CU-104 / L21 · lecture

Liquids: Viscosity, Surface Tension, Vapour Pressure

~8 min read · Tier toggle changes depth (T1 plain · T2 standard · T3 rigour)

BEFORE YOU START

You should be comfortable with the kinetic molecular theory of gases, particularly the concepts of intermolecular forces and the relationship between temperature and molecular kinetic energy.

Why this matters

Liquids occupy a unique intermediate state where molecules are close but still mobile, leading to distinct macroscopic properties.

Unlike gases, which expand to fill their container, liquids maintain a fixed volume while adopting the shape of their container. This behaviour arises because the intermolecular attractive forces in liquids are strong enough to hold molecules in close proximity, yet weak enough to allow them to slide past one another. Understanding the macroscopic properties of liquids—viscosity, surface tension, and vapour pressure—is essential for explaining phenomena ranging from the flow of industrial fluids to the formation of droplets and the boiling of water. These properties are direct consequences of the balance between intermolecular attraction and thermal motion.

The Liquid State: A Molecular Perspective

To understand liquids, we must look at the balance of forces acting on individual molecules. In a solid, molecules are locked in a rigid lattice by strong intermolecular forces. In a gas, molecules are far apart and move independently, with negligible attraction. A liquid sits in between. The molecules are close together, meaning the intermolecular forces (such as hydrogen bonding, dipole-dipole interactions, or London dispersion forces) are significant. However, the thermal energy of the molecules is sufficient to overcome the rigid structure of a solid, allowing the molecules to move freely and flow. This mobility is what defines the liquid state.

Because the molecules are close, the density of a liquid is much higher than that of a gas, similar to a solid. However, unlike a solid, a liquid does not have a fixed shape. The molecules can slide past one another, a process that requires energy to overcome the temporary "cages" formed by surrounding molecules. This resistance to flow is viscosity. Furthermore, molecules at the surface of a liquid experience a net inward force because they lack neighbours above them. This imbalance creates surface tension, which acts like a stretched elastic skin. Finally, because molecules have a distribution of kinetic energies, some at the surface have enough energy to escape into the gas phase. This leads to vapour pressure, a measure of the tendency of a liquid to evaporate. These three properties are not independent; they are all governed by the strength of intermolecular forces and the temperature of the system.

Viscosity: Resistance to Flow

Viscosity is a measure of a fluid's resistance to flow. It can be thought of as "internal friction." When a liquid flows, layers of molecules move at different speeds. The layer near a stationary wall moves slowly, while layers further away move faster. The molecules in adjacent layers exert drag forces on each other due to intermolecular attractions. The stronger these attractions, the more energy is required to shear the liquid, resulting in higher viscosity. For example, honey has a much higher viscosity than water because the sugar molecules in honey form extensive hydrogen bonds, creating a network that resists flow. Water, with its simpler structure and fewer hydrogen bonds per volume, flows much more easily.

Viscosity is highly dependent on temperature. As temperature increases, the average kinetic energy of the molecules increases. This allows molecules to overcome the intermolecular attractions more easily, reducing the internal friction. Consequently, viscosity decreases as temperature rises. This relationship is often non-linear and can be described by the Arrhenius-type equation:

\[ \eta = A \exp\left(\frac{E_a}{RT}\right) \]

where \(\eta\) is the viscosity, \(A\) is a constant, \(E_a\) is the activation energy for flow, \(R\) is the gas constant, and \(T\) is the absolute temperature. The term \(E_a\) represents the energy barrier that molecules must overcome to move past one another. A higher \(E_a\) indicates stronger intermolecular forces and a greater sensitivity of viscosity to temperature changes. This is why cold oil in an engine is thick and hard to pump, while warm oil flows freely.

Surface Tension: The Elastic Skin

Surface tension is the tendency of liquid surfaces to shrink into the minimum surface area possible. This phenomenon arises from the cohesive forces between liquid molecules. In the bulk of the liquid, a molecule is surrounded by other molecules in all directions, so the net force on it is zero. However, a molecule at the surface has neighbours only to its sides and below. It lacks neighbours above. As a result, there is a net inward force pulling the surface molecules into the bulk of the liquid. This creates a state of tension at the surface, analogous to a stretched elastic membrane.

Surface tension, denoted by \(\gamma\), is defined as the force per unit length acting perpendicular to a line drawn on the surface, or equivalently, the energy required to increase the surface area by a unit amount.

\[ \gamma = \frac{F}{L} = \frac{\Delta E}{\Delta A} \]

The units of surface tension are \(\mathrm{N\,m^{-1}}\) or \(\mathrm{J\,m^{-2}}\). Water has a relatively high surface tension due to its strong hydrogen bonding network. This high surface tension allows small insects, such as water striders, to stand on the surface of water without sinking. The weight of the insect depresses the surface, creating a curved meniscus. The vertical component of the surface tension force balances the weight of the insect. If the surface tension were lower, the insect would break through the surface and sink. Surface tension also explains why droplets are spherical; a sphere has the minimum surface area for a given volume, minimizing the energy associated with the surface.

