JC1 Chemistry Tutor Hougang | Real Gas Deviations. Why does pV=nRT give useful answers for a gas in a classroom question but become less accurate at very high pressure or low temperature? The ideal gas equation assumes molecules take up negligible volume and do not exert forces on one another between elastic collisions. Real molecules occupy space and attract or repel each other. The closer they become, or the smaller their thermal energy compared with attractions, the more these missing features matter.
The 2027 Singapore-Cambridge H2 Chemistry 9476 syllabus, Section 3, asks students to state kinetic-theory assumptions, explain why gases approach ideal behaviour at low pressure and relatively high temperature, and describe deviations at very high pressures and very low temperatures. It also includes pV=nRT and molar mass calculations. This guide teaches the assumptions, the pressure–temperature interpretation and worked SI calculations rather than claiming real-gas pressure must always depart in one fixed direction.
- Ideal gas: negligible molecular volume and negligible attraction or repulsion between particles
- Approach to ideal behaviour: low pressure and relatively high temperature
- High-pressure deviation: finite particle size and short-range interactions become important
- Low-temperature deviation: intermolecular attraction matters more relative to thermal motion
- Real-gas pressure can differ either way from a simple ideal prediction depending on the state
- Use p in Pa, V in m³, n in mol and T in K with R≈8.31 J mol⁻¹ K⁻¹
- A quantitative Mᵣ inference needs suitable gas data and the stated model
What the ideal-gas equation represents
The ideal equation relates pressure, volume, amount and kelvin temperature through pV=nRT. It can predict how pressure changes when more particles occupy the same volume or when an ideal gas at fixed volume becomes hotter. It is a model derived from simplifying assumptions about molecular motion.
A model is useful when the neglected effects are small, not because it perfectly describes every real substance. The 2027 H2 syllabus explicitly asks for the limitations of ideality, so students should interpret the physical conditions before assuming the model is exact.
The negligible-molecular-volume assumption
Ideal gas particles are regarded as points relative to the available container volume. At low densities, their actual sizes represent a small fraction of the total, and the approximation can work well. At high densities, molecules have finite electron clouds and cannot occupy the same space freely.
Therefore the volume available to particle centres is not simply the entire geometric container volume in a strongly compressed real gas. The molecule itself does not shrink to zero at high temperature; its relative significance to the container changes.
The no-intermolecular-force assumption
Ideal gas molecules are treated as noninteracting between collisions. Real molecules experience attractions such as dispersion forces, and polar molecules may have additional dipolar interactions. They also repel strongly when their electron clouds overlap too closely.
These forces affect both molecular movement and the measured pressure. They explain why two real gases at the same temperature and density need not follow pV=nRT with identical accuracy.
Random motion and elastic collisions
In the kinetic model, moving particles transfer momentum to the container walls, creating pressure. The model assumes collisions are elastic, so kinetic energy is conserved within the colliding system even though momentum is exchanged.
Molecular motion depends on absolute temperature. A hotter sample at fixed amount and volume generally has higher ideal pressure, but an actual gas can deviate if density and forces are no longer negligible.
Why low pressure helps
With fewer molecules per unit volume at the same temperature, particles are more widely separated. The influence of attractive and repulsive forces declines in many familiar conditions, and their finite occupied volume is a smaller proportion of the available space.
This is the physical reason a dilute real gas tends toward ideal behaviour. Simply memorising ‘low pressure’ without explaining the particle separation is insufficient when an exam asks for a reason.
Why higher temperature helps
Higher absolute temperature means greater average translational kinetic energy in the basic model. Weak intermolecular attractions then have less relative influence on the particles’ trajectories and on gas condensation under suitable conditions.
High temperature improves the ideal approximation when the gas is not simultaneously being compressed into an extreme density. The correct statement is a trend under relevant conditions, not that high temperature turns real particles into dimensionless points.
What happens at very high pressure
Compressing a gas brings molecules closer together. Finite molecular sizes and short-range repulsion become important, making the point-particle assumption less reliable. At sufficiently high density, excluded-volume effects can drive real pressure above the ideal prediction at the same amount, volume and temperature.
Intermolecular attractions can also play a role, especially at less extreme pressures. Do not claim every high-pressure gas automatically has greater pressure than its ideal counterpart without knowing the actual regime.
What happens at very low temperature
Cooling decreases molecular kinetic energy relative to attractive interactions. Molecules can influence one another more strongly and may be able to condense under suitable conditions, behaviour excluded by the attraction-free ideal model.
