“Kelvin or nothing”
Every gas law
Every gas calculation needs absolute temperature. Using °C in Charles's law is the single most common error in the chapter.
Chemistry, Class 11 and 12 · Gujarat Board, CBSE, GUJCET, JEE and NEET
States of Matter and Gas Laws formulas
The gas laws are the most formula-dense part of Class 11 chemistry, and the most predictable. Almost every question is one of the named laws or the ideal gas equation, and the deviations at the end supply the theory mark.
16 formulas, 3 memory hooks, and the 5 mistakes that cost the most marks.
The named laws
| What | Formula | Symbols and notes |
|---|---|---|
| Boyle's law | p₁V₁ = p₂V₂ | at constant temperature and amount |
| Charles's law | V₁/T₁ = V₂/T₂ | at constant pressure; T in kelvin |
| Gay-Lussac's law | p₁/T₁ = p₂/T₂ | at constant volume |
| Combined gas law | p₁V₁/T₁ = p₂V₂/T₂ | the three above in one line |
| Avogadro's law | V ∝ n | equal volumes hold equal numbers of molecules |
The ideal gas
| What | Formula | Symbols and notes |
|---|---|---|
| Ideal gas equation | pV = nRT | R = 8.314 J mol−1 K−1 = 0.0821 L atm mol−1 K−1 |
| In terms of density | pM = ρRT | a quick way to find molar mass from density |
| Dalton's law of partial pressures | ptotal = p₁ + p₂ + … | for non-reacting gases |
| Partial pressure from mole fraction | pi = xi × ptotal | the most used form of Dalton's law |
| Graham's law of diffusion | r₁/r₂ = √(M₂/M₁) | lighter gases diffuse faster |
Real gases and speeds
| What | Formula | Symbols and notes |
|---|---|---|
| van der Waals equation | (p + an²/V²)(V − nb) = nRT | a corrects for attraction, b for molecular volume |
| Compressibility factor | Z = pV/nRT | Z = 1 for an ideal gas |
| Root mean square speed | urms = √(3RT/M) | M in kg per mole |
| Average speed | uav = √(8RT/πM) | slightly less than urms |
| Most probable speed | ump = √(2RT/M) | the smallest of the three |
| Critical temperature | above Tc a gas cannot be liquefied | however great the pressure |
Taught by Darshit Bhatt, founder and lead faculty at Darshit Sir Institute. Instrumentation and Control engineer, with a master's degree and a chartered degree, teaching in Paldi, Ahmedabad since 2006.
Know the formula but not when to use it?
Darshit Sir has taught this in Paldi since 2006, in the classroom and live online.
Memory hooks
How to remember this chapter.
“Light gases are quick”
Graham's law
Rate goes as one over the square root of molar mass. Hydrogen diffuses four times faster than oxygen, because 32 over 2 is 16 and its square root is 4.
“a for attraction, b for bulk”
The van der Waals constants
a corrects the pressure for intermolecular attraction; b corrects the volume for the space the molecules themselves take up.
Where marks go
The mistakes that cost the most.
- Using °C anywhere in a gas law. Kelvin only.
- Mixing units of R. Use 0.0821 with litres and atmospheres, 8.314 with cubic metres and pascals.
- Using grams per mole for M in the speed formulas, which need kilograms per mole.
- Applying the ideal gas equation at high pressure and low temperature, where real gases deviate most.
- Forgetting that Dalton's law needs the gases not to react with each other.
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