Chemistry IA · Structure 1 · Models of the particulate nature of matter · topic 4 of 25

Real gases: how far from ideal? · IB Chemistry IA idea: guide, sample graph and step-by-step plan

a database IA done properly: good choice

The ideal gas law is in every exam. You're going to find out exactly where it stops being true, and by how much.

Difficulty●●○ Medium
KitComputer only: NIST WebBook (or similar), spreadsheet
TimeAbout 10 hours
FitsSL and HL (van der Waals: introduce it yourself)
  • ✓ you like spreadsheets and data
  • ✓ you want to test a model, not just use it
  • ✓ you would rather skip the wet lab

The big idea

← this is your RQ hook!

The ideal gas model treats particles as points with no forces between them. Real gases have size and attractions, so the compressibility factor Z = PVₘ/RT drifts away from 1 as pressure rises. Attractions pull Z below 1, particle size pushes it above 1, and which one wins depends on the gas and the conditions. Your job: get Z from database densities, see how it changes, and test how much of that the van der Waals model explains with just two constants. A clear prediction, real processing and a model to evaluate.

Make it yours: pick one twist

Copying a classic won't show your choices. Pick one of these (or invent your own) and your IA becomes yours.

Swipe for more twists →

Add helium or hydrogen

Repeat for a gas with very weak attractions.

→ Z may rise above 1 instead of falling, so the particle-size term wins. Your explanation now needs both effects.
Change the temperature

Repeat one gas at three temperatures, say 250, 300 and 400 K.

→ The shape of Z against P changes. Check each gas stays gaseous at every point you choose.
Compare three models

Plot ideal, van der Waals and database values together.

→ Your graph has three lines, and the evaluation becomes a judgement of which model fails first, and why.
Fit the constants yourself

Use a spreadsheet solver to find the values of a and b that best fit your Z data.

→ Adds a fitting step with an uncertainty. Your conclusion compares fitted constants with tabulated ones.
Plot against density

Plot Z against amount density (mol L⁻¹) instead of pressure.

→ The low-density part is close to straight, and its gradient links to size and attraction. Different graph, same data.
Give it a purpose

Frame it around a high-pressure gas cylinder: how much gas does it really hold compared with the ideal prediction?

→ A real reason for the introduction. Make sure your pressure range matches the context.

Your Chemistry IA research question: run the check

Write your own question first. Then make sure it ticks every box:

  • Names the independent variables: the pressure range in bar (with step and number of values) and which gases.
  • Names the dependent variable, Z, and how it is worked out: which tabulated quantity, which formula, which units.
  • Fixes the temperature, and says how you checked that no gas liquefies anywhere in your range.
  • Says which model you compare with, and where its constants come from.
  • Is narrow enough: one temperature, three gases, 8 to 12 pressures, one data source for everything.

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The set-up

A database investigation has an apparatus too: where the numbers come from and how they become Z. Sketch yours with your real choices.

densityP / barρ / mol L⁻¹NIST WebBook, isothermal tableZ = P Vₘ / R TVₘ = 1 / ρT = 300 K, held fixedone source, one T, all three gasesunits: bar, L, mol, K together

How your Chemistry IA could be laid out

The usual order for a topic like this, what each part needs to show, and roughly how much of your 3,000 words it takes. The words are all yours.

Research question and context~250
Your question; where real gases matter (storage cylinders, industry); what you predict for each gas and why.
Background chemistry~450
The ideal gas assumptions; what Z measures; the van der Waals model and what each constant stands for; what your graph should look like if the model works.
Data source and selection~300
The database, the exact table used, the temperature, the pressure range and step, why these gases, and how you checked every state is a gas.
Variablestable
Independent, dependent and controlled variables, each with how it is chosen or held constant (one source, one temperature) and its units.
Safety, ethics, environment~60
No lab hazards, so say so. Data ethics: cite the table and its date, keep every value you collected, and say how you handled any point you rejected.
Raw datatable
One clear table per gas: pressure and tabulated density, with units and the source's stated precision.
Processing~250
The conversion to molar volume and then Z, one worked example with units, and how the uncertainty in Z follows from the precision of the table.
Graphs and analysis~400
Z against P for each gas with the ideal line and the model line; what the shape says about forces; how you measure the gap between model and data.
Conclusion~400
Answer with numbers: how Z changes with P for each gas, which deviates most, how far the model follows the data. Stay inside your range.
Evaluation~600, the biggest part!
Limits of the model (what it ignores), the precision of the data, the range and temperature; weaknesses ranked, with improvements linked to each.
Referencesnot counted
Every source for data, constants and theory, with the table date.

