Subtopics - Gaseous State (NEET)
Nine topic blocks: four gas laws (Boyle, Charles, Gay-Lussac, Avogadro), ideal gas equation with gas constant R and Boltzmann constant, deviation from ideality and compressibility factor, Van der Waal's equation with virial reduction, kinetic theory of gases with the kinetic gas equation, molecular velocities (RMS, average, most probable) and kinetic energy, Dalton's law of partial pressure with Amagat's law, Graham's law of diffusion and effusion, and the critical state with critical constants.
1) Gas Laws
Four fundamental laws relating pressure, volume, temperature, and amount of gas. Boyle's Law: V is inversely proportional to P at constant T (PV = constant). Charles's Law: V is directly proportional to T at constant P (V/T = constant). Gay-Lussac's Law: P is directly proportional to T at constant V (P/T = constant). Avogadro's Law: V is directly proportional to n at constant T and P (V/n = constant).
2) Ideal Gas Equation and Gas Constant
Combining Boyle's, Charles's, and Avogadro's laws gives PV = nRT. The universal gas constant R has dimensions of energy per mole per Kelvin. R = 0.0821 L atm/(mol K) = 8.314 J/(mol K) = 1.99 cal/(mol K). The Boltzmann constant k = R/NA = 1.38 x 10^-23 J/K. The gas equation enables calculation of molecular weight (M = mRT/PV) and density (d = PM/RT) of any gas.
3) Deviation from ideality [Ideal Behaviour]
No real gas is truly ideal. The compressibility factor Z = PV/(nRT) measures deviation: Z = 1 for ideal gas, Z < 1 when attractive forces dominate (gas more compressible than ideal), Z > 1 when repulsive forces or molecular volume dominate (gas less compressible). At high temperature and low pressure gases approach ideal behaviour. Near liquefaction, deviation is greatest.
4) Vander Waal's Equation
Van der Waal's corrected the ideal gas equation for molecular volume (b correction) and intermolecular attraction (a/V^2 correction): (P + a/Vm^2)(Vm minus b) = RT for one mole. The constant a measures intermolecular attraction; b is related to molecular volume. At low pressure, Z = 1 minus a/(VmRT). At high pressure, Z = 1 + Pb/(RT). At Boyle temperature TB = a/(Rb), real gas behaves ideally over a wide pressure range.
5) Kinetic theory of Gases
Eight postulates form the kinetic molecular model: gas molecules are tiny elastic spheres with negligible volume, no intermolecular forces, random motion, and average kinetic energy proportional to temperature. The kinetic gas equation PV = (1/3)mNu^2 where m is molecular mass, N is number of molecules, and u^2 is mean square speed. All gas laws can be derived from this equation.
6) Expression of some useful physical quantities
Three molecular speed expressions derived from kinetic theory: RMS velocity u_rms = sqrt(3RT/M), average velocity u_avg = sqrt(8RT/(pi M)), and most probable velocity u_mp = sqrt(2RT/M). Their ratio is sqrt(3) : sqrt(8/pi) : sqrt(2), so u_rms > u_avg > u_mp. Average kinetic energy per molecule = (3/2)kT; per mole = (3/2)RT. KE depends only on temperature, not on molecular identity.
7) Law of partial pressure
Dalton's law: total pressure of a mixture of non-reacting gases equals the sum of their partial pressures. Partial pressure of a component = mole fraction times total pressure. Amagat's law: total volume equals the sum of partial volumes. Both laws hold for ideal gas mixtures. Dalton's law is used to calculate dry gas pressure by subtracting aqueous tension.
8) Diffusion of gases
Diffusion is spontaneous intermixing of gas molecules. Effusion is escape through a tiny hole. Graham's law: at constant T and P, rate of diffusion is inversely proportional to the square root of vapour density (or molar mass). r1/r2 = sqrt(M2/M1). Lighter gases diffuse faster; hydrogen has the highest rate. Used in separation of isotopes (atmolysis) and determining molecular weights.
