Q: Given the standard Gibbs free energy of formation $\Delta G_f^\circ$ for $\mathrm{N_2O(g)}$ is $104.2\ \mathrm{kJ\ mol^{-1}}$ at $298.15\ \mathrm{K}$, what is the equilibrium constant $K$ for its decomposition at this temperature? (Use $R = 8.314\ \mathrm{J\ mol^{-1}\ K^{-1}}$)

$K = \exp\left(-\frac{104200}{8.314 \times 298.15}\right)$

Question 1

Which of the following statements best explains why the electron configuration of boron in its ground state is $1s^2 2s^2 2p^1$?

Accepted Answer

Because boron has five protons and five electrons, which fill the $1s$, $2s$, and one $2p$ orbital according to the Aufbau principle.

Question 2

A sample contains only $^{10}B$ and $^{11}B$ isotopes. If the relative atomic mass of boron is 10.81, what is the approximate percentage abundance of $^{11}B$?

Accepted Answer

$81\%$

Question 3

Which of the following molecules is expected to be linear according to the VSEPR model?

Accepted Answer

$\mathrm{XeF_2}$

Question 4

Which of the following best describes the resonance structures of the nitrate ion ($\mathrm{NO_3^-}$)?

Accepted Answer

There are three resonance structures, each with a double bond to a different oxygen atom.

Question 5

Given the standard Gibbs free energy of formation $\Delta G_f^\circ$ for $\mathrm{N_2O(g)}$ is $104.2\ \mathrm{kJ\ mol^{-1}}$ at $298.15\ \mathrm{K}$, what is the equilibrium constant $K$ for its decomposition at this temperature? (Use $R = 8.314\ \mathrm{J\ mol^{-1}\ K^{-1}}$)

Accepted Answer

$K = \exp\left(-\frac{104200}{8.314 	imes 298.15}ight)$

Question 6

A reaction has a rate constant $k$ that follows the Arrhenius equation: $k = A \exp\left(-\frac{E_a}{RT}\right)$. If a plot of $\ln k$ versus $1/T$ yields a straight line with a slope of $-5000\ \mathrm{K}$, what is the activation energy $E_a$ in $\mathrm{kJ\ mol^{-1}}$? ($R = 8.314\ \mathrm{J\ mol^{-1}\ K^{-1}}$)

Accepted Answer

$E_a = 41.6\ \mathrm{kJ\ mol^{-1}}$

Question 7

For a first-order reaction, the half-life $t_{1/2}$ is given by $t_{1/2} = \frac{\ln 2}{k}$. If the half-life is $19.7\ \mathrm{s}$, what is the value of the rate constant $k$?

Accepted Answer

$k = 0.0352\ \mathrm{s^{-1}}$

Question 8

Which of the following best describes the effect of increasing temperature on the equilibrium constant $K$ for an endothermic reaction?

Accepted Answer

$K$ increases with increasing temperature.

Question 9

A buffer solution is prepared by mixing $0.1\ \mathrm{mol}$ of a weak acid (HA) and $0.1\ \mathrm{mol}$ of its conjugate base (A$^-$) in $1\ \mathrm{L}$ of water. If the $pK_a$ of HA is $7.2$, what is the pH of the solution?

Accepted Answer

$7.2$

Question 10

Which of the following is the correct expression for the solubility product constant $K_{sp}$ for iron(III) iodate, $\mathrm{Fe(IO_3)_3}$, dissolving in water?

Accepted Answer

$K_{sp} = [\mathrm{Fe^{3+}}][\mathrm{IO_3^-}]^6$

Question 11

A galvanic cell is constructed with a standard electrode potential of $E^\circ = 0.34\ \mathrm{V}$. If the reaction quotient $Q = 75$, what is the cell potential at $25^\circ\mathrm{C}$? ($F = 96485\ \mathrm{C\ mol^{-1}}$, $R = 8.314\ \mathrm{J\ mol^{-1}\ K^{-1}}$)

Accepted Answer

$E = 0.34\ \mathrm{V} - \frac{0.0257}{1} \ln 75$

Question 12

Which of the following best describes the trend in first ionization energy across a period in the periodic table?

Accepted Answer

It increases from left to right.

Question 13

Which of the following is the correct balanced equation for the combustion of hydrazine ($\mathrm{N_2H_4}$) in oxygen, producing only nitrogen gas and water?

Accepted Answer

$\mathrm{N_2H_4} + 2 O_2 \rightarrow N_2 + 2 H_2O$

Question 14

Which of the following statements about the molecular geometry of $\mathrm{SO_2}$ is correct?

Accepted Answer

$\mathrm{SO_2}$ is bent due to one lone pair on the sulfur atom.

Question 15

Which of the following best explains why $\mathrm{Fe(OH)_3}$ is more soluble in acidic solution than in pure water?

Accepted Answer

Because $\mathrm{Fe(OH)_3}$ reacts with acid to form $\mathrm{Fe^{3+}}$ and water, shifting the equilibrium to dissolve more solid.

Question 16

Which of the following is the correct Nernst equation for a half-cell reaction at $25^\circ\mathrm{C}$?

Accepted Answer

$E = E^\circ - \frac{0.0592}{n} \log Q$

Question 17

Which of the following best describes the effect of a catalyst on a chemical reaction?

Accepted Answer

It decreases the activation energy, increasing the rate of reaction.

Question 18

Which of the following is the correct expression for the equilibrium constant $K$ for the reaction $2\mathrm{NO_2}(g) \rightleftharpoons 2\mathrm{NO}(g) + \mathrm{O_2}(g)$?

Accepted Answer

$K = \frac{[\mathrm{NO}]^2[\mathrm{O_2}]}{[\mathrm{NO_2}]^2}$

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