# Homework 10

- Page ID
- 204089

Name: ______________________________

Section: _____________________________

Student ID#:__________________________

## Q1

Via the Sonoma State University quantum website, please calculate the number of vibrational modes and their energies (indicate which basis set you are using) for (this requires constricting the molecules and then doing the same calculations you did previously and looking at the vibrations):

- water
- \(CO_2\)
- benzene

## Q2

How many vibrational modes are the in each of the following molecules: \(NH_3\), \(C_6H_6\), \(C_{10}H_8\), \(CH_4\), \(C_2H_2\).

## Q3

In each of the following molecules, identify the vibrations that are IR active (that is you can see in IR spectra): \(N_2\), \(CO\), \(CO_2\) (stretching), \(HCl\).

## Q4

Calculate the vibrational frequency of \(CO\) given the following data: mass of C = 12.01 amu, mass of O = 16 amu, the force constant \(k = 1.86 \times 10^3\; kg\cdot s^{-2}\).

## Q5

Calculate the vibrational energy of the vibration discussed in question Q4, in its ground state of \(v=0\).

## Q6

Assuming the force constant to be the same for \(H_2O\) and \(D_2O\). A normal mode for \(H_2O\) is at \(3650\; cm^{-1}\). Do you expect the corresponding \(D_2O\) wave number to be higher or lower?