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Presented By Presented By Matt Moberly Matt Moberly Vibrational-Rotational Spectra of HCl and DCl Lab Partner: Lab Partner: Mike Stratton Mike Stratton
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Vibrational-Rotational Spectra of HCl and DClpchemlab/documents/PowerPointpresentation... · Vibrational-Rotational Spectra of HCl and DCl Lab Partner: Mike Stratton. ... Vibration

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Page 1: Vibrational-Rotational Spectra of HCl and DClpchemlab/documents/PowerPointpresentation... · Vibrational-Rotational Spectra of HCl and DCl Lab Partner: Mike Stratton. ... Vibration

Presented ByPresented By

Matt MoberlyMatt Moberly

Vibrational-Rotational Spectra of HCl and DCl

Lab Partner:Lab Partner:

Mike StrattonMike Stratton

Page 2: Vibrational-Rotational Spectra of HCl and DClpchemlab/documents/PowerPointpresentation... · Vibrational-Rotational Spectra of HCl and DCl Lab Partner: Mike Stratton. ... Vibration

Presentation OutlineI. Introduction

a. Purposeb. Theoryc. Equations

II. Experimental MethodIII. Results

a. Spectra b. Calculations and Error Analysisc. Theoretical Calculations

IV. ConclusionV. References

Page 3: Vibrational-Rotational Spectra of HCl and DClpchemlab/documents/PowerPointpresentation... · Vibrational-Rotational Spectra of HCl and DCl Lab Partner: Mike Stratton. ... Vibration

Purpose:

• Moment of Inertia, Ie

• Internuclear Separation, re

• Force Constant, k• Evidence of the Isotope Effect

Use the infrared vibrational spectrum of HCl and DCl to obtain the following:

Introduction

Page 4: Vibrational-Rotational Spectra of HCl and DClpchemlab/documents/PowerPointpresentation... · Vibrational-Rotational Spectra of HCl and DCl Lab Partner: Mike Stratton. ... Vibration

Theory:

Simplest rotating diatomic model is the rigid rotor or “dumb-bell” model which can be pictured as two masses joined by a rigid, weightless rod and described by1:

Simplest vibrating diatomic model is a harmonic oscillator described by1:

)()( 21+= υυ hvE

)1(8

)(2

2

+= JJI

hJEπ

Page 5: Vibrational-Rotational Spectra of HCl and DClpchemlab/documents/PowerPointpresentation... · Vibrational-Rotational Spectra of HCl and DCl Lab Partner: Mike Stratton. ... Vibration

)1()()1()1()(~)(~),(21222

21

21 ++−+−+++−+= JJJJDJJBxvv

hcJE

eeeeee υαυυυ

This more complete energy expression contains both rotational and vibrational parts as well as a final coupling portion1

Constant CouplingConstant RotationalDConstant RotationalB

Constantity AnharmonicxFrequency lVibrationav

e

e

e

e

e

−−−−−

α

~

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Infrared absorption or emission can only occur at allowed transition levels

• Vibrational: ν”= 0, ν’= 1• Rotational: ΔJ = ± 1

• R and P branches• Spacing between peaks

Isotope Effect: mass difference between atoms effects the vibrational and rotational energies

• Splitting of peaks (35Cl and 37Cl)• Compaction of heavier isotope spectrum

• Shift to higher wavelengths, λ

Page 7: Vibrational-Rotational Spectra of HCl and DClpchemlab/documents/PowerPointpresentation... · Vibrational-Rotational Spectra of HCl and DCl Lab Partner: Mike Stratton. ... Vibration

Equations:Linear Regression Equation2:

320 4)22(~)(~

)1(

xDxxBvxv eeee −−−+= αα Frequency Forbiddenv =0

~

Rotational Constant3

cIhB

e

e28

)2(

π= ⇒

cBhI

e

e28

)3(

π=

Rotational Constant is rearranged solving forthe Moment of Inertia, Ie

• h, Planks Constant: 6.626076x10-34 J s• c, Velocity of light (in vacuum): 2.99792485 m s-1

