Full set of Notes with Fill-Ins - San Jose State University

Chem 155 Unit 15 276 of 31615. Calculate the ratio of HCl molecules in the first vibrationalexcited state at 25°C relative to the ground state. The IRabsorption appears at 2885 cm -1 .N1 g1kTa. The Boltzmann equation is:N=g 0⋅ e where g00 and g 1are the degeneracies of the states 0 and 1 and for HCl 35may be considered equal, and k is Boltzmann’s constant,T is absolutetemperatureand ΔE is theenergy ofstate 1relative to 0.k 1.38⋅10 − 23 J:= ⋅K−ΔET :=298⋅KkT ⋅ = 4.112× 10 − 21 J2885⋅ cm − 1 ⋅6.626⋅10 − 34 ⋅J⋅s⋅3.0010 10 cm⋅ ⋅ = 5.735× 10 − 20 JsΔE 2885⋅ cm − 1 ⋅6.626⋅10 − 34 ⋅J⋅s⋅3.00⋅10 10 cm:=⋅sN1N0− ΔEkTe− ΔEkT ⋅e=8.784×10 − 7b. Assumingthat the bondstrengths areequal,calculate thevibrationalfrequencythat youexpect for theisotope DCl 35 .1ν VIB ⋅2⋅π1⋅ν DCl 2⋅πν HCl1⋅2⋅πkμk DClμ DClk HClμ HClsinceμk HClm 1 ⋅m 2m 1 + m 2k DClν DClν HClμ HClμ DCl35⋅1μ HCl :=35 + 135⋅2μ DCl :=35 + 2μ HCl= 0.717μ DClν DCl := 2885⋅0.717ν DCl = 2069Page 276 of 316