ABSTRACT infrared spectrums for benzylamine, benzoicnitrile and diphenylamine were given. The point with a highest point or peak was chosen to and frequency of each spectrum at that point and was recorded these frequencies were the frequencies form absorption due to the bonds, benzonitrile, benzylamine and diphenylamine were composed respectively of
(c ≡ 𝑁) ;(C-N) and (C=N) from the deduced frequencies , the provided equation was used to calculate the force constants for each of the three types of carbon nitrogen bonds, from the results obtained it shows that the force constants are directly proportional to the bond strength, such that as we increase the bond order, the relative force constants also increase.

INTRODUCTION
Three Infra-red regions of interest in the electromagnetic spectrum In terms of wavelengths the three regions in micrometers (µm) The first region (NIRS) allows the study of overtones and harmonic or combination vibrations. The MIRS region is to study the fundamental vibrations and the rotation-vibration structure of small molecules, whereas the FIRS region is for the low heavy atom vibrations (metal-ligand or the lattice vibrations).Infrared (IR) light is electromagnetic (EM) radiation with a wavelength longer than that of visible light: ≤0.7µm. One micrometer (µm) is 10-6m Experiments continued with the use of these infrared rays in spectroscopy called, Infrared
Spectroscopy and the first infrared spectrometer was built in 1835. IR Spectroscopy expanded rapidly in the study of materials and for the chemical characterization of materials that are in our planet as well as beyond the planets and the stars. The renowned spectroscopists, Hertzberg, Coblenz and Angstrom in the years that followed had advanced important greatly the cause of Infrared spectroscopy. By 1900 IR spectroscopy became an tool for identification and characterization of chemical compounds and materials[1]
According to the theory of classical mechanics a harmonic oscillator is a particle of mass m that experience a restoring force proportional to its displacement, from the equilibrium position, the particle oscillates about the equilibrium position at characterized frequency all the information stated about simple harmonic oscillator is explained by H ooke’s law it also extended to the father of mechanics Newton using his equations scientifically known to be Newton’s equation of motion by describing the energy of stretching the spring and also describes the vibration of chemical bond. By illustrating that when Two atoms are connected by a covalent bond that behave like two masses on the ends of a spring, when each mass is released from its stationary position they both vibrate with different frequencies since they depend on the masses, and a constant related to the stiffness of the spring. A model of particle oscillating in a parabolic potential is used to describe the vibrational motion of a diatomic molecule A-B in this caliber both atoms move as the bond between them is stretched and compressed and the mass is replaced by the effective mass [2].
Infra-red spectroscopy deals with the interaction between the molecules it covers a range of techniques, normally based on absorption spectroscopy. It can be used to study the chemical substances. Samples may be liquid, solid, or gas the method of infrared spectroscopy is conducted with an instrument called an infrared spectrometer to produce infrared spectrum. An IR spectrum can be visualized in a graph of infrared light absorbance (or transmittance) on the vertical axis vs. frequency or wavelength on the horizontal axis. Typical units of frequency used in IR spectra are reciprocal centimeters
(sometimes called wave numbers), with the symbol cm
−1
. Units of IR wavelength are commonly given in micrometers [3].
Vibrational spectra are presented with vibrational frequencies along the x-axis and the spectral intensities along the y-axis. The experimental vibrational frequencies and spectral intensities are two individual sources of information for molecular structural

determination as well as for analytical applications. From the expressions for the vibrational energy levels, it is clear that they depend on the second and higher derivatives of potential energy with respect to nuclear coordinates. The second derivatives are called
“quadratic (or harmonic) force constants,” while the third and fourth derivatives are respectively called the “cubic and quartic force constants.” The fifth and higher order derivatives are not usually encountered because their magnitudes are small and difficult to determine. Two developments are of particular significance for the calculation of vibrational frequencies. One is the recognition that the first derivatives of energy can be calculated using analytic expressions. The second is the realization of a perturbative method for determining the higher order energy derivatives. These advances have made the predictions of vibrational frequencies very convenient [4].
The type of absorption spectroscopy depends upon frequency range of the electromagnetic radiation absorbed. Microwave spectroscopy involves a transition from one molecular rotational energy to another. Rotational energy level spacing correspond to radiation from the microwave portion of the electromagnetic spectrum. Vibrational spectroscopy measure transition from one molecular vibrational energy level to another and requires a radiation from the infrared portion of the electromagnetic spectrum. UVvisible spectroscopy includes transitions among electron energy level in the molecule, which require radiation from the UV-visible portion of the electromagnetic spectrum. Such transitions after the configuration of the valence electrons in the molecule [5].

