Deck 17: Molecules

Question 1

The bonding of the HF molecule is approximately 43.6% ionic. If its measured electric dipole moment is 6.40 * 10^-30 C · m, its equilibrium separation must be

A) 0.0416 nm
B) 0.132 nm
C) 0.0625 nm
D) 0.0917 nm
E) 0.0224 nm

Answer 1

0.0917 nm

Question 2

The _______ bond is the consequence of proton sharing between two atoms.

A) ionic
B) covalent
C) van der Waals
D) hydrogen
E) metallic

Answer 2

hydrogen

Question 3

The _______ bond is responsible for the bonding of identical or similar atoms.

A) ionic
B) covalent
C) van der Waals
D) hydrogen
E) metallic

Answer 3

covalent

Question 4

The measured minimum potential energy of a NaCl molecule at stable equilibrium distance of 0.236 nm is -5.7 eV. If the Na⁺ and Cl^- are treated as point charges, the electrostatic potential energy is

A) 2.4 eV
B) 3.5 eV
C) 5.4 eV
D) 6.1 eV
E) 6.5 eV

Question 5

The graph shows the potential energy of the Na⁺ and Cl^- ions as a function of their separation. The point that corresponds to the dissociation energy is

A) 1
B) 2
C) 3
D) 4
E) 5

Question 6

The equilibrium separation of the atoms in a given molecule is 0.234 nm and its measured electric dipole moment is 8.76 * 10^-30 C · m. What is the percentage of ionic bonding in this molecule?

A) 18%
B) 21%
C) 23%
D) 27%
E) 29%

Question 7

When the distance between ions is very small,

A) the electrostatic force becomes very small.
B) the resultant force is the electrostatic force.
C) there is a strong quantum mechanical repulsion.
D) the resultant force is gravitational.
E) None of these is correct.

Question 8

If the equilibrium separation of Na⁺ and F^- ions is 0.193 nm, then their electrostatic potential energy (with U = 0 at infinite separation) must be approximately

A) -1.19 * 10^-18 J
B) 1.19 *10^-18 J
C) 7.42 J
D) -7.42 J
E) 4.64 * 10¹⁹ J

Question 9

The bonding of the HF molecule is approximately 43.6% ionic. If its equilibrium separation is 0.917 nm, then its electric dipole moment must be approximately

A) 3.20 * 10^-30 C · m
B) 6.40 * 10^-30 C · m
C) 8.76 * 10^-30 C · m
D) 11.4 * 10^-30 C · m
E) 13.2 * 10^-30 C · m

Question 10

Which one of the following statements is true of the van der Waals bond?

A) Any two separated molecules will be attracted to one another by electrostatic forces.
B) The van der Waals bonds due to electrostatic forces are weaker than the ionic and covalent bonds.
C) At high temperatures, the van der Waals forces are not strong enough to overcome the ordinary thermal agitation of atoms or molecules.
D) At sufficiently low temperatures, the van der Waals forces will cause virtually all substances to condense into a liquid and then a solid form.
E) All of these are correct.

Question 11

The _______ bond is based on the sharing of each valence electron by many atoms.

A) ionic
B) covalent
C) van der Waals
D) hydrogen
E) metallic

Question 12

If the electrostatic potential energy of Na⁺ and F^- ions at their equilibrium separation (with U = 0 at infinite separation) is -1.19 * 10^-18 J, then their equilibrium separation must be approximately

A) 2.14 nm
B) 0.193 nm
C) 0.876 nm
D) 1.32 nm
E) 0.374 nm

Question 13

The symmetric wave function $\Psi$ for two identical, widely separated, finite square wells is best represented by which of the graphs?

A) 1
B) 2
C) 3
D) 4
E) All of these are correct.

Question 14

The figure represents two square wells that are far apart and the symmetric ( $\Psi$ _S) and antisymmetric ( $\Psi$ _A) electron wave functions. Which of the following statements correctly describes the probability distributions and the energies of the wave functions?

A) The energies are the same for these two wave functions but the probability distributions are different.
B) Neither the energies nor the probability distributions are the same for these two wave functions.
C) The probability distributions and energies are the same for these two wave functions.
D) The probability distributions are the same for these two wave functions but the energies are different.
E) None of these is correct.

Question 15

The dissociation energy of an ionic compound is the negative of the potential energy of the positive-negative ion system when the ions are

A) touching.
B) infinitely far apart.
C) still atoms and have not yet been ionized.
D) at the equilibrium separation.
E) completely dissolved in a solvent.

Question 16

The _______ bond is responsible for the bonding of most salts.

