---
title: "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.  | 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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url: "https://nerd-notes.com/ubq/120118/"
date_modified: "2026-08-21T08:41:52+00:00"
---

# 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.

| 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?

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.

| 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?

- **A.** Surface tension: \(\gamma_{\mathrm{N}}>\gamma_{\mathrm{H}}>\gamma_{\mathrm{P}}\) Capillary rise: \(h_{\mathrm{N}}>h_{\mathrm{H}}>h_{\mathrm{P}}\) Longer chains are more polarizable and therefore have stronger cohesive forces; because the tubes have the same radius, the capillary rise follows the surface-tension order.
- **B.** Surface tension: \(\gamma_{\mathrm{N}}>\gamma_{\mathrm{H}}>\gamma_{\mathrm{P}}\) Capillary rise: \(h_{\mathrm{N}}>h_{\mathrm{H}}>h_{\mathrm{P}}\) Longer chains are more polarizable, and the larger values of \(\theta\) indicate stronger adhesion to the coating, so both quantities increase with chain length.
- **C.** Surface tension: \(\gamma_{\mathrm{N}}>\gamma_{\mathrm{H}}>\gamma_{\mathrm{P}}\) Capillary rise: \(h_{\mathrm{P}}>h_{\mathrm{H}}>h_{\mathrm{N}}\) The surface tension increases because the number of hydrogen-bonding sites per molecule increases with chain length, whereas the smaller \(\theta\) for \(\mathrm{P}\) produces the greatest capillary rise.
- **D.** Surface tension: \(\gamma_{\mathrm{N}}>\gamma_{\mathrm{H}}>\gamma_{\mathrm{P}}\) Capillary rise: \(h_{\mathrm{P}}>h_{\mathrm{H}}>h_{\mathrm{N}}\) Each alcohol has the same hydroxyl-group hydrogen-bonding pattern, but increasing chain length increases polarizability and cohesive London dispersion forces. The smaller \(\theta\) for \(\mathrm{P}\) indicates more favorable adhesion, and the values of \(\dfrac{\gamma\cos\theta}{\rho}\) give the capillary-rise order.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120118/*