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

step 1 So in this question, based off of the information that we are told, this is zero order in ethano

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 $$\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2}(g)$$ If the initial concentration of ethanol is $0.020 \mathrm{~mol} \mathrm{~L}^{-1}$, how long will it take for the pressure to reach $1.4$ atm at $327^{\circ} \mathrm{C}$ ?

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
$$\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2}(g)$$
If the initial concentration of ethanol is $0.020 \mathrm{~mol} \mathrm{~L}^{-1}$, how long will it take for the pressure to reach $1.4$ atm at $327^{\circ} \mathrm{C}$ ?

Key Concepts

Zero Order Kinetics

Zero order kinetics describes a reaction in which the rate is independent of the concentration of the reactant. When a plot of concentration versus time is linear, it indicates that the reaction follows zero order behavior. This means that the rate at which the reactant is consumed is constant throughout the course of the reaction, and the reaction rate can be expressed as the negative slope of the concentration-time graph.

Integrated Rate Law for a Zero Order Reaction

For a zero order reaction, the integrated rate law is given by [A] = [A]? - kt, where [A] is the concentration at time t, [A]? is the initial concentration, and k is the rate constant. This equation is essential for determining the time required to reach a certain concentration or extent of conversion, and it emphasizes that the decline in reactant concentration occurs at a constant rate since the rate does not depend on [A].

Reaction Stoichiometry in Gaseous Systems

Reaction stoichiometry involves the mole-to-mole relationships between reactants and products in a chemical reaction. In gas-phase reactions, balanced stoichiometric relationships determine the change in the number of moles of gas as the reaction proceeds. For example, when one mole of a gaseous reactant decomposes to form two moles of gaseous products, the overall number of moles increases, which can directly affect the total pressure of the system under constant volume and temperature conditions.

Relationship Between Concentration, Moles, and Pressure

In gas-phase reactions, the pressure is directly related to the number of moles of gas present via the ideal gas law. As the reaction progresses and changes the number of moles of gaseous species (due to the stoichiometry of the reaction), the total pressure in the system will change if temperature and volume are held constant. Understanding this relationship allows for the calculation of reaction time required to achieve a target pressure by correlating the conversion degree of reactant to the corresponding change in total gas moles and thus the system pressure.

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