Atkins' Physical Chemistry
Atkins' Physical Chemistry
11th Edition
ISBN: 9780198769866
Author: ATKINS, P. W. (peter William), De Paula, Julio, Keeler, JAMES
Publisher: Oxford University Press
Question
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Chapter 11, Problem 11A.7P

(a)

Interpretation Introduction

Interpretation:

The integrated absorption coefficient of CH3I has to be evaluated.

Concept introduction:

The maximum value of the molar absorption coefficient indicates the intensity of a transition.  However, as the absorption bands are spread over a range of wavenumbers, the absorption coefficient at a single wavenumber might not give a true indication of the intensity of transition.  The integrated absorption coefficient is the sum of the absorption coefficients over the entire band and corresponds to the area under the plot of the molar absorption coefficient against wavenumber.

(a)

Expert Solution
Check Mark

Answer to Problem 11A.7P

The integrated absorption coefficient of CH3I is 2.42×105dm3mol1cm2_.

Explanation of Solution

The integrated absorption coefficient is calculated by the formula given below.

    A=12εmaxΔν˜        (1)

Where,

  • A is the integrated absorption coefficient.
  • εmax is the maximum molar extinction coefficient.
  • Δν˜ is the wavenumber.

The Δν˜ is given by the expression below.

    Δν˜=ν˜fν˜i

Where,

  • ν˜f is the final wavenumber.
  • ν˜i is the initial wavenumber.

Therefore, equation (1) can be written as shown below.

    A=12εmax(ν˜fν˜i)        (2)

The value of εmax is 150dm3mol1cm1.

The value of ν˜f is 34483cm1.

The value of ν˜i is 31250cm1.

Substitute the value of εmax, ν˜f, and ν˜i in equation (2).

    A=12×150dm3mol1cm1×(34483cm131250cm1)=12×150dm3mol1cm1×3233cm1=2.42×105dm3mol1cm2_

Therefore, the integrated absorption coefficient is 2.42×105dm3mol1cm2_.

(b)

Interpretation Introduction

Interpretation:

The absorbance expected at the mid-point of the absorption lineshape in a sample cell of length 12.0cm when 1% of the CH3I units exist as dimers has to be calculated.has to be evaluated.

Concept introduction:

The Beer-lambert law states that the intensity of light absorbed by a solution is directly proportional to the concentration of the solution and the path length of that the light has to travel in the solution.  The mathematical expression for Beer-Lambert law is given below.

    A=εcL

(b)

Expert Solution
Check Mark

Answer to Problem 11A.7P

The absorbance expected at the mid-point of the absorption lineshape in a sample cell of length 12.0cm is 0.1836_.

Explanation of Solution

The concentration of CH3I is calculated by the formula given below.

    [CH3I]total=pRT        (3)

Where,

  • [CH3I]total is the concentration of CH3I.
  • p is the pressure.
  • R is the gas constant. (62.364Torrdm3mol1K1)
  • T is the temperature.

The value of p is 2.4Torr.

The value of T is 373K.

Substitute the value of p, R, and T in equation (3).

    [CH3I]total=2.4Torr62.364Torrdm3mol1K1×373K=2.4Torr23261.772Torrdm3mol1=1.03×104moldm3

About 1% of the CH3I units exist as dimmers.

Therefore, the percentage of monomers is 99%.

Therefore, the concentration of CH3I units that exist as monomers is calculated below.

    [CH3I]monomer=99100×1.03×104moldm3=1.02×104moldm3

The mathematical form of Beer-Lambert law is given below.

  A=εcL        (4)

Where,

  • A is the absorbance.
  • ε is the molar extinction coefficient.
  • L is the length.
  • c is the concentration.

The value of ε is 150dm3mol1cm1.

The value of L is 12.0cm.

The value of c is 1.016×104moldm3.

Substitute the value of ε, L, and c in equation (4).

