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.

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.

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 $Q$.

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

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

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

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

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.

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.

Formulas & key concepts

Electrostatic Potential Energy: Energy of interaction between two charged particles.

$$E_{\text{el}} = \frac{kQ_1Q_2}{d}$$

Where: k = Coulomb's constant (8.99 × 10<sup>9</sup> J·m/C<sup>2</sup>), Q = charges, d = distance

Dipole Moment: Measure of charge separation in a molecule.

$$\mu = Qr$$

Where: Q = magnitude of charge, r = distance between charges

Enthalpy from Bond Enthalpies: Estimate reaction enthalpy using bond energies.

$$\Delta H_{\text{rxn}} = \sum (\text{enthalpies broken}) - \sum (\text{enthalpies formed})$$

Where: For gas-phase reactions only

<table style="width:100%; border-collapse: collapse; font-size: 0.85em;"> <tr style="border-bottom: 1px solid #ccc;"><th>Group</th><th>Element</th><th>Configuration</th><th>Lewis Symbol</th></tr> <tr><td>1A</td><td>Li</td><td>[He] 2s<sup>1</sup></td><td>Li·</td></tr> <tr><td>2A</td><td>Be</td><td>[He] 2s<sup>2</sup></td><td>:Be:</td></tr> <tr><td>3A</td><td>B</td><td>[He] 2s<sup>2</sup> 2p<sup>1</sup></td><td>·B·</td></tr> <tr><td>4A</td><td>C</td><td>[He] 2s<sup>2</sup> 2p<sup>2</sup></td><td>:C::</td></tr> <tr><td>5A</td><td>N</td><td>[He] 2s<sup>2</sup> 2p<sup>3</sup></td><td>:N::·</td></tr> <tr><td>6A</td><td>O</td><td>[He] 2s<sup>2</sup> 2p<sup>4</sup></td><td>:O::</td></tr> <tr><td>7A</td><td>F</td><td>[He] 2s<sup>2</sup> 2p<sup>5</sup></td><td>:F:··</td></tr> <tr><td>8A</td><td>Ne</td><td>[He] 2s<sup>2</sup> 2p<sup>6</sup></td><td>:Ne::</td></tr> </table>

$$\text{Lewis Symbols}$$

Bond Order: Half the difference between the number of bonding electrons and antibonding electrons.

$$\text{Bond Order} = \frac{1}{2} (N_b - N_a)$$

Where: N<sub>b</sub> = number of bonding electrons, N<sub>a</sub> = number of antibonding electrons

