The reaction SO2Cl2(g) → SO2(g) + Cl2(g) is first order in SO2Cl2. Using the following kinetic data, determine the magnitude and units of the first-order rate constant: Time (s) Pressure SO2Cl2 (atm) 0 1.000 2500 0.947 5000 0.895 7500 0.848 10,000 0.803

Name: Chemistry: The Central Science
Author: Brown
ISBN: 9780134414232

검증된 단계별 안내

Step 1: Understand that for a first-order reaction, the rate law is expressed as \( \text{Rate} = k [\text{SO}_2\text{Cl}_2] \), where \( k \) is the rate constant.

Step 2: Use the integrated rate law for a first-order reaction, which is \( \ln [\text{SO}_2\text{Cl}_2]_t = -kt + \ln [\text{SO}_2\text{Cl}_2]_0 \), where \([\text{SO}_2\text{Cl}_2]_t\) is the concentration at time \( t \), and \([\text{SO}_2\text{Cl}_2]_0\) is the initial concentration.

Step 3: Rearrange the integrated rate law to solve for \( k \): \( k = \frac{\ln [\text{SO}_2\text{Cl}_2]_0 - \ln [\text{SO}_2\text{Cl}_2]_t}{t} \).

Step 4: Substitute the given pressures (which are proportional to concentrations) and times into the equation for \( k \). For example, use the data at \( t = 2500 \) s: \( k = \frac{\ln(1.000) - \ln(0.947)}{2500} \).

Step 5: Calculate \( k \) for each time interval and average the values to find the consistent rate constant. The units of \( k \) for a first-order reaction are \( \text{s}^{-1} \).

주요 개념

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First-Order Reactions

First-order reactions are chemical reactions where the rate is directly proportional to the concentration of one reactant. In this case, the rate of the reaction SO2Cl2(g) → SO2(g) + Cl2(g) depends solely on the concentration of SO2Cl2. The rate law can be expressed as rate = k[SO2Cl2], where k is the rate constant. This means that as the concentration of SO2Cl2 decreases, the rate of the reaction also decreases.

Rate Constant (k)

The rate constant (k) is a proportionality factor in the rate law that provides insight into the speed of a reaction. For first-order reactions, the units of k are typically expressed in s⁻¹, indicating the rate of change of concentration over time. The magnitude of k can be determined from experimental data, reflecting how quickly the reactant is consumed. A larger k value signifies a faster reaction.

Integrated Rate Law

The integrated rate law for a first-order reaction relates the concentration of the reactant to time. It is expressed as ln([A]₀/[A]) = kt, where [A]₀ is the initial concentration and [A] is the concentration at time t. This equation allows for the calculation of the rate constant k by plotting ln([A]) versus time, yielding a straight line with a slope of -k. This relationship is crucial for analyzing the provided kinetic data.