Moment of Inertia, Ie1

2

)4(

rIe μ= ⇒μ

AeNIr =

)5( Moment of Inertia is rearranged solving for Internuclear Separation, r

• μ, reduced mass: mA mB /(mA +mB )• NA , Avogadro’s Constant

Page 8: Vibrational-Rotational Spectra of HCl and DClpchemlab/documents/PowerPointpresentation... · Vibrational-Rotational Spectra of HCl and DCl Lab Partner: Mike Stratton. ... Vibration

eeexvvv ~2~~

0

)6(

−= *

21

*

*

0

~2~~

)7(

μμ

μμ xvvv

ee−⎟⎟

⎞⎜⎜⎝

⎛=

Frequency of Forbidden Transmission1

Frequency equations are used to solve for the two unknowns

Constantity Anharmonic xe →

Frequency Equation3

21

21~

)8(

⎟⎟⎠

⎞⎜⎜⎝

⎛=

μπA

e

kNc

v 1222 ~4)9(

−= Ae Nvck μπ

Frequency equation is rearranged solving for the Force Constant, k

Page 9: Vibrational-Rotational Spectra of HCl and DClpchemlab/documents/PowerPointpresentation... · Vibrational-Rotational Spectra of HCl and DCl Lab Partner: Mike Stratton. ... Vibration

Experimental Method

Page 10: Vibrational-Rotational Spectra of HCl and DClpchemlab/documents/PowerPointpresentation... · Vibrational-Rotational Spectra of HCl and DCl Lab Partner: Mike Stratton. ... Vibration

Apparatus• Acetone/Dry Ice bath in first trap condense and trap any D2 O/ H2 O or D3 PO4/ H3 PO4

• Liquid N2 bath to protect the pump from formed gasses

Changes to Apparatus4

• Water condenser was not included• Three-way valve was placed at position A • Manometer was placed between first Acetone/Dry

Ice bath and three-way valve

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Preparation of HCl and DCl4

Reaction: 2 PCl5 + 8 D2 O ⌫ 10DCl + 2 D3 PO4– Since D2 O is not pure both HCl and DCl are formed

• Approx. 2g of PCl5 (green) was placed in flask F– Initial reaction used less than 2 grams PCl5 which did not produce sufficient amounts of HCl/DCl gas

• The system was evacuated for approx. 15 minutes• 1.0 ml D2 O was added to flask F with the I.R. cell

opened which produced a violent reaction

Gas Collection• Once reaction was complete, the I.R. cell was

closed, detached, and placed in the infrared spectrophotometer for analysis

Page 12: Vibrational-Rotational Spectra of HCl and DClpchemlab/documents/PowerPointpresentation... · Vibrational-Rotational Spectra of HCl and DCl Lab Partner: Mike Stratton. ... Vibration

HCl and DCl Spectrum

Page 13: Vibrational-Rotational Spectra of HCl and DClpchemlab/documents/PowerPointpresentation... · Vibrational-Rotational Spectra of HCl and DCl Lab Partner: Mike Stratton. ... Vibration

Calculations and Error Analysis:Equation (1): HCl

14

1

1

10

10x5422.6558.10

2954.023.2779~

−−

====

cmDcmBcmcmv

e

e

Herzberg vol. 2 Relative Error

NADB

v

e

e

e

→→→→

%306.0%141.2%682.3~

0

α

NADcmBcmcmv

e

e

e

====

1

1

10

591.103019.0

10.2885~

α

14

1

1

10

10x57.1474.51064.0

65.2086~

−−

====

cmDcmB

cmcmv

e

e

NADcmB

cmcmv

e

e

e

====

1

1

10

445.51118.0

10.2091~

α

NADB

v

e

e

e

→→→→

%537.0%847.4%198.0~

0

α

Equation (1): DCl Herzberg vol. 2 Relative Error

Page 14: Vibrational-Rotational Spectra of HCl and DClpchemlab/documents/PowerPointpresentation... · Vibrational-Rotational Spectra of HCl and DCl Lab Partner: Mike Stratton. ... Vibration