    A=150dm3mol1cm1×1.02×104moldm3×12.0cm=1836×104=0.1836_

Therefore, the absorbance expected at the mid-point of the absorption lineshape in a sample cell of length 12.0cm is 0.1836_.

(c)

Interpretation Introduction

Interpretation:.

The absorbance expected at the mid-point of the absorption lineshape in a sample cell of length 12.0cm when 18% of the CH3I units exist as dimers has to be calculated.  The molar absorption coefficient that would be inferred if dimerization is not considered has to be computed.

Concept introduction:

As mentioned in concept introduction in part (b).

(c)

Expert Solution
Check Mark

Answer to Problem 11A.7P

The absorbance expected at the mid-point of the absorption lineshape in a sample cell of length 12.0cm when 18% of the CH3I units exist as dimmers is 6.3_.  The molar absorption coefficient that would be inferred if dimerization is not considered is 0.122×10-3dm3mol1cm1_.

Explanation of Solution

The concentration of CH3I is calculated by the formula given below.

    [CH3I]total=pRT        (3)

Where,

  • [CH3I]total is the concentration of CH3I.
  • p is the pressure.
  • R is the gas constant. (62.364Torrdm3mol1K1)
  • T is the temperature.

The value of p is 100Torr.

The value of T is 373K.

Substitute the value of p, R, and T in equation (3).

    [CH3I]total=100Torr62.364Torrdm3mol1K1×373K=100Torr23261.772Torrdm3mol1=4.299×103moldm3

About 18% of the CH3I units exist as dimmers.

Therefore, the percentage of monomers is 82%.

Therefore, the concentration of CH3I units that exist as monomers is calculated below.

    [CH3I]monomer=82100×4.299×103moldm3=3.5×103moldm3

The mathematical form of Beer-Lambert law is given below.

  A=εcL        (4)

Where,

  • A is the absorbance.
  • ε is the molar extinction coefficient.
  • L is the length.
  • c is the concentration.

The value of ε is 150dm3mol1cm1.

The value of L is 12.0cm.

The value of c is 3.5×103moldm3.

Substitute the value of ε, L, and c in equation (4).

    A=150dm3mol1cm1×3.5×103moldm3×12.0cm=6300×103=6.3_

Therefore, the absorbance expected at the mid-point of the absorption lineshape in a sample cell of length 12.0cm is 6.3_.

The concentration, c, if dimerization is not considered is 4.299×103moldm3.

Substitute the value of A, L and c in equation (4).

    6.3=ε×4.299×103moldm3×12.0cmε=6.34.299×103moldm3×12.0cm=0.122×10-3dm3mol1cm1_

Therefore, the molar extinction coefficient is 0.122×10-3dm3mol1cm1_.

