(a) Interpretation: The ratio of the populations of two energy states whose energies differ by 500 J at ( a ) 200 K and the trend is to be calculated. Concept introduction: From kinetic theory of gases, we know that the average kinetic energy of a ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as, Probability = e –(ΔE/RT)

Question

9 7 8 C 9 8 200 190 B 5 A -197.72 9 8 7 15 4 3 0: ང་ 200 190 180 147.52 134.98 170 160 150 140 130 120 110 100 90 90 OH 10 4 3 1 2 -143.04 140. 180 170 160 150 140 130 120 110 100 90 CI 3 5 1 2 141.89 140.07 200 190 180 170 160 150 140 130 120 110 100 ៖- 90 129. 126.25 80 70 60 -60 50 40 10 125.19 -129.21 80 70 3.0 20 20 -8 60 50 10 ppm -20 40 128.31 80 80 70 60 50 40 40 -70.27 3.0 20 10 ppm 00˚0-- 77.17 30 20 20 -45.36 10 ppm -0.00 26.48 22.32 ―30.10 ―-0.00

Answer 1

Question

Chapter 1, Problem 1.73E

Interpretation Introduction

(a)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 500 J at (a) 200 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of a ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e ^–(ΔE/RT)

Interpretation Introduction

(b)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 500 J at (b) 500 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of a ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e ^–(ΔE/RT)

Interpretation Introduction

(c)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 500 J at (c) 200 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of a ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e ^–(ΔE/RT)

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9 7 8 C 9 8 200 190 B 5 A -197.72 9 8 7 15 4 3 0: ང་ 200 190 180 147.52 134.98 170 160 150 140 130 120 110 100 90 90 OH 10 4 3 1 2 -143.04 140. 180 170 160 150 140 130 120 110 100 90 CI 3 5 1 2 141.89 140.07 200 190 180 170 160 150 140 130 120 110 100 ៖- 90 129. 126.25 80 70 60 -60 50 40 10 125.19 -129.21 80 70 3.0 20 20 -8 60 50 10 ppm -20 40 128.31 80 80 70 60 50 40 40 -70.27 3.0 20 10 ppm 00˚0-- 77.17 30 20 20 -45.36 10 ppm -0.00 26.48 22.32 ―30.10 ―-0.00

Assign all the carbons

C 5 4 3 CI 2 the Righ B A 5 4 3 The Lich. OH 10 4 5 3 1 LOOP- -147.52 T 77.17 -45.36 200 190 180 170 160 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 ppm B -126.25 77.03 200 190 180 170 160 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 ppm 200 190 180 170 160 150 140 130 120 110 100 90 80 TO LL <-50.00 70 60 50 40 30 20 10 ppm 45.06 30.18 -26.45 22.36 --0.00 45.07 7.5 1.93 2.05 -30.24 -22.36 C A 7 8 5 ° 4 3 7.5 7.0 6.5 6.0 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 ppm 9 8 5 4 3 ཡི་ OH 10 2 7.5 7.0 6.5 6.0 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 5 4 3 2 that th 7 I 7.0 6.5 6.0 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 115 2.21 4.00 1.0 ppm 6.96 2.76 5.01 1.0 ppm 6.30 1.00

Answer 2

Question

Chapter 1, Problem 1.73E

Interpretation Introduction

(a)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 500 J at (a) 200 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of a ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e ^–(ΔE/RT)

Interpretation Introduction

(b)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 500 J at (b) 500 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of a ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e ^–(ΔE/RT)

Interpretation Introduction

(c)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 500 J at (c) 200 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of a ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e ^–(ΔE/RT)

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Answer 3

Question

Chapter 1, Problem 1.73E

Interpretation Introduction

(a)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 500 J at (a) 200 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of a ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e ^–(ΔE/RT)

Interpretation Introduction

(b)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 500 J at (b) 500 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of a ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e ^–(ΔE/RT)

Interpretation Introduction

(c)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 500 J at (c) 200 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of a ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e ^–(ΔE/RT)

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Answer 4

Question

Chapter 1, Problem 1.73E

Interpretation Introduction

(a)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 500 J at (a) 200 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of a ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e ^–(ΔE/RT)

Interpretation Introduction

(b)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 500 J at (b) 500 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of a ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e ^–(ΔE/RT)

Interpretation Introduction

(c)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 500 J at (c) 200 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of a ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e ^–(ΔE/RT)

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Answer 5

Chapter 1, Problem 1.73E

Interpretation Introduction

(a)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 500 J at (a) 200 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of a ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e ^–(ΔE/RT)

Interpretation Introduction

(b)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 500 J at (b) 500 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of a ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e ^–(ΔE/RT)

Interpretation Introduction

(c)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 500 J at (c) 200 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of a ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e ^–(ΔE/RT)

Answer 6

Chapter 1, Problem 1.73E

Interpretation Introduction

(a)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 500 J at (a) 200 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of a ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e ^–(ΔE/RT)

Answer 7

Chapter 1, Problem 1.73E

Interpretation Introduction

(a)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 500 J at (a) 200 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of a ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e ^–(ΔE/RT)

Answer 8

Interpretation Introduction

(b)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 500 J at (b) 500 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of a ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e ^–(ΔE/RT)

Answer 9

Interpretation Introduction

(b)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 500 J at (b) 500 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of a ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e ^–(ΔE/RT)

Answer 10

Interpretation Introduction

(c)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 500 J at (c) 200 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of a ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e ^–(ΔE/RT)

Answer 11

Interpretation Introduction

(c)

Interpretation:

The ratio of the populations of two energy states whose energies differ by 500 J at (c) 200 K and the trend is to be calculated.

Concept introduction:

From kinetic theory of gases, we know that the average kinetic energy of a ideal gas molecule is given by ½ kT for each degree of translation freedom. In this equation k is given as Boltzmann constant and T is given as absolute temperature (in K). Boltzmann effectively utilized this concept to derive a relationship as the natural logarithm of the ratio of the number of particles in two energy states is directly proportional to the negative of their energy separation. Thus, the Boltzmann distribution law is given as,

Probability = e ^–(ΔE/RT)

Answer 12

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