9) The critical state
A state where vapour and liquid phases become indistinguishable. Critical temperature Tc is the temperature above which a gas cannot be liquefied regardless of pressure: Tc = 8a/(27Rb). Critical pressure Pc is the minimum pressure needed to liquefy at Tc: Pc = a/(27b^2). Critical volume Vc = 3b. These constants are derived from Van der Waal's equation by setting the first and second derivatives of P with respect to V equal to zero.
Gaseous State Download Notes & Weightage Plan
For each topic in the Gaseous State chapter below, you get (2) the exact resources to download and how to use them, and (3) a simple importance & time plan so NEET students know what to do first and what to revise last.
Four foundational laws connecting P, V, T, and n. Boyle's, Charles's, Gay-Lussac's, and Avogadro's Laws form the basis for the ideal gas equation.
1) Download Packs For This Topic (And How To Use Them)
Don't download everything and forget it. Use these like a small "attack kit": read → highlight → test → revise the same sheet again.
2) Importance, Weightage & Time Allocation (Practical)
Use this to avoid over-studying. This topic is usually low effort, quick return if your recall is clean.
- Scoring Focus: Always convert temperature to Kelvin first. T(K) = t(C) + 273.15. Using Celsius in V/T or P/T ratios gives wrong answers. NEET distractors are calculated using Celsius temperatures.
- High-risk Area: Forgetting to convert Celsius to Kelvin. A problem at 27 degrees C requires T = 300 K, not 27. This error changes the answer by an order of magnitude in ratio problems.
- Best Practice Style: First step in every gas problem: write T in Kelvin. Then identify which variables are constant and which change. Apply the appropriate gas law ratio.
Ideal Gas Equation and Gas Constant
The unified equation PV = nRT with gas constant R in various units. Boltzmann constant k = R/NA. Density and molecular weight calculations from the gas equation.
1) Download Packs For This Topic (And How To Use Them)
Don't download everything and forget it. Use these like a small "attack kit": read → highlight → test → revise the same sheet again.
2) Importance, Weightage & Time Allocation (Practical)
Use this to avoid over-studying. This topic is usually low effort, quick return if your recall is clean.
- Scoring Focus: d = PM/RT is the most frequently tested formula. Know that M must be in g/mol and d comes out in g/L when R = 0.0821 and P is in atm. Cross-check: N2 at STP has d = 28/22.4 = 1.25 g/L.
- High-risk Area: Using R = 0.0821 when pressure is given in bar or Pa. Mismatched units give wrong density by 1.3% (bar vs atm) or by orders of magnitude (Pa vs atm).
- Best Practice Style: Circle the pressure unit in the question. Pick R accordingly: atm uses 0.0821, kPa uses 8.314, bar uses 0.083. Then substitute with all units written out.
Deviation from ideality [Ideal Behaviour]
Real gases deviate from PV = nRT. Compressibility factor Z quantifies deviation: Z = PV/(nRT). Z = 1 ideal; Z < 1 attractive forces dominate; Z > 1 repulsion/volume dominates.
1) Download Packs For This Topic (And How To Use Them)
Don't download everything and forget it. Use these like a small "attack kit": read → highlight → test → revise the same sheet again.
2) Importance, Weightage & Time Allocation (Practical)
Use this to avoid over-studying. This topic is usually low effort, quick return if your recall is clean.
- Scoring Focus: Two key facts: (1) High temperature and low pressure give ideal behaviour. (2) H2 and He always show Z > 1. NEET assertion-reason questions frequently test these.
- High-risk Area: Confusing Z > 1 (less compressible, repulsive) with Z < 1 (more compressible, attractive). Students sometimes reverse the physical meaning.
- Best Practice Style: Z < 1 means the real gas occupies LESS volume than ideal prediction (attractive forces pull molecules closer). Z > 1 means the real gas occupies MORE volume than ideal (molecular volume matters).