Attractions can lower real pressure relative to a simple ideal prediction in some regimes. However, the sign and magnitude of deviation depend on both temperature and density. Near condensation, a single-gas-phase treatment may fail.
Attraction and finite size have competing effects
Attractive interactions can pull molecules toward one another and reduce pressure contributions compared with noninteracting particles. Excluded volume and short-range repulsion can increase pressure when molecules are crowded.
The effects compete, so real-gas deviations are not always in the same direction. For H2 qualitative questions, identify both omitted effects and explain which pressure or temperature condition makes them important.
An ideal gas cannot itself form an ordinary liquid
A pure mathematical ideal gas contains no attractions between molecules. Without attractions, it cannot model the ordinary liquid phase produced when gas molecules become bound together. Real gases can condense when temperature and pressure favour that state.
If a question involves gas and liquid simultaneously, pV=nRT cannot be applied indiscriminately to the total amount of material as though it were entirely gaseous. Identify the phase and the quantity to which the approximation applies.
A worked pressure calculation
Suppose an ideal 0.0500 mol gas sample is held at 300 K in 2.00 dm³. Convert volume to 0.00200 m³, then calculate p=nRT/V=0.0500×8.31×300/0.00200≈62,300 Pa, or 62.3 kPa.
This is a model prediction under the stated conditions. Without a gas identity and real-gas measurements, one should not invent a numerical correction to the result.
The volume conversion that catches students
One dm³ is 0.001 m³ and one cm³ is 0.000001 m³. Thus 250 cm³ is 2.50×10⁻⁴ m³. Using 250 as though it were a cubic-metre figure introduces a millionfold error into an SI ideal-gas calculation.
Write the volume unit on the substitution line and check that pV and nRT have compatible energy dimensions. These small checks are often more valuable than repeating a calculator operation.
Celsius cannot be used as an absolute ratio
A sample at 27°C is approximately 300 K. If a rigid ideal gas warms from 300 to 330 K at unchanged amount and volume, its pressure increases by the factor 330/300=1.10.
Do not divide Celsius values to predict pressure ratios. The kinetic temperature scale begins at absolute zero, so proportional gas-law relationships need kelvin.
Gas density and Mᵣ
For a pure ideal gas, n=m/M and density ρ=m/V. Combining with pV=nRT gives M=ρRT/p. This allows a molar mass to be estimated from measured gas density, temperature and pressure under appropriate ideal assumptions.
If density is kg m⁻³ with SI units, molar mass is returned in kg mol⁻¹ and can be converted to g mol⁻¹. The distinction matters when comparing with molar masses from the periodic table.
Worked density-to-molar-mass calculation
Suppose a fictional pure ideal gas has density 1.60 kg m⁻³ at 100,000 Pa and 300 K. Then M=(1.60×8.31×300)/100,000≈0.0399 kg mol⁻¹, or 39.9 g mol⁻¹.
The inferred M is compatible with a gas near 40 g mol⁻¹, but the numerical value alone does not prove unique chemical identity. The purity assumption matters.
A gas sample with known mass and volume
A fictional 0.400 g gas sample occupies 250 cm³ at 100 kPa and 300 K. The ideal amount is n=pV/(RT)=100,000×2.50×10⁻⁴/(8.31×300)≈0.0100 mol, giving M≈40.0 g mol⁻¹.
This result agrees with the previous density method because the mass and volume imply the same density. The two formulas are equivalent rearrangements, not different physical laws.
Gas mixtures and Dalton’s Law
A sample containing several gas species has total pressure from the sum of component partial pressures in the ideal mixture model. A density-based calculation may give an average molar mass rather than a single molecule’s formula mass.
To identify individual component pressures, use their mole fractions. Treating the mean molar mass of an air mixture as one molecular identity is an error in interpretation, not simply arithmetic.
Gas collected over water
If a gas is collected above water, the vapour in its gas space contributes to total pressure. For an ideal mixture, pTotal=pDryGas+pWaterVapour. A fictitious total 101.3 kPa with water-vapour pressure 3.2 kPa leaves dry-gas pressure 98.1 kPa.
Using total wet pressure as the intended dry gas’s own pressure overestimates the dry amount. Apply the correct water-vapour value for the specified temperature.
Why gas identity matters
Helium has weak induced-dipole attractions compared with many larger or strongly polar molecules under comparable conditions. Water vapour can exhibit stronger intermolecular interactions, particularly near condensation. Such differences affect the quality of an ideal approximation.
