In these reactions, the concentration decreases linearly with time, and the integrated rate law is expressed as [A] = [A]? - kt, where k has units of concentration/time.

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