Why Food Takes Longer to Cook in the Hills
Understand why real gases deviate from ideal behaviour and apply van der Waals' equation and the compressibility factor, and learn how vapour pressure, viscosity and surface tension of liquids depend on intermolecular forces and temperature.
Why don't real gases always follow the ideal gas equation?
The ideal gas equation assumes gas molecules take up no space and never attract one another. Real molecules do both, which is why gases can be liquefied — and once they are liquids, the same forces decide how easily they evaporate, flow or form drops.
This lesson covers real gases and van der Waals' equation, the compressibility factor, and the properties of liquids.
This lesson covers real gases and van der Waals' equation, the compressibility factor, and the properties of liquids.
Why do real gases deviate from ideal behaviour, and how do you use van der Waals' equation?
**Real gases deviate from ideal behaviour because their molecules attract one another and occupy a finite volume, and van der Waals' equation corrects the ideal gas equation for both: .
Two faulty assumptions of the ideal model:
- No intermolecular attraction — in reality, attractions pull molecules back as they near the wall, so the measured pressure is lower than the ideal pressure
- Negligible molecular volume — in reality, molecules take up space, so the free volume is less than the container volume
Van der Waals' equation:**
- a measures the strength of intermolecular attraction and is larger for easily liquefied gases
- b measures the effective volume of the molecules
When deviation is greatest. At high pressure, molecules are crowded and their own volume matters; at low temperature, they move slowly and attractions matter more. Real gases behave most ideally at low pressure and high temperature.
Worked example. For 1.0 mol of carbon dioxide in 1.0 L at 300 K, with L bar mol, L mol and L bar mol K:
The attraction term dominates, so the real pressure is lower than the ideal value.
An everyday example. The LPG stored as a liquid in a kitchen cylinder can be liquefied under moderate pressure only because of the strong attractions between its molecules.
The substance. A gas can be liquefied only below its critical temperature — above it, no amount of pressure will turn it into a liquid.
Two faulty assumptions of the ideal model:
- No intermolecular attraction — in reality, attractions pull molecules back as they near the wall, so the measured pressure is lower than the ideal pressure
- Negligible molecular volume — in reality, molecules take up space, so the free volume is less than the container volume
Van der Waals' equation:**
- a measures the strength of intermolecular attraction and is larger for easily liquefied gases
- b measures the effective volume of the molecules
When deviation is greatest. At high pressure, molecules are crowded and their own volume matters; at low temperature, they move slowly and attractions matter more. Real gases behave most ideally at low pressure and high temperature.
Worked example. For 1.0 mol of carbon dioxide in 1.0 L at 300 K, with L bar mol, L mol and L bar mol K:
The attraction term dominates, so the real pressure is lower than the ideal value.
An everyday example. The LPG stored as a liquid in a kitchen cylinder can be liquefied under moderate pressure only because of the strong attractions between its molecules.
The substance. A gas can be liquefied only below its critical temperature — above it, no amount of pressure will turn it into a liquid.
Formula
What is the compressibility factor, and what does it tell you about a real gas?
**The compressibility factor compares a real gas with an ideal one: Z equals 1 for an ideal gas, falls below 1 when attractions dominate and rises above 1 when molecular volume dominates.**
Interpreting Z:
- Z = 1 — ideal behaviour
- Z < 1 — negative deviation; attractive forces dominate, and the gas is easier to compress than an ideal gas
- Z > 1 — positive deviation; repulsions and molecular volume dominate, and the gas is harder to compress
- Hydrogen and helium show Z > 1 at most pressures at room temperature, while carbon dioxide shows Z < 1 at moderate pressures
Boyle temperature. The temperature at which a real gas obeys Boyle's law over a wide range of pressures, so Z stays close to 1.
Worked example. For the carbon dioxide sample above, the real pressure is 22.4 bar and the ideal pressure 24.9 bar at the same volume, so
Z is less than 1, so attractive forces are winning.
An everyday example. Engineers designing CNG cylinders for autorickshaws use compressibility data, because natural gas at high pressure does not behave ideally.
The substance. At very high pressure, Z rises above 1 for every gas — once molecules are packed tightly, their own volume always outweighs attraction.
Interpreting Z:
- Z = 1 — ideal behaviour
- Z < 1 — negative deviation; attractive forces dominate, and the gas is easier to compress than an ideal gas
- Z > 1 — positive deviation; repulsions and molecular volume dominate, and the gas is harder to compress
- Hydrogen and helium show Z > 1 at most pressures at room temperature, while carbon dioxide shows Z < 1 at moderate pressures
Boyle temperature. The temperature at which a real gas obeys Boyle's law over a wide range of pressures, so Z stays close to 1.
Worked example. For the carbon dioxide sample above, the real pressure is 22.4 bar and the ideal pressure 24.9 bar at the same volume, so
Z is less than 1, so attractive forces are winning.
An everyday example. Engineers designing CNG cylinders for autorickshaws use compressibility data, because natural gas at high pressure does not behave ideally.
The substance. At very high pressure, Z rises above 1 for every gas — once molecules are packed tightly, their own volume always outweighs attraction.
What are vapour pressure, viscosity and surface tension, and what affects them?
Vapour pressure is the pressure of a liquid's vapour in equilibrium with the liquid, viscosity is a liquid's resistance to flow, and surface tension is the energy needed to increase a liquid's surface area; all three depend on intermolecular forces and change with temperature.