Mathematical correction of ideal gas equation for intermolecular attractions (a/V^2) and molecular volume (b). Behaviour at low and high pressures. Virial equation and Boyle temperature.
1) Download Packs For This Topic (And How To Use Them)
Don't download everything and forget it. Use these like a small "attack kit": read → highlight → test → revise the same sheet again.
2) Importance, Weightage & Time Allocation (Practical)
Use this to avoid over-studying. This topic is usually low effort, quick return if your recall is clean.
- Scoring Focus: At high pressure: Z = 1 + Pb/(RT). At low pressure: Z = 1 minus a/(VmRT). NEET assertion-reason questions directly test these two approximate forms.
- High-risk Area: Confusing which correction to drop at which pressure. At LOW pressure, molecular volume b is negligible (drop b). At HIGH pressure, attraction a/V^2 is negligible (drop a/V^2). Students often reverse this.
- Best Practice Style: Low P means large V, so the b term (small compared to V) vanishes. High P means V is compressed small, so attractive correction a/V^2 becomes negligible compared to the large P.
Eight postulates of the kinetic molecular model. The kinetic gas equation PV = (1/3)mNu^2 connects macroscopic gas properties to molecular motion.
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Don't download everything and forget it. Use these like a small "attack kit": read → highlight → test → revise the same sheet again.
2) Importance, Weightage & Time Allocation (Practical)
Use this to avoid over-studying. This topic is usually low effort, quick return if your recall is clean.
- Scoring Focus: Most tested fact: average KE per molecule = (3/2)kT depends only on temperature. At the same temperature, all ideal gases have the same average KE per molecule regardless of molecular mass.
- High-risk Area: Confusing 'average KE per molecule is the same for all gases at same T' with 'molecular speed is the same'. Speed depends on mass; KE at same T does not.
- Best Practice Style: When a question says 'same temperature, different gases', KE per molecule is identical, but heavier molecules move slower. u_rms = sqrt(3RT/M): M in denominator means heavier gas has lower speed.
Expression of some useful physical quantities
Three molecular speed expressions (RMS, average, most probable) and average kinetic energy per molecule and per mole. The speed ratio sqrt(3) : sqrt(8/pi) : sqrt(2) is a NEET favourite.
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Don't download everything and forget it. Use these like a small "attack kit": read → highlight → test → revise the same sheet again.
2) Importance, Weightage & Time Allocation (Practical)
Use this to avoid over-studying. This topic is usually low effort, quick return if your recall is clean.
- Scoring Focus: u_rms = sqrt(3RT/M) has M in kg/mol when R = 8.314 J/(mol K). The result is in m/s. For NEET calculations, use M in g/mol with appropriate unit conversion. Speed ratio comparisons between gases at same T: u1/u2 = sqrt(M2/M1).
- High-risk Area: Confusing the three speeds. Students pick u_mp formula when u_rms is asked, or vice versa. The coefficient under the square root is the distinguishing factor: 3 for RMS, 8/pi for average, 2 for most probable.
- Best Practice Style: Tag each formula with its coefficient: RMS = 3, AVG = 8/pi approximately 2.55, MP = 2. In MCQs, check which coefficient is used. If the numerator is 2RT: it is most probable, not RMS.
Dalton's law for pressure additivity in gas mixtures. Partial pressure equals mole fraction times total pressure. Amagat's law for volume additivity.
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Don't download everything and forget it. Use these like a small "attack kit": read → highlight → test → revise the same sheet again.
2) Importance, Weightage & Time Allocation (Practical)
Use this to avoid over-studying. This topic is usually low effort, quick return if your recall is clean.
- Scoring Focus: Pi = xi times P. Always convert masses to moles first, then find mole fractions. Equal masses of different gases do NOT give equal partial pressures because their moles differ.
