Q: A hot air balloon is filled with 500 L of helium at 25°C. If the temperature drops to 5°C at constant pressure, what is the new volume of the balloon? (Use Charles's Law.)

$$V_2$$ = $$V_1$$ \frac{$$T_2$$}{$$T_1$$} = 500 \times \frac{278.15}{298.15} = 466\ \text{L}$$

Question 1

Which experimental observation led to the conclusion that light behaves as a stream of particles (photons) rather than as a continuous wave, as predicted by classical physics?

Accepted Answer

The energy of ejected electrons in the photoelectric effect depends on the frequency of incident light, not its intensity.

Question 2

According to the Bohr model, what is the formula for the quantized energy levels of the hydrogen atom?

Accepted Answer

$$E_n = -\frac{Z^2$ m_e e^4$}{8 \$$varepsilon_0$$^2 h^2$ n^2$}$$

Question 3

Which of the following best describes the Born-Oppenheimer approximation in molecular quantum mechanics?

Accepted Answer

It treats nuclei as stationary while solving the Schrödinger equation for electrons.

Question 4

A sample of gas occupies 2.0 L at 1.0 atm and 300 K. If the pressure is increased to 2.0 atm and the temperature to 600 K, what will be the new volume? (Assume ideal gas behavior.)

Accepted Answer

$$V_2$$ = \frac{$$P_1$$ $$V_1$$ $$T_2$$}{$$T_1$$ $$P_2$$} = \frac{1.0 	imes 2.0 	imes 600}{300 	imes 2.0} = 2.0\ 	ext{L}$$

Question 5

Which of the following statements about the electronic configuration of transition metals is correct?

Accepted Answer

When forming +2 ions, transition metals typically lose their 4s electrons before their 3d electrons.

Question 6

Which of the following best explains why the removal of 4s electrons from a transition metal atom results in a more stable +2 ion than removal of 3d electrons?

Accepted Answer

The 4s electrons shield the 3d electrons poorly, so removing them increases the effective nuclear charge felt by the 3d electrons, stabilizing the ion.

Question 7

Which of the following is the correct electron configuration for a Cu$$^{2+}$$ ion?

Accepted Answer

$$1s^2$$ $$2s^2$$ $$2p^6$$ $$3s^2$$ $$3p^6$$ $$3d^9$$

Question 8

Which of the following best describes the difference between a gas and a vapor?

Accepted Answer

A gas is a substance that is in the gaseous state at ordinary temperature and pressure, while a vapor is the gaseous form of a substance that is normally a liquid or solid at ordinary conditions.

Question 9

A hot air balloon is filled with 500 L of helium at 25°C. If the temperature drops to 5°C at constant pressure, what is the new volume of the balloon? (Use Charles's Law.)

Accepted Answer

$$V_2$$ = $$V_1$$ \frac{$$T_2$$}{$$T_1$$} = 500 	imes \frac{278.15}{298.15} = 466\ 	ext{L}$$

Question 10

Which of the following is the correct form of the ideal gas law?

Accepted Answer

$$PV = nRT$$

Question 11

Which of the following statements about transition metal complexes is correct?

Accepted Answer

A ligand is an electron pair donor that forms a coordinate bond with a metal ion.

Question 12

Which of the following ligands is hexadentate?

Accepted Answer

Ethylenediaminetetraacetic acid (EDTA)

Question 13

Which of the following best explains why transition metal complexes are often colored?

Accepted Answer

They absorb visible light due to electronic transitions between d-orbitals split by the ligand field.

Question 14

Which of the following is the correct expression for the Rydberg formula used to calculate the wavelengths of hydrogen spectral lines?

Accepted Answer

$$\frac{1}{\lambda} = R_H \left( \frac{1}{n_1$^2} - \frac{1}{n_2$^2} \right)$$

Question 15

Which of the following best describes the difference in d-orbital splitting between octahedral and tetrahedral transition metal complexes?

Accepted Answer

In octahedral complexes, $$d_{x^2$-y^2$$}$$ and d$$_{$$z^2$$}$$ are at higher energy, while in tetrahedral complexes, d$$_{xy}$$, d$$_{xz}$$, and d$$_{yz}$ are at slightly higher energy.

Question 16

Which of the following transition metal complexes is most likely to be square planar?

Accepted Answer

[Ni(CN)$$_4$$]$$^{2-}$$

Question 17

Which of the following statements about the uncertainty principle is correct?

Accepted Answer

The more precisely the position of a particle is known, the less precisely its momentum can be known, as given by $$\Delta p \Delta x \geq \frac{h}{4\pi}.$$

Question 18

Which of the following is the correct electron configuration for a neutral chromium atom?

Accepted Answer

$$1s^2$$ $$2s^2$$ $$2p^6$$ $$3s^2$$ $$3p^6$$ $$4s^1$$ $$3d^5$$

Question 19

Which of the following best describes the role of iron in biological systems?

Accepted Answer

Iron is a key component of hemoglobin, which transports oxygen in the blood.

Physical and (Bio)Inorganic Chemistry: Atomic Structure, Quantum Theory, and Transition Metals

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