Vapour pressure:
- Rises with temperature, because more molecules gain enough energy to escape
- Lower for liquids with strong intermolecular forces, such as water, and higher for volatile liquids such as acetone
- A liquid boils when its vapour pressure equals the external pressure; at 1 atm, water's normal boiling point is 100 °C
Viscosity:
- Arises from friction between layers of liquid sliding past each other
- Higher for liquids with strong intermolecular forces or large molecules, such as glycerol and honey
- Decreases as temperature rises, because molecules move more freely
Surface tension:
- Molecules at the surface are pulled inward by those below, so the surface acts like a stretched film
- Makes drops spherical and causes capillary rise in narrow tubes
- Decreases as temperature rises, and is lowered by soaps and detergents
An everyday example. Rice and dal take longer to cook at hill stations such as Shimla because the lower air pressure lets water boil below 100 °C — which is why a pressure cooker, raising the boiling point, is so useful there.
The substance. A liquid's boiling point is not fixed — it depends on the external pressure, rising inside a pressure cooker and falling on a mountain.
Vapour pressure:
- Rises with temperature, because more molecules gain enough energy to escape
- Lower for liquids with strong intermolecular forces, such as water, and higher for volatile liquids such as acetone
- A liquid boils when its vapour pressure equals the external pressure; at 1 atm, water's normal boiling point is 100 °C
Viscosity:
- Arises from friction between layers of liquid sliding past each other
- Higher for liquids with strong intermolecular forces or large molecules, such as glycerol and honey
- Decreases as temperature rises, because molecules move more freely
Surface tension:
- Molecules at the surface are pulled inward by those below, so the surface acts like a stretched film
- Makes drops spherical and causes capillary rise in narrow tubes
- Decreases as temperature rises, and is lowered by soaps and detergents
An everyday example. Rice and dal take longer to cook at hill stations such as Shimla because the lower air pressure lets water boil below 100 °C — which is why a pressure cooker, raising the boiling point, is so useful there.
The substance. A liquid's boiling point is not fixed — it depends on the external pressure, rising inside a pressure cooker and falling on a mountain.
Exam tip
What earns full marks on real gases and liquid properties?
When comparing gases, link a larger value of a to easier liquefaction and a larger value of b to larger molecules — and state which effect explains the deviation.
- Van der Waals:
- Compressibility factor: ; Z < 1 for attraction, Z > 1 for repulsion
- Vapour pressure rises with temperature; viscosity and surface tension fall
The trap. Writing that a liquid's viscosity increases with temperature. For liquids, viscosity decreases as temperature rises.
- Van der Waals:
- Compressibility factor: ; Z < 1 for attraction, Z > 1 for repulsion
- Vapour pressure rises with temperature; viscosity and surface tension fall
The trap. Writing that a liquid's viscosity increases with temperature. For liquids, viscosity decreases as temperature rises.
Did you know
How can some insects walk on water?
Water striders skate across ponds without sinking. Their long legs spread their weight over a wide area, and water-repelling hairs on their feet press only lightly on the surface.
Water has a high surface tension because of hydrogen bonding, so its surface behaves like an elastic film that bends under the insect's feet without breaking.
If detergent gets into the pond, surface tension falls sharply, and the film can no longer hold such insects up.
Water has a high surface tension because of hydrogen bonding, so its surface behaves like an elastic film that bends under the insect's feet without breaking.
If detergent gets into the pond, surface tension falls sharply, and the film can no longer hold such insects up.
Exam relevance
How do JEE Main and NEET test real gases, van der Waals' equation and liquids?
Real gases and liquid properties appear in both JEE Main and NEET, often alongside questions on the ideal gas laws.
What gets asked. The meaning of the van der Waals constants a and b, conditions for ideal behaviour, interpreting the compressibility factor and its graphs, critical temperature and liquefaction, and effects of temperature on vapour pressure, viscosity and surface tension.
Question types. Mostly single-correct and assertion-reason questions, with graph-based questions on Z against pressure and some numericals using van der Waals' equation.
Why it matters later. Vapour pressure returns in Solutions for Raoult's law and colligative properties, and intermolecular forces link back to Chemical Bonding and Molecular Structure.
The trap that costs marks. Mixing up a and b — a corrects for attraction and changes the pressure term, while b corrects for molecular volume and changes the volume term.
What gets asked. The meaning of the van der Waals constants a and b, conditions for ideal behaviour, interpreting the compressibility factor and its graphs, critical temperature and liquefaction, and effects of temperature on vapour pressure, viscosity and surface tension.
Question types. Mostly single-correct and assertion-reason questions, with graph-based questions on Z against pressure and some numericals using van der Waals' equation.
Why it matters later. Vapour pressure returns in Solutions for Raoult's law and colligative properties, and intermolecular forces link back to Chemical Bonding and Molecular Structure.
The trap that costs marks. Mixing up a and b — a corrects for attraction and changes the pressure term, while b corrects for molecular volume and changes the volume term.
Key takeaways
What must you be able to do from this lesson?
- Real gases: deviations caused by attraction and molecular volume, corrected by
- Compressibility factor: , below 1 when attractions dominate and above 1 when molecular volume dominates
- Liquids: vapour pressure, viscosity and surface tension, and how temperature and intermolecular forces affect them
Which gas would you expect to have the larger van der Waals constant a, ammonia or helium — and why?
- Compressibility factor: , below 1 when attractions dominate and above 1 when molecular volume dominates
- Liquids: vapour pressure, viscosity and surface tension, and how temperature and intermolecular forces affect them
Which gas would you expect to have the larger van der Waals constant a, ammonia or helium — and why?