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Gas-law questions look easy, and that is the trap. The ideas fit on one line, so students rush, put temperature in Celsius or mix litres with pascals, and lose marks they should have kept. This post works through the core problem types: one gas changing state, a mixture of gases, and diffusion. It points out where the usual mistakes happen and ends with a short practice plan.
Which exams test the gaseous state?
The JEE (Advanced) 2026 information brochure lists "States of Matter: Gases and Liquids" in chemistry, covering gas laws, the ideal gas equation, deviation from ideality and the van der Waals equation, the law of partial pressures and diffusion of gases. The JEE (Main) 2026 syllabus and the NEET (UG) 2026 syllabus from the NMC have no separate states-of-matter unit in chemistry. Both list "equation of state of a perfect gas" under kinetic theory of gases in physics, though, and pV = nRT comes up all through chemistry: the NCERT chapter on equilibrium uses it to convert Kc into Kp. The current NCERT Class 11 Part I contents no longer list a states-of-matter unit. Check the current year's syllabus before you plan.
Why do the units matter so much?
pV = nRT works in any unit system as long as R matches the units you use. The CODATA value of the molar gas constant, published by NIST, is 8.314462618 J per mol per kelvin. Since 1 L bar equals 100 J, the same constant is 0.08314 L bar per mol per kelvin. Pick one set and stay with it:
SI: p in pascals, V in cubic metres, R = 8.314. Remember that 1 L = 0.001 m³.
Chemist's set: p in bar, V in litres, R = 0.08314.
Temperature is always in kelvin: add 273.15 (or 273) to Celsius.
The molar volume is another trap. NIST gives the molar volume of an ideal gas at 273.15 K and 100 kPa as 22.711 L, and at 273.15 K and 101.325 kPa as 22.414 L. If a question says 1 bar, 22.4 L is the wrong number. If it gives no conditions, use pV = nRT directly.
Worked example 1: one gas changing state
A gas occupies 2.50 L at 27 °C and 1.00 bar. What is its volume at 127 °C and 2.00 bar?
The amount of gas is fixed, so p₁V₁/T₁ = p₂V₂/T₂.
Convert temperatures: T₁ = 300 K, T₂ = 400 K.
V₂ = V₁ × (p₁/p₂) × (T₂/T₁) = 2.50 × (1.00/2.00) × (400/300) = 1.67 L.
Check it makes sense. Doubling the pressure halves the volume; heating from 300 K to 400 K raises it by a third. The answer is a little below the starting 2.50 L, as it should be.
The common mistake: using 127/27 instead of 400/300 gives 5.88 L, more than double the start volume after compression. Any answer that moves the wrong way is your signal to check the temperatures.
Worked example 2: Dalton's law of partial pressures
A 10.0 L flask at 300 K holds 4.0 g of helium and 16.0 g of oxygen. Find the total pressure and each partial pressure.
Moles: He = 4.0/4.0 = 1.00 mol; O₂ = 16.0/32.0 = 0.500 mol. Total n = 1.50 mol.
Total pressure: p = nRT/V = 1.50 × 0.08314 × 300 / 10.0 = 3.74 bar.
Mole fractions: He = 1.00/1.50 = 0.667; O₂ = 0.333.
Partial pressures: He = 0.667 × 3.74 = 2.49 bar; O₂ = 0.333 × 3.74 = 1.25 bar. They add up to 3.74 bar.
The common mistake: splitting the pressure by mass. Oxygen is 80% of the mass here but only a third of the moles, so it supplies only a third of the pressure. Partial pressure follows moles, because each molecule hits the walls regardless of how heavy it is.
To check the units, redo step 2 in SI: p = 1.50 × 8.314 × 300 / 0.0100 = 374,000 Pa, which is 3.74 bar. The same answer tells you the conversions were right.
Worked example 3: Graham's law of diffusion
At the same temperature and pressure, the rate of diffusion is inversely proportional to the square root of molar mass. How much faster does helium diffuse than oxygen?
Rate(He)/Rate(O₂) = √(32/4) = √8 = 2.83. Helium diffuses about 2.8 times faster.
The common mistake: putting the masses the wrong way up. The lighter gas must come out faster, so the ratio for He over O₂ must be greater than 1.
Why can you solve these and still not understand gases?
Chemistry teachers have long assumed that a student who can solve gas problems understands the molecules behind them. Nurrenbern and Pickering (1987) set out to test whether that assumption holds, and Sawrey (1990) revisited the question, concluding that being able to solve a numerical problem does not mean a student understands its molecular basis. For you, that means also practising questions with no numbers: what happens to the particles when you heat a sealed flask, or why a lighter gas spreads faster. Our post on the kinetic theory of gases covers the particle picture.
When you get a gas problem wrong and cannot see why, the Fermi Problem Library has worked problems with a step-by-step solver that explains the reasoning rather than printing an answer, so you can find the exact line where your units went wrong.
A practice routine for the gaseous state
Day 1: Ten one-gas problems. Write units beside every number before solving.
Day 2: Eight mixture problems using partial pressures and mole fractions, including two where you collect a gas over water.
Day 3: Four diffusion problems and four conceptual questions with no numbers.
Day 4: A mixed, timed set of twelve. Mark each error as units, temperature, mass-instead-of-moles or concept.
A week later: Redo only the questions you got wrong.
Tonight, take one gas problem you have already solved and redo it in the other unit set; if both answers match, your conversions are sound.
