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Section III · Topic guide

Gas laws

Section III — Sciences · a free, hand-written guide with worked reasoning and adaptive practice that finds your weak spots.

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The short answer

The ideal gas law PV = nRT and the relationships behind it — with the Kelvin trap.

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Try the reasoning style

Section I · Humanities & Social SciencesIllustrative example

We treat forgetting as a failure — a lapse to be patched with reminders and records. Yet a mind that kept everything could not think; it would drown in the undifferentiated noise of every moment it had ever lived. To forget is not so much to lose information as to decide, mostly without our noticing, what was never worth keeping.

The author's argument relies most directly on which unstated assumption?

Pick an option to see how the tutor reasons to the answer — not just whether you were right.

How to reason to the answer

Not quite — the answer is B.

Work backwards from the conclusion: a mind that ‘kept everything’ supposedly ‘could not think.’ That only follows if thinking means leaving most of experience out — so B is the premise the argument quietly rests on. A raises reliability, which the passage never weighs; C contradicts ‘mostly without our noticing’; D smuggles in a claim about intellect the passage never makes. The question rewards finding the hidden premise, not recalling a fact.

Gases are wonderfully predictable: squeeze one and its pressure rises; heat it and it expands. The ideal gas law, , captures all of it, and the simpler gas laws are just special cases where you hold one variable fixed.

The Organic Chemistry Tutor — Boyle's, Charles', and the ideal gas law.

One master equation

— pressure × volume = moles × gas constant × temperature. The individual laws follow by holding things constant: Boyle's ( at fixed T), Charles' ( at fixed P), Gay-Lussac's ( at fixed V).

Always use Kelvin

Temperature in gas-law calculations must be in Kelvin (). Using Celsius gives nonsense — for example, "doubling" from 1 °C to 2 °C is almost no change in absolute terms, but 274 K to 548 K is a real doubling. This is the single most common gas-law mistake.

The simple gas laws (fix one variable)

Boyle's law (constant T)

  • Squeeze the volume → pressure rises

Charles' law (constant P)

  • Heat the gas → it expands
  • (T in Kelvin)

Worked example

A gas occupies 6 L at a pressure of 2 atm. If the temperature is constant and the pressure is increased to 3 atm, what is the new volume?

Check yourself

At constant pressure, the absolute (Kelvin) temperature of a fixed amount of gas is doubled. What happens to its volume?

Key takeaways

  • Ideal gas law: .
  • Boyle's: (constant T). Charles': (constant P).
  • Always convert temperature to Kelvin (K = °C + 273).
  • Squeezing volume raises pressure; heating raises volume (or pressure).
  • The simple laws are just PV = nRT with one variable held fixed.

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