- High-risk Area: Using mass fractions instead of mole fractions. If 56 g N2 and 44 g CO2 are mixed, moles are 2 and 1, so mole fractions are 2/3 and 1/3, not 56/100 and 44/100.
- Best Practice Style: Step 1: convert all masses to moles (divide by molar mass). Step 2: find mole fraction = moles of component / total moles. Step 3: Pi = xi times P_total.
Graham's law: rate of diffusion inversely proportional to sqrt(molar mass). Multiple forms for volume, time, and pressure variations. Applied in atmolysis for isotope separation.
1) Download Packs For This Topic (And How To Use Them)
Don't download everything and forget it. Use these like a small "attack kit": read → highlight → test → revise the same sheet again.
2) Importance, Weightage & Time Allocation (Practical)
Use this to avoid over-studying. This topic is usually low effort, quick return if your recall is clean.
- Scoring Focus: r1/r2 = sqrt(M2/M1). When times are given for equal volumes: r1/r2 = t2/t1 (inverse). When a gas takes 3 times longer than He to effuse: r_gas/r_He = 1/3, so M_gas = 9 times M_He = 36 u.
- High-risk Area: Inverting the ratio. If gas X takes twice as long as H2 to diffuse the same volume, rX/rH2 = 1/2, NOT 2. Squaring gives M_X/M_H2 = 4, so M_X = 8. Students who set the ratio as 2 get M_X = 0.5, which is nonsensical.
- Best Practice Style: Identify which gas is faster from the problem context. Faster gas has lower M. Set up r_fast/r_slow = sqrt(M_slow/M_fast). Confirm your ratio gives the faster gas a higher rate.
Critical temperature, pressure, and volume define the point where gas-liquid distinction vanishes. Derived from Van der Waal's equation. Determines ease of gas liquefaction.
1) Download Packs For This Topic (And How To Use Them)
Don't download everything and forget it. Use these like a small "attack kit": read → highlight → test → revise the same sheet again.
2) Importance, Weightage & Time Allocation (Practical)
Use this to avoid over-studying. This topic is usually low effort, quick return if your recall is clean.
- Scoring Focus: Tc determines whether a gas can be liquefied at a given temperature. If T > Tc, no amount of pressure works. NEET tests this concept directly when asking about gas liquefaction.
- High-risk Area: Confusing Tc with boiling point. Critical temperature is the maximum T for liquefaction; boiling point is the T where liquid vapour pressure equals atmospheric pressure. They are different quantities.
- Best Practice Style: Link critical state to Van der Waal's constants: high a (strong attraction) means high Tc (easier to liquefy). Low a (weak attraction like He) means very low Tc (extremely hard to liquefy).
Gaseous State Chapter NEET Traps & Common Mistakes (Topic-Wise)
Each subtopic below is of the Gaseous State chapter and shows what NEET students usually do wrong in NEET examination, a short example of the mistake, and how NEET frames the question to trick you with close options are given below.
Mistake Snapshot (What Students Do Wrong)
- Using the wrong velocity formula (RMS vs average vs most probable): The three velocity expressions differ only in the coefficient under the square root: 3RT/M for RMS, 8RT/(pi M) for average, 2RT/M for most probable. NEET distractors substitute one coefficient for another. Picking u_mp = sqrt(2RT/M) when the question asks for u_rms = sqrt(3RT/M) gives an answer that is sqrt(2/3) = 0.816 times too low.
- Assuming doubling temperature doubles the speed: Since u = sqrt(constant times T/M), doubling T multiplies speed by sqrt(2), not 2. To double the speed, temperature must be quadrupled (T2 = 4T1). NEET expects you to know this sqrt relationship.
RMS velocity of N2 at 300 K: u_rms = sqrt(3 x 8.314 x 300 / 0.028) = sqrt(267214) = 517 m/s. At 1200 K: u = 517 x sqrt(1200/300) = 517 x 2 = 1034 m/s. A student who says 'temperature quadrupled so speed quadrupled' gets 2068 m/s, which is wrong.