However, chemical identity alone is not enough: pressure, temperature, phase and density are still essential. No element or molecule is guaranteed to behave exactly ideally under all physical conditions.
A qualitative H2 answer template
At very high pressure, molecules approach closely, so their finite volume and intermolecular interactions are no longer negligible. At very low temperature, average kinetic energy is smaller and attractions become comparatively significant, sometimes leading toward condensation.
At low pressure and high temperature, these neglected effects generally diminish in relative importance, so real gases can approach ideal behaviour. This links the named condition to the underlying physics.
What a real experimental discrepancy means
A measured real gas pressure may differ from the ideal prediction because of genuine intermolecular forces and particle size. It may also differ because of a leaking apparatus, incorrect temperature, moisture or inaccurate volume measurement.
An H2 evaluation should distinguish model limitation from measurement error using the available evidence instead of treating any discrepancy as proof the experiment was careless.
Three common concept mistakes
Error one: ‘Molecules have no volume in real life.’ They do; only the ideal approximation neglects it. Error two: ‘At high pressure attractive forces disappear.’ They do not; close proximity makes molecular interactions more relevant. Error three: ‘The real pressure is always below ideal.’ Excluded-volume effects can reverse the direction.
A tutor should ask what physical condition the student is describing and whether attractions or repulsions are likely to matter, not accept memorised slogans.
A week of short targeted practice
Start with kinetic assumptions, then write an explanation of low-pressure ideality. Next compare high pressure and low temperature in different diagrams of particle separation and energy. Follow with two pV=nRT questions, including one molar mass calculation.
Finally tackle a mixed wet-gas problem and one data-based question where a real measurement differs from ideal behaviour. Record whether each error is conceptual or a unit conversion.
A three-student tutorial approach
One student may know the physics but make Kelvin errors, another may calculate correctly but claim every real gas has lower pressure, and a third may use wet-gas total pressure for the dry product. These require different independent follow-up questions.
eduKateSG’s premium model offers three-student, 1.5-hour weekly tutorials at 8 Fourth Avenue, Singapore 268674, near Sixth Avenue MRT, not in Hougang. Families should confirm the actual group, tutor, fees and travel.
Frequently asked questions
Does high pressure always make pReal greater than pIdeal? Not necessarily across all conditions; interactions compete. What are the two main ideal-gas assumptions? Negligible molecular volume and intermolecular forces. Why does low temperature matter? Attraction can become important relative to kinetic energy.
Can the model give Mᵣ? Yes with suitable pressure, volume, temperature and amount or density information. Does the 2027 H2 syllabus prescribe this topic? Yes, Section 3(a–d), including qualitative deviations.
An initial-rate question is not a gas-law question
An increase in gas pressure can reflect a greater number of gas molecules, a higher temperature or a smaller volume. It does not by itself tell how quickly a chemical reaction is taking place. Pressure is a state variable; reaction rate describes change with time.
If a chemical reaction produces gas, a pressure–time graph can support a kinetic analysis under appropriately controlled volume and temperature. But a static pV=nRT calculation uses the amount present at one state. Combining these ideas requires distinguishing a quantity from its gradient.
A student should label whether the examination is asking for final pressure, change in pressure or rate of product formation before selecting a formula.
The ideal limit does not set intermolecular force to zero in reality
Real molecules always have electron clouds capable of dispersion interactions. Saying a gas ‘approaches ideal behaviour’ does not mean the molecules physically lose those interactions. It means their effect on the observed pressure-volume relationship becomes small enough relative to the other conditions.
At sufficiently dilute conditions, a real gas may be described accurately by a simple ideal approximation even though the underlying molecules have nonzero size and intermolecular attraction. That is the difference between a physical model and a literal description of matter.
This language is important for scientifically honest H2 answers: ‘intermolecular forces are negligible’ is context-specific, while ‘there are no intermolecular forces’ is generally false for real particles.
What the pressure of a mixture does not show
If nitrogen and oxygen share a container, both contribute to the total pressure under the ideal-mixture model. A high total pressure may arise because the mixture contains many molecules; it does not uniquely identify whether any one gas has strong attractions.
To calculate a particular species partial pressure, use Dalton’s Law and its mole fraction. To discuss whether the overall mixture is ideal, inspect the temperature, pressure and interaction assumptions. These are separate questions even when they use the same pressure unit.
A learner who substitutes total pressure for an individual gas in a partial-pressure or chemical equilibrium expression is confusing the state of the mixture with a component’s contribution.
