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Ch.14 - Chemical Kinetics
Brown - Chemistry: The Central Science 15th Edition
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Tutti i libri di testoBrown 15th EditionCh.14 - Chemical KineticsProblema 43a
Capitolo 14, Problema 43a

As described in Exercise 14.41, the decomposition of sulfuryl chloride (SO2Cl2) is a first-order process. The rate constant for the decomposition at 660 K is 4.5 × 10-2 s-1. (a) If we begin with an initial SO2Cl2 pressure of 450 torr, what is the partial pressure of this substance after 60 s?

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Identify the type of reaction: The decomposition of sulfuryl chloride (SO2Cl2) is a first-order reaction. This means the rate of reaction is directly proportional to the concentration of SO2Cl2.
Use the first-order rate equation: The formula for a first-order reaction is \( P_t = P_0 e^{-kt} \), where \( P_t \) is the partial pressure at time \( t \), \( P_0 \) is the initial pressure, \( k \) is the rate constant, and \( t \) is the time.
Substitute the known values into the equation: You have \( P_0 = 450 \) torr, \( k = 4.5 \times 10^{-2} \) s\(^{-1}\), and \( t = 60 \) s. Plug these values into the equation to find \( P_t \).
Calculate the exponent: Compute \( -kt \) which is \( -4.5 \times 10^{-2} \times 60 \). This will give you the exponent for the exponential function.
Evaluate the expression: Calculate \( e^{-kt} \) using the exponent from the previous step, then multiply by the initial pressure \( P_0 \) to find the partial pressure \( P_t \) after 60 seconds.

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First-Order Reactions

First-order reactions are chemical processes where the rate of reaction is directly proportional to the concentration of one reactant. This means that as the concentration decreases, the rate of reaction also decreases. The mathematical representation involves a natural logarithm, allowing for the calculation of concentration or pressure over time using the equation: ln([A]₀/[A]) = kt, where [A]₀ is the initial concentration, [A] is the concentration at time t, k is the rate constant, and t is time.
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First-Order Reactions

Rate Constant (k)

The rate constant (k) is a proportionality factor in the rate law of a chemical reaction, reflecting the speed of the reaction at a given temperature. For first-order reactions, k has units of s⁻¹, indicating how quickly the reactant is consumed. The value of k can vary with temperature, and it is crucial for calculating the concentration or pressure of reactants over time in kinetic studies.
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Equilibrium Constant K

Partial Pressure

Partial pressure is the pressure exerted by a single component of a gas mixture. In the context of a reaction, it helps in understanding how the concentration of a reactant changes over time. For gases, the partial pressure can be related to the number of moles of the gas and the volume of the container, following Dalton's Law of Partial Pressures, which states that the total pressure is the sum of the partial pressures of each gas in the mixture.
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Domanda del libro di testo

The first-order rate constant for the decomposition of N2O5, 2 N2O5(g) → 4 NO2(g) + O2(g), at 70°C is 6.82×10-3 s-1. Suppose we start with 0.0250 mol of N2O5(g) in a volume of 2.0 L. (c) What is the half-life of N2O5 at 70°C?

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Domanda del libro di testo

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Domanda del libro di testo

As described in Exercise 14.41, the decomposition of sulfuryl chloride (SO2Cl2) is a first-order process. The rate constant for the decomposition at 660 K is 4.5 × 10-2 s-1. (b) At what time will the partial pressure of SO2Cl2 decline to one-tenth its initial value?

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(a) The gas-phase decomposition of SO2Cl2, SO2Cl2(g) → SO2(g) + Cl2(g), is first order in SO2Cl2. At 600 K the half-life for this process is 2.3 × 105 s. What is the rate constant at this temperature?

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(b) At 320°C the rate constant is 2.2 × 10-5 s-1. What is the half-life at this temperature?

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