How NEET Frames The Trap
NEET asks: 'RMS velocity of a gas at 27 degrees C is v. At what temperature will the RMS velocity become 2v?' The correct answer is 1200 K (4 times 300 K), not 600 K (2 times 300 K). NEET places 600 K as a distractor.
Q. The RMS velocity of a gas at 300 K is v. The temperature at which the RMS velocity becomes 2v is
A. 1200 K B. 600 K C. 900 K D. 150 K
Trick: u_rms is proportional to sqrt(T). To double u, T must be quadrupled: T2 = 4 x 300 = 1200 K (Option A). Option B (600 K) is the 'doubled temperature' distractor, giving speed = v times sqrt(2), not 2v. Option C (900 K) gives sqrt(3) times v. Option D (150 K) halves the speed.
Mistake Snapshot (What Students Do Wrong)
- Using R = 0.0821 when pressure is in Pa or bar: R = 0.0821 L atm/(mol K) is valid only when P is in atm and V is in litres. When P is in Pa, use R = 8.314. When P is in bar, use R = 0.083. Using mismatched units gives density or molecular weight off by a factor of 101.325 (Pa vs atm) or 1.013 (bar vs atm).
- Forgetting to convert temperature to Kelvin: PV = nRT requires T in Kelvin. Substituting T = 27 instead of T = 300 gives an answer 11 times too large (300/27). NEET routinely gives temperature in Celsius and places the Celsius-substitution answer as a distractor.
Density of N2 at 227 degrees C and 5 atm. d = PM/(RT) = 5 x 28 / (0.0821 x 500) = 140/41.05 = 3.41 g/L. If student uses T = 227: d = 140/(0.0821 x 227) = 7.51 g/L, which is the distractor.
How NEET Frames The Trap
NEET gives temperature as 227 degrees C and expects conversion to 500 K. When a student forgets to add 273, the wrong answer matches a distractor option exactly.
Q. What is the density of N2 gas at 227 degrees C and 5.00 atm pressure? (R = 0.0821 L atm/(mol K), M = 28 g/mol)
A. 3.41 g/L B. 7.51 g/L C. 1.71 g/L D. 6.84 g/L
Trick: T = 227 + 273 = 500 K. d = PM/(RT) = (5 x 28)/(0.0821 x 500) = 3.41 g/L (Option A). Option B (7.51) uses T = 227. Option C halves the answer. Option D doubles it.
Mistake Snapshot (What Students Do Wrong)
- Inverting the rate-time relationship for equal volumes: When equal volumes of two gases diffuse, the rate ratio r1/r2 = t2/t1 (times are inversely proportional to rates). Students who write r1/r2 = t1/t2 get the inverse ratio. If gas X takes 3 times longer than H2 for the same volume, rX/rH2 = 1/3, not 3.
- Confusing vapour density with absolute density in Graham's law: Graham's law uses vapour density (unitless, temperature-independent) or molecular weight. Absolute density (g/L) depends on T and P. Substituting absolute density at non-STP conditions without adjusting for T and P gives incorrect molecular weight ratios.
A gas takes 3 times as long as He (M = 4) to effuse. r_gas/r_He = t_He/t_gas = 1/3. M_gas/M_He = (r_He/r_gas)^2 = 9. M_gas = 9 x 4 = 36 u. If student writes r_gas/r_He = 3 (inverting): M_gas = M_He/9 = 0.44 u, which is physically impossible.
How NEET Frames The Trap
NEET states a gas takes N times longer than a reference gas. The rate of the slower gas is 1/N of the reference. Squaring gives the MW ratio. Students who set rate equal to N get M_gas = M_ref/N^2, yielding an impossibly small molecular weight that appears as a distractor.