Vapour Pressure: The Equilibrium Constant

Vapour pressure is the pressure exerted by a vapour in dynamic equilibrium with its liquid phase. When a liquid is placed in a closed container, molecules at the surface with sufficient kinetic energy escape into the gas phase (evaporation). Simultaneously, gas-phase molecules collide with the liquid surface and return to the liquid phase (condensation). Initially, the rate of evaporation exceeds the rate of condensation. As the concentration of vapour increases, the rate of condensation increases until it equals the rate of evaporation. At this point, the system is in dynamic equilibrium, and the pressure of the vapour remains constant. This constant pressure is the vapour pressure.

Vapour pressure is a measure of the volatility of a liquid. A liquid with strong intermolecular forces, such as glycerol, has a low vapour pressure because it is difficult for molecules to escape the liquid phase. A liquid with weak intermolecular forces, such as diethyl ether, has a high vapour pressure because molecules escape easily. Vapour pressure increases with temperature. As temperature rises, the average kinetic energy of the molecules increases, and a larger fraction of molecules have enough energy to overcome the intermolecular attractions and escape. The relationship between vapour pressure and temperature is described by the Clausius-Clapeyron equation:

\[ \ln\left(\frac{P_2}{P_1}\right) = \frac{\Delta H_{\mathrm{vap}}}{R} \left(\frac{1}{T_1} - \frac{1}{T_2}\right) \]

where \(P_1\) and \(P_2\) are the vapour pressures at temperatures \(T_1\) and \(T_2\), \(\Delta H_{\mathrm{vap}}\) is the enthalpy of vaporisation, and \(R\) is the gas constant. This equation shows that the vapour pressure increases exponentially with temperature. The boiling point of a liquid is the temperature at which its vapour pressure equals the external atmospheric pressure. At this point, bubbles of vapour can form within the bulk of the liquid, not just at the surface.

Tier 3 · watch out

A common misconception is that vapour pressure depends on the volume of the liquid or the size of the container. In reality, vapour pressure is an intensive property that depends only on the identity of the liquid and the temperature. As long as some liquid is present, the vapour pressure will be the same regardless of whether you have a drop or a litre of the liquid, provided the temperature is constant. The amount of liquid affects the time taken to reach equilibrium, but not the final equilibrium pressure. C

Worked example

Problem. The vapour pressure of ethanol is 5.95 kPa at 20.0 °C and 17.88 kPa at 40.0 °C. Calculate its enthalpy of vaporisation in kJ mol^-1.

Convert temperatures: \(T_1 = 293.15\ \mathrm{K}\), \(T_2 = 313.15\ \mathrm{K}\).
Rearrange the Clausius–Clapeyron equation: \(\Delta H_{\mathrm{vap}} = \dfrac{R \ln(P_2/P_1)}{1/T_1 - 1/T_2}\).
Pressure ratio: \(\ln(17.88/5.95) = \ln(3.005) = 1.1003\).
Inverse temperatures: \(1/293.15 - 1/313.15 = 0.0034112 - 0.0031934 = 2.1787 \times 10^{-4}\ \mathrm{K^{-1}}\).
Substitute: \(\Delta H_{\mathrm{vap}} = \dfrac{8.314 \times 1.1003}{2.1787 \times 10^{-4}} = 4.199 \times 10^{4}\ \mathrm{J\,mol^{-1}} = 42.0\ \mathrm{kJ\,mol^{-1}}\), close to the tabulated value of about 42 kJ mol^-1 near room temperature.

\[ \Delta H_{\mathrm{vap}} = \frac{R\ln(P_2/P_1)}{1/T_1 - 1/T_2} \approx 42.0\ \mathrm{kJ\,mol^{-1}} \]

Units check. \(\mathrm{J\,mol^{-1}\,K^{-1}}\) (the logarithm is dimensionless) divided by \(\mathrm{K^{-1}}\) gives \(\mathrm{J\,mol^{-1}}\). Only the ratio of pressures enters, so kPa can be used directly.

CHECK YOURSELF

Three quick tests

Why does the viscosity of a liquid decrease as temperature increases?
Answer
Increased thermal energy allows molecules to overcome intermolecular attractions more easily, reducing internal friction.
How does surface tension arise at the molecular level?
Answer
Surface molecules experience a net inward force due to the lack of neighbours above, creating a tension that minimises surface area.
If a liquid has a high vapour pressure, what can you infer about its intermolecular forces?
Answer
The intermolecular forces are relatively weak, allowing molecules to escape into the gas phase easily.

UNIT

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NOTES

Lecture notes checked line by line by the editor; every number in the worked example was recomputed.

Results cited: — · Threads: energy, structure