What your Chemistry IA graph could look like

draw the ideal line too ✓

Made-up data, to show you the form of a strong graph, not the answer. Yours will use your gas, your temperature and your source. example only

051015202530354045500.600.650.700.750.800.850.900.951.001.051.10Pressure P / bar (from the table)Compressibility factor Z (± 0.01)van der Waals modelideal gas, Z = 1database values, with error barsthe gap grows with pressure:is it bigger than the error bars?ILLUSTRATIVE · MADE-UP DATA
  • Z = 1 is the ideal gas. Draw it, so the reader sees the deviation.
  • Data and model on one graph, with error bars on the data.
  • The scale starts at 0.60, not zero, so the deviation is visible. Say so in the text.
  • If the data sit away from the model by more than the error bars, say so and explain what the model leaves out.
  • Another graph to consider: Z against amount density. At low density it is close to straight, and its gradient relates to the size and attraction terms.

Your game plan

trial run on ONE gas first

Tick steps off as you go. We'll remember on this device.

0 of 11 done

  1. Read and predictRead about the ideal gas assumptions and the compressibility factor. Before opening any data, write down what you predict for Z of each gas as pressure rises, and why one gas should deviate more than another.
  2. Trial run (1 lesson)Pull one isothermal table for one gas. Which columns are given, in what units, to how many figures? Work out Z for two rows by hand. Is it close to 1 at the lowest pressure? If not, check your units.
  3. Choose temperature, range and gasesPick the temperature, at least 8 pressures and your gases. Check every point is gas, not liquid. Decide which model constants you will use, and where from.
  4. CollectCopy each table into its own sheet, with the source and date. Keep the raw sheet untouched and do all processing on a copy.
  5. ProcessBuild the Z column with formulas. Convert units once, in labelled cells. Decide how you will estimate the uncertainty in Z from the table's precision.
  6. ModelCalculate Z from the van der Waals equation at the same pressures. Check that it agrees with the data at the lowest pressure before you trust it elsewhere.
  7. Graph and comparePlot data and model with error bars. Decide how you will measure the gap (difference, percentage difference) so that it answers your question.
  8. InterpretLink the shape to attractions and size. Where does the model hold and where does it fail? Is the gap bigger than your uncertainty?
  9. EvaluateRank the weaknesses: data precision, model limits, range, one temperature. Make every improvement specific to one of them.
  10. Write, then cutWrite in the order of the layout above. Tables, calculations, graphs and references are not counted, so let them carry the detail.
  11. Check before your teacher's draftRun the checklist, then get your RQ or draft checked. Your teacher reads one draft only, so make it count.

Chemistry you'll need

Traps to avoid in this Chemistry IA

  • A gas that liquefies in your range: carbon dioxide at 300 K gets close to its liquefaction pressure (the 60-odd bar region), so some 'gas' rows may really be liquid.
  • Unit mix-ups between bar, kPa, litres, cubic metres, moles and kilograms, so Z comes out wildly wrong. A quick check: Z must be close to 1 at the lowest pressure.
  • Mixing data from different sources, so some of the 'deviation' is just disagreement between the sources.
  • Using van der Waals constants from a different unit system (atm against bar, litres against cubic metres) as if they were interchangeable.
  • Explaining Z below 1 as 'attractions' and never explaining a case where Z is above 1.
  • Quoting Z to six figures when the density in the table has three or four.
  • An evaluation that says 'the database might be wrong' without comparing the data's stated precision with the size of the effect.

More Chemistry IA ideas like this

Make sure it's yours

This guide shows how a topic like this is usually approached. It is not an IA. Your question, choices, data, analysis and words must be your own: change something, tell your teacher where the idea came from, and follow your school's rules on outside help.

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