Chemical Bonding — Hard Practice Quiz

A Chemistry cheat sheet for Chemical Bonding — every key formula with its symbols defined — plus a hard-level practice quiz to test recall.

Practice quiz

1. A diatomic molecule has a dipole moment $\mu$. If the distance between the two charges forming the dipole is increased by $50\%$ while the magnitude of the charges remains constant, how does the electrostatic potential energy between these two charges change?

   • It decreases to $2/3$ of its original value.
   • It increases to $3/2$ of its original value.
   • It decreases to $1/2$ of its original value.
   • It remains unchanged.

   Answer: It decreases to $2/3$ of its original value.

2. Calculate the enthalpy change for the gas-phase reaction: $CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(g)$. Use the provided average bond enthalpies.

   • $-808 \text{ kJ/mol}$
   • $+808 \text{ kJ/mol}$
   • $-1354 \text{ kJ/mol}$
   • $+1354 \text{ kJ/mol}$

   Answer: $-808 \text{ kJ/mol}$

3. Consider two hypothetical diatomic molecules, $X_2$ and $Y_2$. If $X_2$ has a bond order of $3$ and $Y_2$ has a bond order of $1$, how would you expect the electrostatic potential energy between the nuclei of the bonded atoms in $X_2$ to compare to that in $Y_2$, assuming similar charge magnitudes on the nuclei?

   • $E_{\text{el}}$ for $X_2$ would be more negative (lower) than for $Y_2$.
   • $E_{\text{el}}$ for $X_2$ would be less negative (higher) than for $Y_2$.
   • $E_{\text{el}}$ for $X_2$ would be equal to $E_{\text{el}}$ for $Y_2$.
   • The relationship cannot be determined without knowing the specific elements.

   Answer: $E_{\text{el}}$ for $X_2$ would be more negative (lower) than for $Y_2$.

4. A molecule has a dipole moment $\mu_1$ due to two charges $Q$ and $-Q$ separated by a distance $r_1$. If the distance between the charges is increased to $r_2 = 3r_1$, and the magnitude of the charges is simultaneously reduced to $Q_2 = \frac{1}{2}Q_1$, what is the ratio of the new electrostatic potential energy $E_{\text{el},2}$ to the original $E_{\text{el},1}$?

   • $1/12$
   • $1/6$
   • $1/3$
   • $1/2$

   Answer: $1/12$

5. Estimate the enthalpy change for the gas-phase hydrogenation of ethene to ethane: $C_2H_4(g) + H_2(g) \rightarrow C_2H_6(g)$. Use the provided average bond enthalpies.

   • $-124 \text{ kJ/mol}$
   • $+124 \text{ kJ/mol}$
   • $-2826 \text{ kJ/mol}$
   • $+2702 \text{ kJ/mol}$

   Answer: $-124 \text{ kJ/mol}$

6. Determine the average bond order for each N-O bond in the nitrate ion, $NO_3^-$.

   • $1$
   • $1.33$
   • $1.5$
   • $2$

   Answer: $1.33$

7. For a diatomic molecule with charges $Q$ and $-Q$ separated by distance $d$, the electrostatic potential energy is $E_{\text{el}}$ and the dipole moment is $\mu$. Derive an expression for Coulomb's constant $k$ in terms of $E_{\text{el}}$, $\mu$, and $Q$.

   • $k = \frac{-E_{\text{el}}\mu}{Q^3}$
   • $k = \frac{E_{\text{el}}\mu}{Q^3}$
   • $k = \frac{-E_{\text{el}}Q}{\mu^2}$
   • $k = \frac{E_{\text{el}}Q}{\mu^2}$

   Answer: $k = \frac{-E_{\text{el}}\mu}{Q^3}$

8. The gas-phase reaction $N_2(g) + 3H_2(g) \rightarrow 2NH_3(g)$ has an experimental enthalpy change of $\Delta H_{\text{rxn}} = -92 \text{ kJ/mol}$. Given the average bond enthalpies for $H-H$ ($436 \text{ kJ/mol}$) and $N-H$ ($391 \text{ kJ/mol}$), calculate the average bond enthalpy for the $N \equiv N$ triple bond.

   • $946 \text{ kJ/mol}$
   • $854 \text{ kJ/mol}$
   • $1038 \text{ kJ/mol}$
   • $473 \text{ kJ/mol}$

   Answer: $946 \text{ kJ/mol}$

9. Determine the average bond order for each C-O bond in the carbonate ion, $CO_3^{2-}$.

   • $1$
   • $1.33$
   • $1.5$
   • $2$

   Answer: $1.33$

10. Consider two diatomic molecules, $A-B$ and $X-Y$. Molecule $A-B$ has an average bond length of $1.20 \text{ \AA}$ and molecule $X-Y$ has an average bond length of $1.54 \text{ \AA}$. Assuming the magnitudes of the charges on the bonded atoms are comparable for both molecules, which molecule would likely have a more negative (more stable) electrostatic potential energy between its constituent atoms, and what does this imply about its bond enthalpy?

    • $A-B$ would have a more negative $E_{\text{el}}$ and a higher bond enthalpy.
    • $X-Y$ would have a more negative $E_{\text{el}}$ and a higher bond enthalpy.
    • $A-B$ would have a more negative $E_{\text{el}}$ and a lower bond enthalpy.
    • $X-Y$ would have a more negative $E_{\text{el}}$ and a lower bond enthalpy.

    Answer: $A-B$ would have a more negative $E_{\text{el}}$ and a higher bond enthalpy.