A graph of pressure against inverse volume
For a fixed ideal amount at fixed temperature, p=nRT(1/V). Thus pressure plotted against inverse volume is a straight line through the origin under the mathematical model, with gradient nRT. This is an alternative representation of Boyle’s Law.
A real-gas dataset may not follow a perfect straight line over a wide pressure range. Departures can indicate the influence of particle size or interactions, though the particular experimental method and uncertainties still need evaluation.
If a question provides measured values, plot the stated quantities and compare the actual trend with the ideal prediction rather than assume a straight line simply because the equation is familiar.
How to distinguish an excluded-volume effect
Imagine a gas compressed until molecule-to-molecule separation becomes similar to molecular dimensions. The total physical space available for the centres of molecules is reduced by their finite size. The ideal model’s assumption that molecules occupy no volume then becomes poor.
A useful analogy is packing balls into a box: even if balls are free to move, they cannot occupy the same location. This analogy explains the size effect but should not be stretched into a claim that all gas molecules are rigid macroscopic spheres.
The H2 answer should mention molecular volume and crowding, not merely ‘more collisions’ without identifying what the ideal law neglected.
How to distinguish an attraction effect
Two nearby molecules can exert attraction due to their electron distributions. In the right pressure-temperature range, these attractions change how molecules approach the walls and one another, contributing to a measured deviation from noninteracting kinetic predictions.
At low temperature, attractions can become more significant compared with thermal motion. Condensation can become possible, but the onset depends on actual pressure and the chemical species.
The helpful explanation is not ‘cold makes molecules stick permanently’. Instead say the attractive interactions can increasingly influence a real gas as its kinetic energy falls.
Why a real gas can have Z below one
The optional compressibility factor Z=pV/(nRT) can be below one when the real measured pV is less than the ideal reference at the same amount and temperature. Attractive interactions can account for this in a suitable physical regime.
Suppose a hypothetical state has pV=950 J and nRT=1,000 J. Z=0.950. This demonstrates a five percent deviation below the ideal reference; it does not uniquely prove that the only microscopic cause is attraction.
The 2027 syllabus does not demand memorising advanced equations of state, so students can use this enrichment as a way to think about observed data rather than as an extra compulsory formula.
Why a real gas can have Z above one
When excluded-volume and short-range repulsion become important at a sufficiently high density, measured pV can exceed nRT in a real system. In the same optional Z notation, the ratio is above one.
For a fictional pV=1,100 J and nRT=1,000 J, Z=1.10. The state is ten percent above the ideal reference. It would be unsupported to claim every real gas at every high pressure has this exact direction or magnitude.
A student should describe the competitive effects honestly and use supplied data when the question requests a sign.
A fixed-volume pressure calculation with measured deviation
Consider a fictional ideal prediction of 200 kPa at a specified volume, amount and temperature. A real measurement yields 190 kPa in one trial. The absolute difference is 10 kPa, and the relative deviation from the ideal prediction is (190−200)/200×100=−5.0%.
The negative sign means the measured pressure is lower than the reference prediction, not that the pressure itself is negative. A corresponding Z-like ratio of measured to ideal pressure at the same n, T and V would be 0.950.
The calculation can establish the deviation numerically; further experimental evidence is required to decide whether attraction, apparatus error or an unstated condition caused it.
A second fixed-volume deviation calculation
Now suppose a different hypothetical real gas at the same named ideal reference pressure of 200 kPa is measured at 230 kPa. Its percentage deviation is (230−200)/200×100=+15%.
The difference demonstrates why a prediction about deviation direction should be tied to a real dataset or chemical conditions. The two samples cannot be described by the same simple unqualified correction factor merely because both are gases.
A student who writes ‘high pressure always gives a negative deviation’ should be challenged with this changed case and asked to identify the missing assumptions.
Gas compressibility is not a chemical reaction
Strongly compressing a gas changes physical spacing and pressure; it does not automatically break molecules into atoms or change their chemical formulas. Finite-size effects and attractions are physical intermolecular phenomena under the gas-state topic.
If a reaction or decomposition is also occurring, the number of gas particles may change, requiring stoichiometry before a gas-law calculation. These are separate causes of pressure change and may coexist in a real system.
A student should not invoke bond breaking to explain routine nonideality unless the question actually supplies evidence of a chemical change.
The wrong use of a molar gas volume shortcut
Some chemistry problems supply an approximate gas molar volume such as 24.0 dm³ mol⁻¹ at a specified temperature and pressure. It cannot be applied automatically at all pressures and temperatures because the gas volume per mole changes with state.