MATERIALS
IR spectrum for
(1) Benzonitrile
(2) Benzyl amine
(3) Diphenyl imine
PROCEDURE
The IR spectrum for benzonitrile, benzyl amine and diphenyl imine was obtained. The frequency of the absorption due to the C-N, C=N, AND C ≡ N was found. From these frequencies the force constants for the three types a carbon nitrogen bonds was calculated to compare the three force constants to relative strengths of these three bonds.
RESULTS
Calculations
Mass of the Nitrogen atom:
M
N
=
𝑀
𝑁
14.01×10
−3 𝑘𝑔/𝑚𝑜𝑙
6.022×10 23 mol −1
= 2.326 × 10 −26 𝑘𝑔
Mass of the carbon atom
M
C
=
𝑀
𝑁
12.01×10
−3 𝑘𝑔/𝑚𝑜𝑙
6.022×10 23 mol − 1
= 1.994 × 10^ − 26𝑘𝑔
Reduced mass 𝜇 = 𝑚𝑎.𝑚𝑏 𝑚𝑎+𝑚𝑏
=
(2.326×10
−26
(2.326×10 −26 𝑘𝑔)(1.994×10
−26 𝑘𝑔)+(1.994×10 𝑘𝑔)
−26 𝑘𝑔)
= 1.074
× 10 −26 𝑘𝑔 𝜇 = (𝐶 ≡ 𝑁) = 𝜇(𝐶 = 𝑁) = 𝜇(𝐶 − 𝑁) = 1.074 𝑥10
−26 𝑘𝑔

CALCUTION OF FORCE CONSTANT
Benzonitrile (C ≡ 𝑵) v = 2225cm -1 from the spectrum v =
1
2𝜋
√ 𝑘 𝑚 v 2 =( (
1
2𝜋 𝑘
√ 𝑚
) 2 k = v 2 4 𝜋
2
𝐶
2 𝜇
=(2225cm -1 ) 2 (4 𝜋
2
)(3.00𝑥10
8 ) 2
(1.074𝑥10
−26
) =189.15N/m
Benzylamine(C – N) v=1737cm -1 from the spectrum k = v 2 4 𝜋 C 2 𝜇 = (1737.29cm
-1 ) 2 (4 𝜋)(3𝑋10 8 ) 2 (1.074𝑋10 −26 )
=1151.73N/m
Diphenylamine(C=N) v=1739cm -1 from the spectrum k = v 2 4 𝜋 2
C 2 𝜇
K =(1739cm -1 ) 2 (4 𝜋 2 )(3X10 8 ) 2 (1.074X10-26kg)
=1154.45N/m
Questions
1.mass of carbon atom m
C
=
𝑀
𝑁
=
12.01𝑘𝑔/𝑚𝑜𝑙
6.022𝑥10 23
= 1.994x10
-26 kg v=
1
2𝜋
√
510.40𝑁/𝑚
2.867𝑥10 −27
=2238.41cm
-1
.. ..
2.i : O=C=O:
ii.CO
2
HAS C – O single bond
Mass of carbon atom

