AP Chemistry
3.3 Solids, Liquids, and Gases
3.1 Intermolecular and Interparticle Forces
A student compares the equilibrium capillary rise of three straight-chain alcohols in identical narrow tubes coated with the same polar material. Measurements at \(25^{\circ}\text{C}\) are shown in the table. The contact angle \(\theta\) reflects the balance between adhesive attractions to the coating and cohesive attractions within the liquid.
For a liquid in a capillary tube of radius \(r\), the equilibrium rise \(h\) is given by
\[ h=\dfrac{2\gamma\cos\theta}{\rho g r} \]
Which choice correctly ranks, from greatest to least, both the surface tensions and the equilibrium capillary rises and gives the correct molecular-level explanation?
| Sample | Alcohol | Surface tension, \(\gamma\) (\(\text{mN/m}\)) | Density, \(\rho\) (\(\text{g/mL}\)) | \(\theta\) | \(\cos\theta\) |
|---|---|---|---|---|---|
| \(\mathrm{P}\) | \(\text{1-propanol}\), \(\text{CH}_3(\text{CH}_2)_2\text{OH}\) | \(24\) | \(0.80\) | \(0^{\circ}\) | \(1.00\) |
| \(\mathrm{H}\) | \(\text{1-hexanol}\), \(\text{CH}_3(\text{CH}_2)_5\text{OH}\) | \(26\) | \(0.81\) | \(30^{\circ}\) | \(0.87\) |
| \(\mathrm{N}\) | \(\text{1-nonanol}\), \(\text{CH}_3(\text{CH}_2)_8\text{OH}\) | \(29\) | \(0.83\) | \(60^{\circ}\) | \(0.50\) |
For a liquid in a capillary tube of radius \(r\), the equilibrium rise \(h\) is given by
\[ h=\dfrac{2\gamma\cos\theta}{\rho g r} \]
Which choice correctly ranks, from greatest to least, both the surface tensions and the equilibrium capillary rises and gives the correct molecular-level explanation?
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