<table style="width:100%; border-collapse: collapse; font-size: 0.85em;"> <thead> <tr style="border-bottom: 2px solid #444;"> <th style="padding: 4px; text-align: left;">Bond</th> <th style="padding: 4px; text-align: left;">D (kJ/mol)</th> <th style="padding: 4px; text-align: left;">Bond</th> <th style="padding: 4px; text-align: left;">D (kJ/mol)</th> </tr> </thead> <tbody> <tr><td style="padding: 2px;">C-H</td><td style="padding: 2px;">413</td><td style="padding: 2px;">C-C</td><td style="padding: 2px;">348</td></tr> <tr><td style="padding: 2px;">C-N</td><td style="padding: 2px;">293</td><td style="padding: 2px;">C-O</td><td style="padding: 2px;">358</td></tr> <tr><td style="padding: 2px;">C-F</td><td style="padding: 2px;">485</td><td style="padding: 2px;">C-Cl</td><td style="padding: 2px;">328</td></tr> <tr><td style="padding: 2px;">C-Br</td><td style="padding: 2px;">276</td><td style="padding: 2px;">C-I</td><td style="padding: 2px;">240</td></tr> <tr><td style="padding: 2px;">C-S</td><td style="padding: 2px;">259</td><td style="padding: 2px;">Si-H</td><td style="padding: 2px;">323</td></tr> <tr><td style="padding: 2px;">Si-Si</td><td style="padding: 2px;">226</td><td style="padding: 2px;">Si-C</td><td style="padding: 2px;">301</td></tr> <tr><td style="padding: 2px;">Si-O</td><td style="padding: 2px;">368</td><td style="padding: 2px;">N-H</td><td style="padding: 2px;">391</td></tr> <tr><td style="padding: 2px;">N-N</td><td style="padding: 2px;">163</td><td style="padding: 2px;">N-O</td><td style="padding: 2px;">201</td></tr> <tr><td style="padding: 2px;">N-F</td><td style="padding: 2px;">272</td><td style="padding: 2px;">N-Cl</td><td style="padding: 2px;">200</td></tr> <tr><td style="padding: 2px;">N-Br</td><td style="padding: 2px;">243</td><td style="padding: 2px;">H-H</td><td style="padding: 2px;">436</td></tr> <tr><td style="padding: 2px;">H-F</td><td style="padding: 2px;">567</td><td style="padding: 2px;">H-Cl</td><td style="padding: 2px;">431</td></tr> <tr><td style="padding: 2px;">H-Br</td><td style="padding: 2px;">366</td><td style="padding: 2px;">H-I</td><td style="padding: 2px;">299</td></tr> <tr><td style="padding: 2px;">O-H</td><td style="padding: 2px;">463</td><td style="padding: 2px;">O-O</td><td style="padding: 2px;">146</td></tr> <tr><td style="padding: 2px;">O-F</td><td style="padding: 2px;">190</td><td style="padding: 2px;">O-Cl</td><td style="padding: 2px;">203</td></tr> <tr><td style="padding: 2px;">O-I</td><td style="padding: 2px;">234</td><td style="padding: 2px;">S-H</td><td style="padding: 2px;">339</td></tr> <tr><td style="padding: 2px;">S-F</td><td style="padding: 2px;">327</td><td style="padding: 2px;">S-Cl</td><td style="padding: 2px;">253</td></tr> <tr><td style="padding: 2px;">S-Br</td><td style="padding: 2px;">218</td><td style="padding: 2px;">S-S</td><td style="padding: 2px;">266</td></tr> <tr style="border-top: 1px solid #666;"><td colspan="4" style="padding: 4px; font-weight: bold; text-align: center;">Multiple Bonds</td></tr> <tr><td style="padding: 2px;">C=C</td><td style="padding: 2px;">614</td><td style="padding: 2px;">C≡C</td><td style="padding: 2px;">839</td></tr> <tr><td style="padding: 2px;">C=N</td><td style="padding: 2px;">615</td><td style="padding: 2px;">C≡N</td><td style="padding: 2px;">891</td></tr> <tr><td style="padding: 2px;">C=O</td><td style="padding: 2px;">799</td><td style="padding: 2px;">C≡O</td><td style="padding: 2px;">1072</td></tr> <tr><td style="padding: 2px;">N=N</td><td style="padding: 2px;">418</td><td style="padding: 2px;">N≡N</td><td style="padding: 2px;">941</td></tr> <tr><td style="padding: 2px;">O=O</td><td style="padding: 2px;">495</td><td style="padding: 2px;">S=O</td><td style="padding: 2px;">523</td></tr> <tr><td style="padding: 2px;">S=S</td><td style="padding: 2px;">418</td><td style="padding: 2px;"></td><td style="padding: 2px;"></td></tr> </tbody> </table>

$$\text{Average Bond Enthalpies}$$

$$\text{Average Bond Lengths}$$

Practice quiz

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.
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: $-808 \text{ kJ/mol}$
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 $Y_2$.
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: $1/12$
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: $-124 \text{ kJ/mol}$
Determine the average bond order for each N-O bond in the nitrate ion, $NO_3^-$.
- $1$
- $1.33$
- $1.5$
- $2$
Answer: $1.33$
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: $k = \frac{-E_{\text{el}}\mu}{Q^3}$
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: $946 \text{ kJ/mol}$
Determine the average bond order for each C-O bond in the carbonate ion, $CO_3^{2-}$.
- $1$
- $1.33$
- $1.5$
- $2$
Answer: $1.33$
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.

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Chemical Bonding — Hard Practice Quiz

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Dipole Moment: Measure of charge separation in a molecule.

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