[VISUAL] Fig. 1: IR spectrum of CF4, intensity vs. wavenumber in cm–1 Fig. 2: IR spectrum of SiF4, i — Analytical Chemistry — Spectroscopy Chemistry Question
Infrared Spectroscopy of Tetrahedral Molecules
[VISUAL]
Fig. 1: IR spectrum of CF4, intensity vs. wavenumber in cm–1
Fig. 2: IR spectrum of SiF4, intensity vs. wavenumber in cm–1
(CF4 absorbs at 1280 cm–1, SiF4 absorbs at 1010 cm–1)
The IR spectrum indicates vibrations that depend on the force constant k of the bonds that keep the atoms together and the so–called reduced mass \mu.
The reduced mass \mu for the highest frequency vibration in a XY4 molecule is given by:
\mu = \frac{3 m_X m_Y}{3 m_X + 4 m_Y}
and the vibrational frequency \nu is given by \omega = 2 \pi \nu = \sqrt{\frac{k}{\mu}}.
Calculate the force constant of CF4 and SiF4 and compare their relative strengths with each other.
Model Answer
From the diagram: \tilde{\nu}(CF4) = 1280 cm–1, \tilde{\nu}(SiF4) = 1010 cm–1
hence \nu(CF4) = 38.4 × 10^12 s–1, \nu(SiF4) = 30.3 × 10^12 s–1
Reduced mass \mu calculation:
\mu = \frac{3 m_X m_Y}{3 m_X + 4 m_Y}
\mu(CF4) = 6.11 g mol–1 N_A–1 = 1.01 × 10–23 g
\mu(SiF4) = 9.99 g mol–1 N_A–1 = 1.66 × 10–23 g
Using \omega^2 = \frac{k}{\mu} ⇒ k = 4 \pi^2 \nu^2 \mu:
hence k(CF4) = 4 \pi^2 (38.4 × 10^12 s–1)^2 × 1.01 × 10–23 g = 588 N m–1
and k(SiF4) = 4 \pi^2 (30.3 × 10^12 s–1)^2 × 1.66 × 10–23 g = 602 N m–1
The force constants of the two compounds are almost identical.
The heats of formation of CF4 and SiF4 are –1222 kJ mol –1 and –1615 kJmol –1.
What kind of relation is there between them and the force constants of vibration that you have calculated?
Model Answer
The heats of formation and the force constants do not match. They are not expected to match, since the initial states of the compounds need to be taken into account. In addition, the vibrational force constant describes the potential just in the vicinity of the zero point but not far away from it.
The enthalpies of vaporization of carbon and silicon are 717 kJmol –1 and 439 kJmol –1.
Take these values into account and comment on the relation between the heat of formation of the gases and the vibrational frequencies again.
Model Answer
Taking into account the heat of vaporization, we obtain the heats of formation of CF4 and SiF4 from C and Si vapours of –1939 kJ mol –1 and –2054 kJ mol –1. This is the reason why we can assume a similar shape of the energy curve of breaking the bonds between C and F and between Si and F, since the extrapolation from the curvature close to the bonding distance to the rest of the curve is quite good.