A) ionic
B) covalent
C) van der Waals
D) hydrogen
E) metallic

Question 17

The graph shows the potential energy of the Na⁺ and Cl^- ions as a function of their separation. The point that corresponds to the equilibrium separation is

A) 1
B) 2
C) 3
D) 4
E) 5

Question 18

The energy required to ionize sodium is 5.14 eV. If the energy needed to form Na⁺ and F^- ions from neutral sodium and fluorine atoms is 1.69 eV, the electron affinity of fluorine is

A) 3.45 eV
B) 5.14 eV
C) 1.69 eV
D) 6.83 eV
E) 2.79 eV

Question 19

When a NaCl molecule is formed from neutral Na and Cl atoms,

A) a net input of energy is required.
B) there is no net output of energy.
C) a net output of energy is obtained.
D) the molecule forms a covalent bond.
E) None of the above is correct.

Question 20

The energy released by an atom's acquisition of one electron is called its

A) molecular orbital energy.
B) ionic bond.
C) exclusion-principle repulsion.
D) acquisition energy.
E) electron affinity.

Question 21

The reduced mass of a two-body system in which the masses of the bodies are 2 u and
5 u is

A) 3.50 u
B) 1.40 u
C) 1.73 u
D) 0.71 u
E) 0.29 u

Question 22

Transitions between vibrational states of different electronic states result in the emission of photons in or near the _______ portion of the electromagnetic spectrum.

A) microwave
B) visible
C) far infrared
D) X-ray
E) ultraviolet

Question 23

The magnetron of a microwave oven generates a frequency of 2.45 GHz. This frequency corresponds to the first vibrational level, , of a water molecule. Assuming that the energy is given by , the moment of inertia of the water molecule is

A) 7.81 * 10^-46 kg.m²
B) 3.23 * 10^-45 kg.m²
C) 1.37 *10^-45 kg.m²
D) 3.44 * 10^-45 kg.m²
E) 6.85 * 10^-45 kg.m²

Question 24

The reduced mass of a two-body system is 2.1 u. If one of the masses is 3 u, then what is the mass of the second body?

A) 5 u
B) 7 u
C) 9 u
D) 6 u
E) 4 u

Question 25

From the frequency of vibration the effective force constant of the HCl molecule is found to be 840 N/m. In order to appreciate the stiffness of the binding force, or imaginary "spring," between the H and Cl, calculate how far a spring of the same stiffness would extend if a 10 kg weight were hung from it.

A) 0.12 cm
B) 8.3 m
C) 12 mm
D) 8.3 mm
E) 12 cm

Question 26

The energy of a diatomic molecule can best be understood in terms of

A) electronic motion.
B) vibrational motion.
C) rotational motion.
D) electronic and vibrational motions.
E) electronic, vibrational, and rotational motions.

Question 27

The first two non-zero rotational energies of a N₂ molecule are 0.493 meV and 1.48 meV. The two nitrogen atoms are separated by

A) 0.110 nm
B) 0.192 nm
C) 0.214 nm
D) 0.096 nm
E) 0.089 nm

Question 28

If the H₂ molecule has a rotational energy of E_0r = 0.040 MeV, what is the average distance between the two atoms?

A) 1.0 * 10^-13 m
B) 3.2 * 10^-11 m
C) 1.0 * 10^-10 m
D) 1.0 * 10^-20 m
E) 1.4 * 10^-10 m

Question 29

The separation distance of the atoms in N₂ (mass = 28 u) is 0.0773 nm. The characteristic rotational energy E_0r for the N₂ molecule is approximately

A) 3.27* 10^-4 eV
B) 2.48 * 10^-4 eV
C) 4.96 * 10^-4 eV
D) 1.24 * 10^-4 eV
E) 1.58 *10^-4 eV

Question 30

The mass of the cesium atom is 133 u and that of the chlorine atom is 35.5 u. The reduced mass of CsCl is approximately

A) 28.0 u
B) 169 u
C) 97.5 u
D) 84.3 u
E) 63.7 u

Question 31

The two oxygen atoms in the O₂ molecule are separated by 0.12 nm. What is the wavelength of the photon emitted when the O₂ goes from = 2 to = 1 rotational states?

A) 38 mm
B) 34 mm
C) 1.1 mm
D) 1.7 mm
E) 6.9 mm

Question 32

The antisymmetric wave function $\Psi$ for two identical, closely spaced, finite square wells is best represented by which of the graphs?

A) 1
B) 2
C) 3
D) 4
E) All of these are correct.

Question 33

Which of the following statements about covalent bonding is true?

A) In molecules with two or more bonds, the angles between the bonds are fixed.
B) Each covalent bond involves the sharing of one electron each from two atoms.
C) The two electrons forming a covalent bond must have opposite spins.
D) An atom can form more than one covalent bond.
E) All of the above statements are correct.

