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?

검증된 단계별 안내

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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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.

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.

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.

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?

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

First-Order Reactions

Rate Constant (k)

Partial Pressure