At high pressure and low temperature, real-gas deviations can make a fixed shortcut especially inappropriate. When the question gives actual p, V and T, pV=nRT under its stated ideal assumption is safer than a memorised volume from another condition.
Always check whether the molar volume is provided as a reference datum and whether the gas is assumed to behave ideally.
The mass of a gas sample stays the same under physical compression
If a sealed gas cylinder is compressed mechanically without gas entering or leaving and no chemical transformation occurs, its gas mass and mole amount remain fixed. Pressure can rise while the same number of particles occupies less space.
Students sometimes infer that a higher pressure automatically means more moles. That is true only if volume and temperature conditions are also controlled appropriately; in a fixed-amount compression, pressure rises without increasing n.
Write which of n, T and V is held constant before interpreting a pressure observation.
Pressure can rise because temperature changed
At fixed amount and volume, ideal p is proportional to T. If a sealed ideal system changes from 300 K to 360 K, the predicted pressure multiplies by 1.20. That increase is not evidence of new gas being produced.
A real gas near high density may not follow the exact proportion, but the same basic state variables still need consideration. A temperature measurement error can masquerade as a discrepancy between measured and predicted pressure.
A good evaluation checks thermal equilibration of the gas before using a measured pV dataset.
An isothermal compression exercise
A fictional ideal sample at 100 kPa and 2.00 dm³ is compressed isothermally to 0.500 dm³. Since p₁V₁=p₂V₂ under the ideal fixed-n, fixed-T model, p₂=100×2.00/0.500=400 kPa.
If measured real pressure were 425 kPa, it would exceed that prediction by 25 kPa, or 6.25%. The calculation does not identify which interaction dominates, but it quantifies the difference.
This exercise connects ordinary algebra to a careful physical distinction between ideal reference and real observation.
A comparison between a gas molecule and a noble-gas atom
A monatomic gas such as argon consists of individual atoms, but these still have electron clouds and dispersion attractions. A diatomic gas such as nitrogen contains bonded atoms, and its molecules also have finite size and intermolecular interactions.
Being monatomic does not make a gas truly ideal, just as having a polar bond does not automatically make the gas strongly nonideal in all circumstances. Chemical identity affects interactions, but state conditions determine their importance.
The same ideal kinetic principles can be applied to many kinds of gas under suitable approximations.
Why a large heavy molecule may deviate more
Larger molecules often have more polarisable electron clouds and stronger dispersion attractions than small species, under comparable relevant conditions. Their physical sizes may also be more significant when crowded.
This can contribute to greater nonideal behaviour, but mass alone is not the full explanation. Molecular shape, polarity, temperature and density matter. A student should not simply rank real-gas deviations by relative molecular mass with no interaction reasoning.
The important links to the bonding chapter are induced-dipole attraction and physical size.
A small helium versus water-vapour comparison
Helium has comparatively weak intermolecular attractions, while water vapour contains strongly polar molecules that can hydrogen bond under suitable environments. This helps explain why their tendencies toward condensation and deviations can differ.
Even so, comparing them requires appropriate matched temperatures and pressures. A description that omits state conditions may be too vague to justify a precise ranking.
Use the case as a conceptual illustration, not as evidence that helium is always perfectly ideal or that water vapour always behaves as a liquid.
A worked mole-ratio check
Take a sample whose ideal gas-law calculation gives 0.0200 mol at specified pressure, volume and temperature. If the sample is pure oxygen O₂, it contains 0.0200 mol oxygen molecules and 0.0400 mol oxygen atoms.
If a learner mistakenly uses 0.0400 mol in pV=nRT for an undissociated oxygen gas, the predicted pressure doubles incorrectly. The gas law counts independently moving gas molecules in this case, not the individual atoms bonded inside them.
This connects the gaseous-state chapter with the mole concept and prevents a subtle particle-counting error.
A final checklist for H2 questions
Start by writing the real physical state and whether the question explicitly assumes ideal behaviour. For conceptual explanation, identify particle spacing, finite size, attractive forces and relative kinetic energy. For calculations, confirm p, V, n, R and T units.
After calculating, check whether the inferred result is the amount of gas molecules, average mixture molar mass or a pure substance’s molar mass. Do not use a wet total pressure when a dry component is required.
The central lesson is that sound Chemistry starts with what is present and what assumptions apply, not just which formula looks familiar.
Related JC1 Chemistry learning
Dalton’s Law and partial pressures · Gas collected over water · H2 Chemistry mathematics · Intermolecular forces · Counting molecules and moles
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