Question 34

The energies due to the electronic excitations of a molecule are of the order of 1 eV, whereas

A) the energies of vibration and rotation are much larger than this.
B) the energy of vibration is much larger and the energy of rotation much smaller than this.
C) the energies of vibration and rotation are of this same order of magnitude.
D) the energies of vibration and rotation are found to be both larger and smaller than 1 eV.
E) the energies of vibration and rotation are much smaller than this.

Question 35

The two oxygen atoms in the O₂ molecule are separated by 0.12 nm. What are the values of the two lowest nonzero rotational energies of O₂?

A) 9.0 * 10^-5 eV and 1.8 * 10^-4 eV
B) 3.6 * 10^-4 eV and 11 *10^-4 eV
C) 3.6 *10^-4 eV and 7.2 *10^-4 eV
D) 1.8 * 10^-4 eV and 11*10^-4 eV
E) 3.6 * 10^-4 eV and 22 *10^-4 eV

Question 36

When examined with a grating spectrograph, the discharge from helium gas has bright radiation at a relatively few discrete wavelengths; the discharge from nitrogen gas has radiation in bands with a very large number of discrete wavelengths. What is the reason for this difference in the spectra of these two gases?

A) The atoms of the helium gas have two electrons whereas the atoms of the nitrogen gas have many electrons; therefore, the nitrogen gas gives a more complicated spectrum.
B) The nitrogen gas has molecules that have rotational and vibrational energies that produce bands of closely spaced wavelengths in the spectrum.
C) The nitrogen gas discharge is hotter, which "smears out" the wavelengths of the radiation according to Planck's law for blackbody radiation.
D) The levels of the helium atoms can be obtained from the Bohr theory of atoms, which gives a few relatively discrete allowed energies, whereas nitrogen must be described by the band theory, which gives continuous bands of allowed energies.
E) None of these is correct.

Question 37

The effective force constant of the CO molecule is 1.86 kN/m. With 12 u for the mass of the carbon atom and 16 u for the mass of the oxygen atom, the frequency of vibration of the CO molecule is

A) 14.2 *10¹³ Hz
B) 2.47 * 10¹³ Hz
C) 6.42 * 10¹³ Hz
D) 9.76 * 10¹³ Hz
E) 5.93 * 10¹³ Hz

Question 38

Transitions within a given set of rotational energy levels yield photons in the _________ portion of the electromagnetic spectrum.

A) microwave
B) visible
C) far infrared
D) X-ray
E) ultraviolet

Question 39

Gases such as CO₂ and methane are considered greenhouse gases. This is because

A) they are the most common in the atmosphere allowing them to trap more heat than the other gases.
B) they form covalent bonds and hence can easily act as a shield for heat.
C) the vibrational modes of the molecules are in the infrared region which imply that they readily absorb radiant heat thus preventing it from escaping into space.
D) the gases are formed by human activity resulting in offsetting the natural balance in the gas concentrations.
E) None of the above statements is correct.

Question 40

The reduced mass of a system of two particles whose masses are m₁ and m₂ is

A) µ = (m₁ + m₂)/m₁ · m₂
B) µ = (m₁ + m₂)/m₁
C) µ = m₁/(m₁ + m₂)
D) µ = m₁ · m₂/m₁
E) µ = m₁ · m₂/(m₁ + m₂)

Question 41

In the absorption spectrum of the diatomic molecule HCl the central frequency is at
8)67 * 10¹³ Hz, while the absorption peaks on either side are separated by 5.9 *10¹¹ Hz. What is the average moment of inertia of a rotating HCl molecule?

A) 1.4 *10^-47 kg.m²
B) 7.1 * 10^-48 kg.m²
C) 1.1 * 10^-45 kg.m²
D) 2.8 *10^-47 kg.m²
E) None of these is correct.

Question 42

The characteristic energy of rotation E_0r for the O₂ molecule is 1.78 *10^-4 eV. Calculate the frequency of the photon absorbed for the excitation from the l = 3 to l = 4 rotational level of this diatomic molecule.

A) 4.3 * 10¹⁰ Hz
B) 3.0 *10¹¹ Hz
C) 1.9 *10¹¹ Hz
D) 3.4 * 10¹¹ Hz
E) 5.6* 10¹¹ Hz

Question 43

In the absorption spectrum of the diatomic molecule HCl the central frequency is at
8)67 *10¹³ Hz, while the absorption peaks on either side are separated by 5.9 *10¹¹ Hz. What is the energy of the lowest vibrational state?

A) 0.18 eV
B) 0.27 eV
C) 0.36 eV
D) 2.4 meV
E) 1.2 meV

Question 44

In the absorption spectrum of the diatomic molecule HCl the central frequency is at
8)67 * 10¹³ Hz, while the absorption peaks on either side are separated by 5.9 *10¹¹ Hz. What is the difference in energy between neighboring vibrational levels?

A) 0.18 eV
B) 0.27 eV
C) 0.36 eV
D) 2.4 meV
E) 1.2 meV