Chemical Forums
Chemistry Forums for Students => Undergraduate General Chemistry Forum => Topic started by: jaychouf4n on June 19, 2008, 06:00:15 AM

Can someone please explain to me the relation between bond enthalpy and μ where μ= 3 m(A) . m(b) / 3 m(A) +4m(B)
I'm given the bond enthalpy of ZH_{4} where Z is an unknown element.
This is in a question using Hooke's law about vibrational frequency and finding the force constant of k by substitution into the vibrational frequency equation.
Thank you :)

This equation should help:
E=hν
Are you sure that μ isn't the reduced mass (http://en.wikipedia.org/wiki/Reduced_mass)? and therefore should be:
μ=((m_{Z}+3m_{H})m_{H})/(m_{Z}+4m_{H}) i think, assuming that you have ZH_{4} and not just ZH.

frequency of radiation: E = hv
is not the same as vibrational frequency
v = (1/2π)*sqrt(k/μ)
The former refers to the wave properties of a photon while the latter refers to the mechanical properties of a system that follows spring mechanics.
Now in spectroscopy there is a relationship between the wavelength of absorption and the vibrational frequency between two atoms, however the wavelength refers to the energy being absorbed, and the frequency to the vibration between two atoms.
Vibrational frequencies can be used in computational chemistry to calculate energies, as it turns out Hookes law provides very good approximations when performing these calculations. However, calculating energies using vibrational frequencies is very computing intensive.
In a very simplistic way you have
ΔU = ΔH + W
ΔU is the change in internal energy
ΔH is the change in enthalpy
W is work
under certain conditions for a system at equilibrium you can assume that ΔU = 0
that leaves
ΔH = W
for a vibrating system work can be described by hookes law
Ws=(1/2)kx_{0}^{2} (1/2)kx_{0}^{2 } where x are components of distance and k is the spring constant.
It also turns out that K the force constant is the second derivative of the potential energy of a system with respect to the bond length.
If you let P = potential energy and R= bond length then
k = d^{2}V(R)/dR^{2}
Valdo