Q. A certain gas takes three times as long to effuse out as helium (M = 4). Its molecular mass is
A. 36 u B. 12 u C. 27 u D. 9 u
Trick: r_gas/r_He = 1/3 (slower gas, lower rate). (r_He/r_gas)^2 = 9 = M_gas/M_He. M_gas = 9 x 4 = 36 u (Option A). Option B (12) uses ratio = 3 instead of 1/3. Option C (27) cubes instead of squaring. Option D (9) forgets to multiply by M_He.
Mistake Snapshot (What Students Do Wrong)
- Using mass fraction instead of mole fraction for partial pressure: Partial pressure = mole fraction x total pressure. Mole fraction requires converting mass to moles first. Equal masses of O2 (M = 32) and CH4 (M = 16) give mole ratios of 1:2, not 1:1. Using mass ratios directly as mole fractions gives wrong partial pressures.
- Applying Dalton's law to reacting gas mixtures: Dalton's law applies only to non-reacting gases. NH3 and HCl react to form NH4Cl, so their mixture does not obey Dalton's law. NEET tests this exception as a standalone MCQ.
Equal masses of O2 and CH4 mixed at total pressure 1 atm. Moles O2 = m/32, moles CH4 = m/16 = 2(m/32). Total moles = 3(m/32). x_O2 = 1/3, P_O2 = 1/3 atm. x_CH4 = 2/3, P_CH4 = 2/3 atm. Student using mass fractions: each is 1/2, giving P = 0.5 atm for each, which is wrong.
How NEET Frames The Trap
NEET gives 'equal masses' of two gases with different molecular weights. This signals that moles are unequal. The distractor option uses mass fraction = 0.5 for each gas.
Q. Equal masses of methane and oxygen are mixed in a container at 25 degrees C. The fraction of total pressure exerted by oxygen is
A. 1/3 B. 2/3 C. 1/2 D. 8/9
Trick: Let mass = m each. Moles CH4 = m/16, moles O2 = m/32. x_O2 = (m/32)/((m/16)+(m/32)) = 1/3. Fraction = 1/3 (Option A). Option C (1/2) uses mass fraction instead of mole fraction. Option B (2/3) is the CH4 fraction.
Mistake Snapshot (What Students Do Wrong)
- Dropping the wrong correction term at a given pressure: At low pressure, molecular volume b is negligible (large V, so Vm >> b). Drop b to get Z = 1 minus a/(VmRT). At high pressure, V is small, so a/Vm^2 is negligible compared to large P. Drop a/V^2 to get Z = 1 + Pb/(RT). Dropping the wrong term reverses the Z prediction.
- Claiming H2 shows Z < 1 at low pressure: For H2 and He, the intermolecular attraction constant a is negligibly small. The volume correction b dominates even at low pressure, so Z > 1 at all pressures. Students who apply the general pattern (Z < 1 at low P) to H2 and He answer assertion-reason questions incorrectly.
For N2 at low pressure: Z = 1 minus a/(VmRT). Since a is significant for N2, Z dips below 1. For H2 at low pressure: a is nearly zero, so Z = 1 + Pb/(RT) > 1. Student who says 'all gases show Z < 1 at low P' picks the wrong assertion-reason option for H2.
How NEET Frames The Trap
NEET assertion-reason: 'Assertion: Z for H2 is always greater than 1. Reason: At low pressure, repulsive forces dominate for H2.' The correct response requires knowing that for H2, a is so small that even the low-pressure Z expression gives Z > 1.
Q. Dominance of strong repulsive forces among the molecules of a gas (Z = compressibility factor)
A. Depends on Z and indicated by Z = 1 B. Depends on Z and indicated by Z > 1 C. Depends on Z and indicated by Z < 1 D. Is independent of Z
Trick: When repulsive forces (or molecular volume) dominate, real gas molecules occupy more space than ideal gas prediction. Z = PV_real/(nRT) > 1 (Option B). Z = 1 is ideal. Z < 1 means attractions dominate. Option D is incorrect because Z directly measures the force balance.