Question

In: Chemistry

Calculate the absorption frequency corresponding to the –C-H stretching vibration treating the group as a simple...

Calculate the absorption frequency corresponding to the –C-H stretching vibration treating the group as a simple diatomic C-H molecule with a force constant of k= 5.0 102 N/m. (Hint: use the actual mass of the two atoms to determine the reduced mass. Note that N is the unit of a force.) Repeat the calculation for the deuterated bond.

Expert Solution

1) as we know that

= reduced mass = m1 ( mass of hydrogen ) =1 amu = 1.66 * 10^-27 kg

mass of carbon = 12 amu = 12 * 1.66 * 10^-27 Kg = 19.92 * 10^-27 Kg

m₁m₂/m₁+m₂ = 1.66 * 10^-27 * 19.92 * 10^-27 / 1.66 * 10^-27 + 19.92 * 10^-27

= 33.067 * 10 ^-54 / 21.58 * 10^-27 = 1.53 * 10^-27

vibrational spectra of diatomic molecule --> = 1/2c (k / )^1/2

where = adsorption frequency , c = speed of light in (cm) , k = force constant

= 1/2 * 3.142* 3 10¹⁰ ( 5.0* 10² / 15.3 10^-28)^1/2

= 0.053 * 10^-10 ( 0.33 10³⁰ ) ^1/2 = 0.053 * 0.57 * 10^-10 * 10¹⁵ = 3021 cm^-1

2) for deutrium = 2 amu = 2 * 1.66 * 10^-27 Kg = 3.32 * 10^-27 kg

= reduced mass = m₁m₂/m₁+m₂ = 3.32 * 10^-27 * 19.92 * 10^-27 / 3.32 * 10^-27 + 19.92 * 10^-27

= 66.13 * 10 ^-54 / 23.24 * 10^-27 = 2.845 * 10^-27

vibrational spectra of diatomic molecule --> = 1/2c (k / )^1/2

= 1/2 * 3.142* 3 10¹⁰ ( 5.0* 10² / 28.45 10^-28)^1/2

= 0.053 * 10^-10 ( 0.176 * 10³⁰ ) ^1/2 = 0.053 *0.419 * 10^-10 * 10¹⁵ = 2220.7 cm^-1

queen_honey_blossom answered 2 years ago

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