Question

Calculate the fundamental frequency of H Cl 1 35 bond if its force constant value is 516 N m-1

Answer 1

Answer on Question#40739-Chemistry-Inorganic Chemistry

Question

Calculate the fundamental frequency of H Cl 1 35 bond if its force constant value is $516\ \mathrm{N}\cdot \mathrm{m}^{-1}$.

Solution

The fundamental vibration frequency of a chemical bond is calculated by the formula:

$$v_o = \frac{1}{2\pi} \sqrt{\frac{k}{\mu}} \ ,$$

where, and $k$ is the force constant of the bond ($k = 516\ \mathrm{N}\cdot \mathrm{m}^{-1}$) and $\mu$ is the reduced mass of the diatomic molecule, equal to

$$\mu = \frac{m_1 \cdot m_2}{m_1 + m_2}$$

In case of H–Cl $m_1 = 1\cdot 10^{-27}\ \mathrm{kg}$ (H) and $m_2 = 35\cdot 10^{-27}\ \mathrm{kg}$ (Cl). Thus

$$\mu = \frac{1 \cdot 10^{-27} \cdot 35 \cdot 10^{-27}}{1 \cdot 10^{-27} + 35 \cdot 10^{-27}} = 9.7 \cdot 10^{-28}\ \mathrm{kg}$$

The fundamental frequency of H–Cl bond is

$$v_o = \frac{1}{2\pi} \sqrt{\frac{k}{\mu}} = \frac{1}{2 \cdot 3.14} \sqrt{\frac{516}{9.7 \cdot 10^{-28}}} = 1.2 \cdot 10^{14}\ s^{-1} = 1.2 \cdot 10^5\ \mathrm{GHz}$$

Answer: $1.2 \cdot 10^{14}\ \mathrm{s}^{-1}$