Ask AI: Calculate the force constants of the C=O bonds with the values of carbon monoxide (1902 cm-1).make it short

To calculate the force constant \( k \) of the C=O bond using the vibrational frequency, you can use the following formula: \[ k = 4\pi^2c^2 \mu \nu^2 \] Where: - \( c \) is the speed of light (approximately \( 3 \times 10^{10} \) cm/s) - \( \mu \) is the reduced mass of the C and O atoms (in grams) - \( \nu \) is the vibrational frequency (in cm\(^{-1}\)) Given: - \( \nu = 1902 \) cm\(^{-1}\) 1. Calculate the reduced mass (\( \mu \)): \[ \mu = \frac{m_C \cdot m_O}{m_C + m_O} \] Where: - \( m_C = 12 \) amu - \( m_O = 16 \) amu Convert the mass to grams (1 amu = \( 1.66054 \times 10^{-24} \) g): \[ \mu = \frac{12 \cdot 16 \cdot (1.66054 \times 10^{-24} \text{ g})}{(12 + 16) \cdot (1.66054 \times 10^{-24} \text{ g})} \] \[ \mu \approx 1.14 \times 10^{-23} \text{ g} \] 2. Calculate the force constant (\( k \)): \[ k = 4\pi^2 (3 \times 10^{10} \text{ cm/s})^2 (1.14 \times 10^{-23} \text{ g}) (1902 \text{ cm}^{-1})^2 \] \[ k \approx 1871.1 \text{ N/m} \] Therefore, the force constant of the C=O bond in carbon monoxide is approximately 1871.1 N/m.