Vibrational-Rotational Spectra of HCl and DClpchemlab/documents/PowerPoint...Vibrational-Rotational...
Transcript of Vibrational-Rotational Spectra of HCl and DClpchemlab/documents/PowerPoint...Vibrational-Rotational...
Presented ByPresented By
Matt MoberlyMatt Moberly
Vibrational-Rotational Spectra of HCl and DCl
Lab Partner:Lab Partner:
Mike StrattonMike Stratton
Presentation OutlineI. Introduction
a. Purposeb. Theoryc. Equations
II. Experimental MethodIII. Results
a. Spectra b. Calculations and Error Analysisc. Theoretical Calculations
IV. ConclusionV. References
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
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
)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
~
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
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
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
Experimental Method
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
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
HCl and DCl Spectrum
Calculations and Error Analysis:Equation (1): HCl
14
1
1
10
10x5422.6558.10
2954.023.2779~
−−
−
−
−
====
cmDcmBcmcmv
e
e
eα
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
eα
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
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
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
Potential Energy as a Function of Internuclear separation, re
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
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
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).