Ch.14 - Chemical Kinetics

Brown - Chemistry: The Central Science 14th Edition

Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232당신이 사용하는 게 아니라요?교과서 변경

Brown 14th Edition

Ch.14 - Chemical Kinetics

문제 101

14장, 문제 101

The rate of a first-order reaction is followed by spectroscopy, monitoring the absorbance of a colored reactant at 520 nm. The reaction occurs in a 1.00-cm sample cell, and the only colored species in the reaction has an extinction coefficient of 5.60 * 10^3 M^-1 cm^-1 at 520 nm. If the absorbance falls to 0.250 at 30.0 min, calculate the rate constant in units of s^-1.

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

검증된 단계별 안내

Start by using Beer's Law to relate absorbance (A) to concentration (C) of the colored species. Beer's Law is given by:

A = ε C l

, where

ε

is the extinction coefficient,

C

is the concentration, and

l

is the path length of the sample cell.

Given that the absorbance (A) is 0.250, the extinction coefficient (

ε

) is

5.60 \times 10^{3}

M^-1 cm^-1, and the path length (

l

) is 1.00 cm, solve for the concentration (

C

) using the equation:

C = \frac{A}{ε l}

For a first-order reaction, the rate constant (

k

) can be determined using the integrated rate law:

A = A o \times e^{- k t}

, where

A

is the absorbance at time

t

A o

is the initial absorbance, and

k

is the rate constant.

Rearrange the integrated rate law to solve for the rate constant (

k

k = \frac{- \ln (\frac{A}{A})}{t}

. Substitute the values for

A

A o

, and

t

(converted to seconds) into the equation.

Calculate the rate constant (

k

) using the rearranged equation. Ensure that the time is converted from minutes to seconds by multiplying by 60, as the rate constant is required in units of s^-1.

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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. This means that as the concentration of the reactant decreases, the rate of the reaction also decreases. The rate law for a first-order reaction can be expressed as rate = k[A], where k is the rate constant and [A] is the concentration of the reactant.

Beer-Lambert Law

The Beer-Lambert Law relates the absorbance of light to the properties of the material through which the light is traveling. It states that absorbance (A) is equal to the product of the extinction coefficient (ε), the concentration (c) of the absorbing species, and the path length (l) of the sample: A = εcl. This law is crucial for quantifying the concentration of colored species in solution using spectroscopy.

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 rate constant has units of s^-1, indicating the reaction's dependence on time. The value of k can be determined from experimental data, such as changes in absorbance over time, allowing for the calculation of reaction kinetics.