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At 300 K which speed has the greatest fraction of molecules per unit speed interval?  b. At 1000 K which speed has the greatest fraction of molecules per unit speed interval?

At 300 K which speed has the greatest fraction of molecules per unit speed interval?  b. At 1000 K which speed has the greatest fraction of molecules per unit speed interval?

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
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a. At 300 K which speed has the greatest fraction of molecules per unit speed interval? 

b. At 1000 K which speed has the greatest fraction of molecules per unit speed interval?

8 ChemActivity G1 Gases (I) Model 5: The Maxwell Distribution of Molecular Speeds. Not all gas particles within a collection of particles (at constant temperature) have the same velocity-some particles are moving slowly, others are moving rapidly. The problem of how to determine the most probable distribution of speeds was solved by J. Clerk Maxwell. Starting with the following assumptions, The probability of a molecular state depends only on the energy of the molecular state. The same probability distribution applies for all kinds of molecules. Maxwell's equation for the distribution of speeds is the following: 4nv2( m3/2 e-mv2/2kT 2TKT fraction of molecules per unit speed interval = (7) where k (Boltzmann's constant) = 1.38066 x 10-23 JK-4 %3D Table 1. The Speeds of Gaseous N2 Molecules. fraction of molecules fraction of molecules molecule per unit speed interval per unit speed interval at 300 K (s/m) speed of (m/s) at 1000 K (s/m) 0. 25 1.87 x 10-5 7.40 x 10-5 2.84 x 10-4 9.60 x 10-4 1.63 x 10-3 1.96 x 10-3 1.84 x 10-3 1.43 x 10-3 9.39 x 10-4 5.28 x 10-4 1.09 x 10-4 4.07 x 10-5 1.33 x 10-5 3.84 x 10-6 9.77 x 10-7 2.20 x 10-7 4.39 x 10-8 7.77 x 10-9 1.22 x 10-9 1.70 x 10-10 2.11 x 10-11 3.08 x 10-6 1.23 x 10-5 4.85 x 10-5 1.85 x 10-4 3.82 x 10-4 6.03 x 10-4 8.10 x 10-4 9.69 x 10-4 1.06 x 10-3 1.07 x 10-3 9.15 x 10-4 7.78 x 10-4 6.28 x 10-4 4.84 x 10-4 3.56 x 10-4 2.51 x 10-4 1.69 x 10-4 1.10 x 10-4 6.81 x 10-5 4.07 x 10-5 2.34 x 10-5 50 100 200 300 400 500 600 700 800 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
Transcribed Image Text:8 ChemActivity G1 Gases (I) Model 5: The Maxwell Distribution of Molecular Speeds. Not all gas particles within a collection of particles (at constant temperature) have the same velocity-some particles are moving slowly, others are moving rapidly. The problem of how to determine the most probable distribution of speeds was solved by J. Clerk Maxwell. Starting with the following assumptions, The probability of a molecular state depends only on the energy of the molecular state. The same probability distribution applies for all kinds of molecules. Maxwell's equation for the distribution of speeds is the following: 4nv2( m3/2 e-mv2/2kT 2TKT fraction of molecules per unit speed interval = (7) where k (Boltzmann's constant) = 1.38066 x 10-23 JK-4 %3D Table 1. The Speeds of Gaseous N2 Molecules. fraction of molecules fraction of molecules molecule per unit speed interval per unit speed interval at 300 K (s/m) speed of (m/s) at 1000 K (s/m) 0. 25 1.87 x 10-5 7.40 x 10-5 2.84 x 10-4 9.60 x 10-4 1.63 x 10-3 1.96 x 10-3 1.84 x 10-3 1.43 x 10-3 9.39 x 10-4 5.28 x 10-4 1.09 x 10-4 4.07 x 10-5 1.33 x 10-5 3.84 x 10-6 9.77 x 10-7 2.20 x 10-7 4.39 x 10-8 7.77 x 10-9 1.22 x 10-9 1.70 x 10-10 2.11 x 10-11 3.08 x 10-6 1.23 x 10-5 4.85 x 10-5 1.85 x 10-4 3.82 x 10-4 6.03 x 10-4 8.10 x 10-4 9.69 x 10-4 1.06 x 10-3 1.07 x 10-3 9.15 x 10-4 7.78 x 10-4 6.28 x 10-4 4.84 x 10-4 3.56 x 10-4 2.51 x 10-4 1.69 x 10-4 1.10 x 10-4 6.81 x 10-5 4.07 x 10-5 2.34 x 10-5 50 100 200 300 400 500 600 700 800 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
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