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Gaseous State formulas

Master Gaseous State through 22 JEE Advanced-level formulas, systematically structured with every variable spelled out. Revise concept-wise, identify the areas where you need improvement, and focus your preparation with greater precision.

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Gaseous State, every formula

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Boyle's law
$P V = constant (T const)$
Charles's law
$\frac{V}{T} = constant (P const)$
Q1MCQCharles's law
At constant pressure, $V$ varies with absolute temperature as:
- A
  $V\propto T$
- B
  $V\propto\dfrac1T$
- C
  $V\propto T^{2}$
- D
  $V=$ const
Gay-Lussac's law
$\frac{P}{T} = constant (V const)$
Q1MCQGay-Lussac
At constant volume, $P$ varies with temperature as:
- A
  $P\propto T$
- B
  $P\propto\dfrac1T$
- C
  $P=$ const
- D
  $P\propto T^{2}$
Avogadro's law
$V \propto n (P, T const)$
Q1MCQAvogadro's law
At the same T and P, equal volumes of gases contain:
- A
  equal numbers of molecules
- B
  equal masses
- C
  equal densities
- D
  equal speeds
Ideal gas equation
$P V = n R T$
Combined gas law
$\frac{P _{1} V _{1}}{T _{1}} = \frac{P _{2} V _{2}}{T _{2}}$
Q1MCQCombined gas law
The combined gas law is:
- A
  $\dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2}$
- B
  $P_1V_1=P_2V_2$
- C
  $\dfrac{V_1}{T_1}=\dfrac{V_2}{T_2}$
- D
  $PV=nRT$
Gas constant
$R = 0.0821 L atm mol^{- 1} K^{- 1} = 8.314 J mol^{- 1} K^{- 1}$
Q1MCQGas constant
The value of $R$ in L·atm units is:
- A
  $0.0821$
- B
  $8.314$
- C
  $1.987$
- D
  $22.4$
Dalton's law of partial pressures
$P = P_{1} + P_{2} + \dots$
Partial pressure (mole fraction)
$P_{i} = x_{i} P_{t o t a l}$
Density of a gas
$ρ = \frac{P M}{R T}$
Q1MCQGas density
The density of an ideal gas is:
- A
  $\dfrac{PM}{RT}$
- B
  $\dfrac{RT}{PM}$
- C
  $PMRT$
- D
  $\dfrac{PM}{R}$
Graham's law of diffusion
$\frac{r _{1}}{r _{2}} = \frac{M _{2}}{M _{1}}$
Q1MCQGraham's law
The rate of diffusion of a gas varies with molar mass as:
- A
  $\dfrac{1}{\sqrt{M}}$
- B
  $\sqrt{M}$
- C
  $M$
- D
  $\dfrac{1}{M}$
RMS speed
$u_{r m s} = \frac{3 R T}{M}$
Q1MCQRMS speed
The rms speed of gas molecules is:
- A
  $\sqrt{\dfrac{3RT}{M}}$
- B
  $\sqrt{\dfrac{2RT}{M}}$
- C
  $\sqrt{\dfrac{8RT}{\pi M}}$
- D
  $\sqrt{\dfrac{RT}{M}}$
Average speed
$u_{a v g} = \frac{8 R T}{π M}$
Q1MCQAverage speed
The average speed of gas molecules is:
- A
  $\sqrt{\dfrac{8RT}{\pi M}}$
- B
  $\sqrt{\dfrac{3RT}{M}}$
- C
  $\sqrt{\dfrac{2RT}{M}}$
- D
  $\sqrt{\dfrac{RT}{M}}$
Most probable speed
$u_{m p} = \frac{2 R T}{M}$
Q1MCQMost probable speed
The most probable speed is:
- A
  $\sqrt{\dfrac{2RT}{M}}$
- B
  $\sqrt{\dfrac{3RT}{M}}$
- C
  $\sqrt{\dfrac{8RT}{\pi M}}$
- D
  $\sqrt{\dfrac{RT}{M}}$
Kinetic energy per mole
$K E = \frac{3}{2} R T$
Q1MCQKE per mole
The kinetic energy of one mole of an ideal gas is:
- A
  $\tfrac32 RT$
- B
  $\tfrac12 RT$
- C
  $RT$
- D
  $\tfrac32 nRT$
van der Waals equation
$(P + \frac{a n ^{2}}{V ^{2}}) (V - nb) = n R T$
Q1MCQvan der Waals
The van der Waals equation is:
- A
  $\left(P+\dfrac{an^{2}}{V^{2}}\right)(V-nb)=nRT$
- B
  $PV=nRT$
- C
  $(P-a)(V+b)=nRT$
- D
  $P(V-nb)=nRT$
Compressibility factor
$Z = \frac{P V}{n R T}$
Q1MCQCompressibility
The compressibility factor is:
- A
  $\dfrac{PV}{nRT}$
- B
  $\dfrac{nRT}{PV}$
- C
  $PVnRT$
- D
  $\dfrac{P}{nRT}$
Critical temperature
$T_{c} = \frac{8 a}{27 R b}$
Q1MCQCritical temperature
The critical temperature in van der Waals terms is:
- A
  $\dfrac{8a}{27Rb}$
- B
  $\dfrac{a}{27b^{2}}$
- C
  $3b$
- D
  $\dfrac{a}{Rb}$
Critical pressure
$P_{c} = \frac{a}{27 b ^{2}}$
Q1MCQCritical volume
The critical volume in van der Waals terms is:
- A
  $3b$
- B
  $b$
- C
  $\dfrac{a}{27b^{2}}$
- D
  $27b$
Critical volume
$V_{c} = 3 b$
Q1MCQBoyle temperature
The Boyle temperature is:
- A
  $\dfrac{a}{Rb}$
- B
  $\dfrac{8a}{27Rb}$
- C
  $3b$
- D
  $\dfrac{a}{27b^{2}}$
Boyle temperature
$T_{B} = \frac{a}{R b}$
Molar volume at STP
$V_{m} = 22.4 L$
Q1MCQIdeal gas Z
For an ideal gas, the compressibility factor $Z$ equals:
- A
  $1$
- B
  $0$
- C
  $>1$ always
- D
  $<1$ always

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Gaseous State formulas

Gaseous State, every formula

Boyle's law

Charles's law

Gay-Lussac's law

Avogadro's law

Ideal gas equation

Combined gas law

Gas constant

Dalton's law of partial pressures

Partial pressure (mole fraction)

Density of a gas

Graham's law of diffusion

RMS speed

Average speed

Most probable speed

Kinetic energy per mole

van der Waals equation

Compressibility factor

Critical temperature

Critical pressure

Critical volume

Boyle temperature

Molar volume at STP

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