Water (contact angle θ ≈ 20° with glass) rises in a glass capillary tube. Mercury (contact angle θ ≈ 140° with glass) is placed in an identical tube. What happens to the mercury, and why?
AMercury rises like water, but more slowly due to its much greater density
BMercury stays level — its very high surface tension exactly balances the adhesive and cohesive forces
CMercury rises even higher than water because its surface tension is larger
DMercury is depressed below the external liquid level because cohesive forces among mercury atoms dominate over adhesion to glass, causing the meniscus to curve downward and net force to push down
The direction of capillary effect depends on the contact angle θ. When θ < 90° (water-glass), adhesion to the wall dominates, the meniscus curves upward, and liquid is pulled up. When θ > 90° (mercury-glass), cohesion dominates, the meniscus curves downward, and the liquid is pushed *down* — depression. The capillary rise formula h = 2γ cosθ/(ρgr) gives negative h when θ > 90° (since cosθ < 0), confirming depression. High surface tension (mercury has γ ≈ 490 mN/m vs. water's 72 mN/m) amplifies the effect in magnitude but doesn't change its direction, which is governed by the contact angle.
Question 2 Multiple Choice
Water rises to height h in a capillary tube of radius r. The tube is replaced with one of radius r/2 (half the original). What is the new capillary rise height?
Ah/2 — narrower tubes offer less area for adhesion
Bh — capillary rise depends on fluid properties and contact angle, not tube radius
C2h — capillary rise is inversely proportional to tube radius (h ∝ 1/r)
D4h — cross-sectional area decreases fourfold, amplifying the rise
From h = 2γ cosθ/(ρgr), the rise height is inversely proportional to r. Halving r doubles h. The physical reasoning: with smaller r, the surface tension force (proportional to circumference, 2πrγ cosθ) decreases, but the weight of liquid lifted (proportional to cross-sectional area, πr²hρg) decreases faster (as r²). At equilibrium, h must increase to compensate, and the math gives h ∝ 1/r. This is why plants can draw water 100 meters up through narrow xylem vessels but a bucket cannot.
Question 3 True / False
Surface tension can be understood both as a force per unit length (N/m) acting along an interface and as the Gibbs free energy cost per unit area (J/m²) of creating new surface — these two descriptions are physically equivalent.
TTrue
FFalse
Answer: True
N/m and J/m² are dimensionally identical (J = N·m, so J/m² = N·m/m² = N/m). The equivalence is not just dimensional — it reflects the same underlying physics viewed in two frames. Mechanically, γ is a force per unit length pulling the surface inward, minimizing area. Thermodynamically, γ = (∂G/∂A)_{T,P,n}, the energy cost of expanding the surface. Both descriptions say the same thing: the system minimizes surface area to minimize free energy. The driving force for droplet sphericity, bubble formation, and capillary rise all follow from either framing.
Question 4 True / False
Water has the highest surface tension of any common liquid.
TTrue
FFalse
Answer: False
Mercury has a much higher surface tension than water: γ_mercury ≈ 485–490 mN/m, while γ_water ≈ 72 mN/m at room temperature. Mercury's exceptionally strong metallic cohesion (delocalized electron interactions, not just van der Waals forces) makes its surface molecules far more strongly attracted to each other than to almost any interface. This is why mercury forms convex menisci in glass (cohesion >> adhesion to glass) and why liquid mercury beads into nearly spherical droplets. Water has unusually high surface tension *for a molecular liquid* (due to hydrogen bonding), but mercury exceeds it.
Question 5 Short Answer
Explain the thermodynamic origin of surface tension. Why are surface molecules in a higher-energy state than bulk molecules, and how does this relate to the tendency of liquids to minimize their surface area?
Think about your answer, then reveal below.
Model answer: In the bulk of a liquid, each molecule is surrounded by neighbors on all sides, and all intermolecular attractions are satisfied. A molecule at the surface has neighbors on only one side — the other side faces vapor or vacuum — so its intermolecular interactions are only partially satisfied. This incomplete coordination places surface molecules in a higher-energy state than bulk molecules. The excess energy per unit area is the surface tension γ = (∂G/∂A)_{T,P,n}. Since systems minimize Gibbs free energy at constant T and P, a liquid spontaneously minimizes its surface area to reduce the number of energetically unfavorable surface molecules — which is why droplets are spherical, bubbles are round, and liquids climb capillary tubes only as far as the free-energy balance requires.
The thermodynamic framing makes clear why surface tension is not a purely mechanical property but reflects intermolecular physics. Strong cohesive forces (mercury) → high γ; weaker cohesion (organic solvents) → lower γ. Temperature reduces γ because thermal energy partially compensates the energy penalty of surface molecules — the surface becomes less thermodynamically costly as kT becomes comparable to the intermolecular binding energy.