[mrorganiclover]

Good day all

Question:

The force constant of H35Cl is 480.5 Nm-1. Calculate the fundamental vibrations of this molecule in the following units:

i) frequency (s-1)
ii) wavenumber (cm-1)

My attempt:

μH35Cl = 1.627 x 10^-27 kg

v = 1/2π x (480.5kg m s^-2/1.627 x 10^-27 kg)^1/2

v = 0.1592 x (2.953 x 10^29 m s^-2)^1/2

v = 0.1592 x (5.434 x 10^14 s^-1)

v = 8.651 x 10^13 s^-1

wavenumber = 2.886 x 10^3 cm^-1

Thanks

[mjc123]

Your calculation is correct, however there is a complication. Atkins, for example, gives the wavenumber as 2991 cm^-1 and the force constant as 516 N/m.
2886 cm^-1 is the experimental frequency of the vibrational transition (as also appears from the spectrum given by Atkins), and the value of 480.5 N/m for the force constant, quoted in several references, is presumably calculated from this. But this neglects the anharmonicity. This http://cccbdb.nist.gov/exp2.asp?casno=7647010 gives the values ω_e = 2990.925 cm^-1 and ω_ex_e = 52.8 cm^-1, from which the transition frequency ω = ω_e - 2ω_ex_e = 2885.3 cm^-1.
Thus your given value of the force constant would appear to be wrong, but as I say, your calculation based on it is right.