gmcmI 24010x651.2 −=

Equation (3): HCl Herzberg vol. 2 Relative Error

gmcmI 24010x643.2 −= %307.0

gmcmI 24010x114.5 −=

Equation (3): DCl Herzberg vol. 2 Relative Error

gmcmI 24010x141.5 −= %534.0

Equation (5): HCl

cmre810x277.1 −=

Herzberg vol. 2

cmre810x2746.1 −=

Relative Error

%162.0

Equation (5): DCl

cmre810x272.1 −=

Herzberg vol. 2

cmre810x2749.1 −=

Relative Error

%258.0

Page 15: Vibrational-Rotational Spectra of HCl and DClpchemlab/documents/PowerPointpresentation... · Vibrational-Rotational Spectra of HCl and DCl Lab Partner: Mike Stratton. ... Vibration

Equation (6&7): Equil. Vibrating Frequency for HCl and anharmonicity c o n s t a n t

071.0198.230~

62.3239~1

1

==

=−

e

ee

e

xcmxv

cmv

Equation (9): HCl

dynecmk 1510x057.6 −=

dynecmklit1510x159.5 −=

%414.17=Δ

Theoretical Calculations5:

HF Results

1

1

8

977.952.3372~10313.1

===

cmBcm v

cm xr

e

e

e

MP Results

1

1

8

502.1015.3049~10280.1

===

cmBcm v

cm xr

e

e

e

Page 16: Vibrational-Rotational Spectra of HCl and DClpchemlab/documents/PowerPointpresentation... · Vibrational-Rotational Spectra of HCl and DCl Lab Partner: Mike Stratton. ... Vibration

Potential Energy as a Function of Internuclear separation, re

Page 17: Vibrational-Rotational Spectra of HCl and DClpchemlab/documents/PowerPointpresentation... · Vibrational-Rotational Spectra of HCl and DCl Lab Partner: Mike Stratton. ... Vibration

Potential Curve of HCl using Hartree-Fock (HF) and Moeller-Plessett (MP) Theories

HCL Potential Cuve

-460.4

-460.2

-460

-459.8

-459.6

-459.4

-459.2

-4590 1 2 3 4 5 6

Internuclear Separation, 10-10 m

Ener

gy, J

HF MP

Page 18: Vibrational-Rotational Spectra of HCl and DClpchemlab/documents/PowerPointpresentation... · Vibrational-Rotational Spectra of HCl and DCl Lab Partner: Mike Stratton. ... Vibration

Conclusion

•Largest Source of Error likely from Spectra Readings– Force Constant– Coupling Constant

– Reduce systematic error by “zooming” in– Use a new I.R. Cell

•Internuclear Separation fluctuates with Moment of Inertia, Ie , obtained is an average

•xe shows anharmonicity of HCl molecule is small•Isotope Effect observed for 35Cl and 37Cl

Page 19: Vibrational-Rotational Spectra of HCl and DClpchemlab/documents/PowerPointpresentation... · Vibrational-Rotational Spectra of HCl and DCl Lab Partner: Mike Stratton. ... Vibration

References1 Shoemaker et. al., Expt. In Physical Chemistry, 6th ed. pg. 397.

2 Poshusta, R.D HCl Spectrum Analysis, Mathcad 20 Dec. 1997.

3 Herzberg, G. Molecular Spectra and Molecular Structure I: Spectra of Diatomic Molecules. 2d ed., chp.III. Van Nostrand, Princeton , N.J. (1950).

4 Henscheid, Leonard. Supplement to Expt. 38: Rotation- Vibration Spectrum of HCl and DCl. Chemistry 334 Handout, Washington State University (1998).

5 Poshusta, R.D. Expt.38B: Modeling the Spectrum of HCl with Ab Initio Quantum Chemistry. Chemistry 334 Handout, Washington State University (1998).