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AP Chemistry
3.3 Solids, Liquids, and Gases
3.1 Intermolecular and Interparticle Forces
AdvancedMCQMathematicalConceptual21.7k
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.

SampleAlcoholSurface 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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