Question

Calculations predict the following bond strengths for the pentafluorobenzene: 410.0 kJ/mol for the C−H bond and 525.0 kJ/mol for the C−F bond. NOTE: Bond strengths are directly related to force constants. Using the bond strength data above, predict the stretching frequency in wavenumbers (cm−1) of a C−F bond in a sample of pentafluorobenzene.

Answer 1

The C-F bond stretching frequency in pentafluorobenzene is related to the bond strength and can be predicted to be high, as the C-F bond strength is strong at 525.0 kJ/mol. However, an exact numerical prediction would require additional information about the reduced mass and the relationship between bond strength and force constant.

Step-by-step explanation:

The student is asking for the prediction of the stretching frequency of the C-F bond in pentafluorobenzene using the given bond strengths of 410.0 kJ/mol for C−H and 525.0 kJ/mol for C−F. The bond strength correlates directly with the force constant, which is a factor in calculating the stretching frequency. To estimate the stretching frequency (v) in wavenumbers (cm-1), we would typically use the equation v = (1/2π) * sqrt(k/μ), where k is the force constant (related to bond strength) and μ is the reduced mass of the C−F system. While the exact calculation requires more information about the reduced mass and the relationship between bond energy and the force constant, the higher bond strength of C−F compared to C−H suggests that the C−F stretching frequency will be higher than the C−H stretching frequency.

Without the necessary constants to directly calculate the stretching frequency, we cannot provide an exact number. However, because the force constants are higher for stronger bonds and stiffer bonds vibrate at higher frequencies, we can infer that the frequency will be relatively high for the C-F bond in pentafluorobenzene, as indicated by its high bond strength of 525.0 kJ/mol.

Answer 2

The stretching frequency of a C-F bond in pentafluorobenzene can be predicted using the bond strength and the relationship between force constant and stretching frequency in wavenumbers, considering the reduced mass of carbon and fluorine.

Step-by-step explanation:

The prediction of the stretching frequency of a C-F bond in pentafluorobenzene based on bond strength involves the use of infrared spectroscopy principles and the concept of force constants. The bond strength is directly related to the force constant 'k' in Hooke's Law, which is used to describe the vibrational motion of a diatomic molecule. Specifically, the stretching frequency 'v' (in wavenumbers, cm-1) for a bond can be calculated using the equation:

v = (1/2πc) * √(k/μ)

where 'c' is the speed of light in cm/s, 'k' is the force constant in dynes/cm, and μ is the reduced mass of the two atoms in the bond in grams. Given that the bond strength for a C-F bond is 525.0 kJ/mol, and taking into account the mass of carbon and fluorine to calculate the reduced mass, one could predict the stretching frequency using the relevant constants and conversion factors. However, the exact numerical prediction would require the conversion of bond strength to force constant, which is not provided in this context. Nevertheless, one could expect that the stretching frequency for C-F would be higher than that of C-H due to the stronger bond strength and therefore a higher force constant 'k'.