What a learner can do afterwards
- Reads a compression factor plot and says where attraction dominates and where repulsion does
- Explains what each term of the van der Waals equation is correcting
- Defines fugacity as an effective pressure and activity as an effective concentration, and states the standard state each refers to
- Says which measurements go wrong if activities are replaced by concentrations in a concentrated solution
- Reads a Z chart plotted against reduced pressure and reduced temperature and says why one chart serves many gases
1 · Read
Gas tanks and pipes push gases far from ideal behaviour, so chemists track the gap with the compression factor Z through Z = PV over nRT. Where attraction dominates, molecules pull closer and Z dips below 1. Where size dominates, Z climbs above 1.
Take 1.00 mol at 400 K in a 0.0300 cubic metre tank at 100000 Pa. First nRT is 1.00 times 8.314 times 400, which is 3325.6 J. Then PV is 100000 times 0.0300, which is 3000 J. Divide 3000 by 3325.6 and Z is about 0.90, so attraction is winning at this state.
The van der Waals equation corrects both faults: one term for attraction pull, one for occupied space. Fugacity is the effective pressure that keeps the ideal equations working for real gases, and activity is the effective concentration for solutions, each measured against its standard state. You met the chemical potential sliding with the log of a fraction in an ideal mixture; in real gases and solutions it slides with fugacity or activity instead.
In concentrated solutions, swapping activities for plain concentrations corrupts equilibrium constants and cell potentials. At very high pressure almost every gas tops 1 as packed size resists squeeze. Near the critical point both faults act at once, so Z swings furthest from 1 there. Reduced pressure and temperature divide by critical values, so one Z chart fits many gases.
Read Z to see which fault wins, then use fugacity and activity to keep the old equations honest.
2 · Watch
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Where it sits
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.