m
C
=
𝑀
𝑁
=
12.01𝑋10
−3 𝑘𝑔/𝑚𝑜𝑙
6.022𝑥10 23 𝑚𝑜𝑙 −1
= 1.994x10
-26
Mass of oxygen atom m
O
=
𝑀
𝑁
=
16.00𝑋10
−3 𝑘𝑔/𝑚𝑜𝑙
6.022𝑥10 23 𝑚𝑜𝑙 −1
=2.657x10
-26 kg 𝜇 =
(𝑚𝑂)(𝑚𝐶) 𝑚0+𝑚𝐶
=
(1.994𝑥10
−26
)(2.657𝑥10
−26
)
1.994𝑥10 −26 +2.657𝑥10 −26
=1.139X10
-26 kg
∴ 𝑣 =
1
2𝜋𝐶
√ 𝑘 𝜇
Mass of hydrogen atom m
H
=
𝑀
𝑁
=
1.008𝑥10 −3 𝑘ℎ/𝑚𝑜𝑙
6.022𝑥10 23
= 1.674 x10 -27 kg
REDUCED MASS 𝜇 = 𝑚𝐻𝑚𝐶 𝑚𝐻+𝑚𝐶
=
1.674𝑋10 −27 𝑘𝑔)(1.994𝑥10 −26 )
1.674𝑥10 −27 +1.994𝑥10 −26
= 1.544x10
-27 kg 𝑣 =
1
2𝜋𝑐
√ 𝑘 𝜇 𝑣
2
1
= (
4𝜋 𝑘 𝑐𝜇
)
∴ 𝑘 = 𝑣
2
4𝜋
2 𝑐
2 𝜇 =(3050cm -1 )(4 𝜋
2
) (3x10 8 )(1.544x10
-27 kg)
𝑀 ii) m
2H
=
𝑁𝐴
=510.40N/m

=
2(
1.008𝑋10−3𝑘𝑔 𝑚𝑜𝑙
)
6.022𝑥10^23𝑚𝑜𝑙 −1
=3.348x10
-27 kg 𝜇 =
(𝑚2𝐻)(𝑚𝐶) 𝑚2𝐻+𝑚𝐶
=
3.348𝑋10
−27
)(1.994𝑋10
−26
3.348𝑋10 −27 +1.994𝑋10 −26
)
=2.867 X10 -27 kg
DISCUSSSION
Infra-red (IR) spectroscopy deals with the interaction between a molecule and radiation from the IR region of the EM spectrum (IR region = 4000- 400cm -1 ) the cm -1 unit is the wave number scale and is given by 1/(wavelength in cm) the vibrational frequency was obtained to be directly proportional to the order. The recorded frequency were then used to calculate the force constants for each spectrum using the provided equations.
The force constants for benzonitrile, bemnzylamine and diphenylamine we respectively
1889.15N/m, 1154.45/M AND 1151.73N/m from these values, it was deduced that the force constants increases with an increase in bond strength.
CONCLUSSION
The relationship between the strength of chemical bond and its vibrational frequency was found to be directly proportional. It shows that an increase in bond order was characterized by increasing vibrational frequency. IR spectroscopy has been highly successful in measuring the degree of polymerization in polymer manufacture. IR spectroscopy is useful for identifying and characterizing substances and confirming their identity since the IR spectrum is the “fingerprint” of a substance. Therefore, IR also has a forensic purpose and IR spectroscopy is used to analyze substances, such as, alcohol, drugs, fibers, blood and paints.

REFERENCE
1. Elliot and E. Ambrose, Nature, Structure of Synthetic Polypeptides 165, 921 (1950);
D.L.Woernley, Infrared Absorption Curves for Normal and Neoplastic Tissues and
Related Biological Substances, Current Research, Vol. 12, , 1950 , 516p
2. Atkins physical chemistry 11 th edition textbook chapter page 273-274.
3.
Atkins PW, de Paula J (2009). Elements of physical chemistry (5th ed.). Oxford:
Oxford U.P. p. 459. ISBN 978-0-19-922672-6
4. Krivanek OL, Lovejoy TC, Dellby N, Aoki T, Carpenter RW, Rez P, et al. (October
2014). "Vibrational spectroscopy in the electron microscope". Nature. 514 (7521): 209 –
12. Bibcode : 2014Natur.514..209K
5. COURY L. (2011). Conductance measurements part 1, 10 th edition, Macmillan, New
YORK, USA pg 91-96

UNIVERSITY OF LIMPOPO
FACULTY OF SCIENCE AND AGRICULTURE
SCHOOL OF PHYSICAL AND MINERAL SCIENCES
Department of Chemistry
MODULE CODE
DATE :
:
SCHA031
26/02/2020
Experiment 03
TITLE OF THE EXPERIMENT
DETERMINATION OF FORCE CONSTANTS FROM VIBRATIONAL FREQUENCIES
BY: PHASHA LA
201700287