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Chapter 11 Solutions

Atkins' Physical Chemistry

Ch. 11 - Prob. 11E.2STCh. 11 - Prob. 11F.2STCh. 11 - Prob. 11A.1DQCh. 11 - Prob. 11A.2DQCh. 11 - Prob. 11A.3DQCh. 11 - Prob. 11A.1AECh. 11 - Prob. 11A.1BECh. 11 - Prob. 11A.2AECh. 11 - Prob. 11A.2BECh. 11 - Prob. 11A.3AECh. 11 - Prob. 11A.3BECh. 11 - Prob. 11A.4AECh. 11 - Prob. 11A.4BECh. 11 - Prob. 11A.5AECh. 11 - Prob. 11A.5BECh. 11 - Prob. 11A.6AECh. 11 - Prob. 11A.6BECh. 11 - Prob. 11A.7AECh. 11 - Prob. 11A.7BECh. 11 - Prob. 11A.8AECh. 11 - Prob. 11A.8BECh. 11 - Prob. 11A.9AECh. 11 - Prob. 11A.9BECh. 11 - Prob. 11A.10AECh. 11 - Prob. 11A.10BECh. 11 - Prob. 11A.11AECh. 11 - Prob. 11A.11BECh. 11 - Prob. 11A.12AECh. 11 - Prob. 11A.12BECh. 11 - Prob. 11A.1PCh. 11 - Prob. 11A.2PCh. 11 - Prob. 11A.3PCh. 11 - Prob. 11A.4PCh. 11 - Prob. 11A.5PCh. 11 - Prob. 11A.7PCh. 11 - Prob. 11A.8PCh. 11 - Prob. 11A.9PCh. 11 - Prob. 11A.11PCh. 11 - Prob. 11B.1DQCh. 11 - Prob. 11B.2DQCh. 11 - Prob. 11B.3DQCh. 11 - Prob. 11B.4DQCh. 11 - Prob. 11B.5DQCh. 11 - Prob. 11B.6DQCh. 11 - Prob. 11B.7DQCh. 11 - Prob. 11B.8DQCh. 11 - Prob. 11B.1AECh. 11 - Prob. 11B.1BECh. 11 - Prob. 11B.3AECh. 11 - Prob. 11B.3BECh. 11 - Prob. 11B.4BECh. 11 - Prob. 11B.5AECh. 11 - Prob. 11B.5BECh. 11 - Prob. 11B.6AECh. 11 - Prob. 11B.6BECh. 11 - Prob. 11B.7AECh. 11 - Prob. 11B.7BECh. 11 - Prob. 11B.8AECh. 11 - Prob. 11B.8BECh. 11 - Prob. 11B.9AECh. 11 - Prob. 11B.9BECh. 11 - Prob. 11B.10AECh. 11 - Prob. 11B.10BECh. 11 - Prob. 11B.11AECh. 11 - Prob. 11B.11BECh. 11 - Prob. 11B.12AECh. 11 - Prob. 11B.12BECh. 11 - Prob. 11B.13AECh. 11 - Prob. 11B.13BECh. 11 - Prob. 11B.14AECh. 11 - Prob. 11B.14BECh. 11 - Prob. 11B.1PCh. 11 - Prob. 11B.2PCh. 11 - Prob. 11B.3PCh. 11 - Prob. 11B.4PCh. 11 - Prob. 11B.5PCh. 11 - Prob. 11B.6PCh. 11 - Prob. 11B.7PCh. 11 - Prob. 11B.8PCh. 11 - Prob. 11B.9PCh. 11 - Prob. 11B.10PCh. 11 - Prob. 11B.11PCh. 11 - Prob. 11B.12PCh. 11 - Prob. 11B.13PCh. 11 - Prob. 11B.14PCh. 11 - Prob. 11C.1DQCh. 11 - Prob. 11C.2DQCh. 11 - Prob. 11C.3DQCh. 11 - Prob. 11C.4DQCh. 11 - Prob. 11C.1AECh. 11 - Prob. 11C.1BECh. 11 - Prob. 11C.2AECh. 11 - Prob. 11C.2BECh. 11 - Prob. 11C.3AECh. 11 - Prob. 11C.3BECh. 11 - Prob. 11C.4AECh. 11 - Prob. 11C.4BECh. 11 - Prob. 11C.5AECh. 11 - Prob. 11C.5BECh. 11 - Prob. 11C.6AECh. 11 - Prob. 11C.6BECh. 11 - Prob. 11C.7AECh. 11 - Prob. 11C.7BECh. 11 - Prob. 11C.8AECh. 11 - Prob. 11C.8BECh. 11 - Prob. 11C.2PCh. 11 - Prob. 11C.3PCh. 11 - Prob. 11C.4PCh. 11 - Prob. 11C.5PCh. 11 - Prob. 11C.6PCh. 11 - Prob. 11C.7PCh. 11 - Prob. 11C.8PCh. 11 - Prob. 11C.9PCh. 11 - Prob. 11C.10PCh. 11 - Prob. 11C.11PCh. 11 - Prob. 11C.12PCh. 11 - Prob. 11C.13PCh. 11 - Prob. 11C.15PCh. 11 - Prob. 11C.17PCh. 11 - Prob. 11C.18PCh. 11 - Prob. 11C.19PCh. 11 - Prob. 11D.1DQCh. 11 - Prob. 11D.2DQCh. 11 - Prob. 11D.3DQCh. 11 - Prob. 11D.1AECh. 11 - Prob. 11D.1BECh. 11 - Prob. 11D.2AECh. 11 - Prob. 11D.2BECh. 11 - Prob. 11D.3AECh. 11 - Prob. 11D.3BECh. 11 - Prob. 11D.4AECh. 11 - Prob. 11D.4BECh. 11 - Prob. 11D.5AECh. 11 - Prob. 11D.5BECh. 11 - Prob. 11D.6AECh. 11 - Prob. 11D.6BECh. 11 - Prob. 11D.7AECh. 11 - Prob. 11D.7BECh. 11 - Prob. 11D.2PCh. 11 - Prob. 11E.1DQCh. 11 - Prob. 11E.1AECh. 11 - Prob. 11E.1BECh. 11 - Prob. 11E.2AECh. 11 - Prob. 11E.2BECh. 11 - Prob. 11E.3AECh. 11 - Prob. 11E.3BECh. 11 - Prob. 11E.1PCh. 11 - Prob. 11E.2PCh. 11 - Prob. 11F.1DQCh. 11 - Prob. 11F.2DQCh. 11 - Prob. 11F.3DQCh. 11 - Prob. 11F.4DQCh. 11 - Prob. 11F.5DQCh. 11 - Prob. 11F.6DQCh. 11 - Prob. 11F.1AECh. 11 - Prob. 11F.1BECh. 11 - Prob. 11F.2AECh. 11 - Prob. 11F.2BECh. 11 - Prob. 11F.3AECh. 11 - Prob. 11F.3BECh. 11 - Prob. 11F.4AECh. 11 - Prob. 11F.4BECh. 11 - Prob. 11F.5AECh. 11 - Prob. 11F.5BECh. 11 - Prob. 11F.6AECh. 11 - Prob. 11F.6BECh. 11 - Prob. 11F.7AECh. 11 - Prob. 11F.7BECh. 11 - Prob. 11F.8AECh. 11 - Prob. 11F.8BECh. 11 - Prob. 11F.9AECh. 11 - Prob. 11F.9BECh. 11 - Prob. 11F.10AECh. 11 - Prob. 11F.10BECh. 11 - Prob. 11F.11AECh. 11 - Prob. 11F.11BECh. 11 - Prob. 11F.12AECh. 11 - Prob. 11F.12BECh. 11 - Prob. 11F.13AECh. 11 - Prob. 11F.13BECh. 11 - Prob. 11F.1PCh. 11 - Prob. 11F.2PCh. 11 - Prob. 11F.3PCh. 11 - Prob. 11F.4PCh. 11 - Prob. 11F.5PCh. 11 - Prob. 11F.6PCh. 11 - Prob. 11F.7PCh. 11 - Prob. 11F.8PCh. 11 - Prob. 11F.9PCh. 11 - Prob. 11F.10PCh. 11 - Prob. 11F.11PCh. 11 - Prob. 11F.12PCh. 11 - Prob. 11G.1DQCh. 11 - Prob. 11G.2DQCh. 11 - Prob. 11G.3DQCh. 11 - Prob. 11G.4DQCh. 11 - Prob. 11G.5DQCh. 11 - Prob. 11G.1AECh. 11 - Prob. 11G.1BECh. 11 - Prob. 11G.2AECh. 11 - Prob. 11G.2BECh. 11 - Prob. 11G.1PCh. 11 - Prob. 11G.2PCh. 11 - Prob. 11G.3PCh. 11 - Prob. 11G.4PCh. 11 - Prob. 11G.5PCh. 11 - Prob. 11G.6PCh. 11 - Prob. 11.1IACh. 11 - Prob. 11.5IACh. 11 - Prob. 11.8IA
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