JEE Mains Chemistry · Some Basic Concepts of Chemistry

Gas Laws and Gas Volumes

PV = nRT and its special cases, gas volumes in reactions, and Dalton's law of partial pressures.

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Why this matters

Thirty PYQs, twenty-one of them numerical and two from 2026. Sixteen use the ideal gas equation or one of its special cases, a few of them on real gases and molecular speeds. Seven turn a reaction into a volume of gas, and seven split a total pressure into partial pressures. Units decide most of the wrong answers here.

Concept 1 of 3: The ideal gas equation and its special cases

PV=nRT

contains every gas law. Hold two of

P

V

T

and

n

fixed and the other two are in direct or inverse proportion. Put

n=\frac{m}{M}

and it gives the molar mass from a mass or a density.

Definition

$PV=nRT$ , with $R=0.0821$ L atm K $^{-1}$ mol $^{-1}$ $=0.083$ L bar K $^{-1}$ mol $^{-1}$ $=8.314$ J K $^{-1}$ mol $^{-1}$ .
Units: $T$ in kelvin; 1 atm $=760$ torr $=760$ mmHg; 1 bar $=10^{5}$ Pa; 1 dm $^3=1$ L.
Boyle: $P_1V_1=P_2V_2$ . Charles: $\frac{V_1}{T_1}=\frac{V_2}{T_2}$ . A rigid tank: $\frac{P_1}{T_1}=\frac{P_2}{T_2}$ .
$M=\frac{dRT}{P}$ . At fixed $T$ , a plot of $P$ against $d$ is a straight line through the origin, and $PV$ against $P$ is flat.
Real gas: $Z=\frac{PV}{nRT}$ ; at high pressure $Z=1+\frac{Pb}{RT}$ . Units: $a$ in atm dm $^6$ mol $^{-2}$ , $b$ in dm $^3$ mol $^{-1}$ .
Speeds: $u_{rms}=\sqrt{\frac{3RT}{M}}$ , $u_{mp}=\sqrt{\frac{2RT}{M}}$ , $u_{avg}=\sqrt{\frac{8RT}{\pi M}}$ .

Ideal gas equation

PV=nRT=\frac{m}{M}RT\quad\Rightarrow\quad M=\frac{dRT}{P}

Worked example

1.6

g of a gas fills a

1.0

L flask at

1.23

atm and 300 K. Find its molar mass (

R=0.082

L atm K

^{-1}

mol

^{-1}

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

JEE Mains · 2022 · 26 June 2022 · Q32Moderate

Example 1 · Some Basic Concepts of Chemistry · Gas Laws and Gas Volumes

An evacuated glass vessel weighs

40.0\text{ }g

when empty,

135.0\text{ }g

when filled with a liquid of density

0.95\text{ }g{\text{ }mL}^{- 1}

and

40.5\text{ }g

when filled with an ideal gas at

0.82\text{ }atm

250\text{ }K

. The molar mass of the gas in

gmol^{- 1}

is: (Given:

R = 0.082\text{ }L\text{ }atm{\text{ }K}^{- 1}{\text{ }mol}^{- 1}

)

Celsius in the gas equation

Every

T

PV=nRT

and in the gas laws is in kelvin. Using 27 for 27 °C instead of 300 changes the answer by a factor of about eleven.

Match R to the units

0.082 goes with atm and litres, 0.083 with bar and litres, 8.314 with pascals and cubic metres. Mixing them is off by a factor of 1000 or more.

Drill 15 more on the ideal gas equation and its special cases

Concept 2 of 3: Gas volumes in reactions

At one temperature and pressure, equal volumes hold equal moles. So the coefficients of a gas reaction are also its volume ratios, and the moles of a metal turn straight into litres of hydrogen.

Definition

Gay-Lussac: gases react in volumes in the ratio of their coefficients, measured at the same $T$ and $P$ .
$\mathrm{Mg+2HCl\rightarrow MgCl_2+H_2}$ : 1 mol of $\mathrm{H_2}$ per mol of Mg. $\mathrm{2Al+6HCl\rightarrow2AlCl_3+3H_2}$ : $1.5$ mol of $\mathrm{H_2}$ per mol of Al.
$V=n\times V_m$ , with $V_m$ as the stem states: 22.4 or 22.7 L.
Fixed volume and temperature: pressures follow the moles. For $\mathrm{A(g)\rightarrow2B(g)+\tfrac12C(g)}$ , a fraction $\alpha$ reacted gives $P=P_0\left(1+\tfrac32\alpha\right)$ .

Volume from moles

V_{\text{gas}}=n\,V_m,\qquad\frac{V_A}{V_B}=\frac{\nu_A}{\nu_B}

Worked example

What volume of

\mathrm{H_2}

at STP (22.4 L mol

^{-1}

) forms when

5.4

g of Al reacts with excess HCl?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

JEE Mains · 2023 · 31 January 2023 · Q55Moderate

Example 2 · Some Basic Concepts of Chemistry · Gas Laws and Gas Volumes

Zinc reacts with hydrochloric acid to give hydrogen and zinc chloride. The volume of hydrogen gas produced at STP from the reaction of

11.5\text{ }g

of zinc with excess

HCl

L

(Nearest integer)

\text{~(Given : Molar mass of~}Zn\text{~is~}65.4\text{ }g{\text{ }mol}^{- 1}\text{~and Molar volume of~}H_{2}\text{~at~}STP = 22.7\text{ }L\text{~)}

Only gases count

Coefficients are volume ratios only for gases at one temperature and pressure. A solid, or water that has condensed, adds no gas volume.

Drill 6 more on gas volumes in reactions

Concept 3 of 3: Partial pressures and gas mixtures

Each gas in a mixture pushes as if it were alone in the vessel. Its share of the total pressure is its share of the moles, so change masses to moles before you split the pressure.

Definition

$p_i=x_iP$ , with $x_i=\frac{n_i}{\sum n}$ ; and $P=\sum p_i$ .
From a mass percentage: take 100 g, convert each gas to moles, then find $x$ .
Bulbs joined at one temperature: $P=\frac{\sum P_iV_i}{\sum V_i}$ .
Moist gas: only the dry gas obeys Boyle's law. While liquid water remains, the water vapour pressure stays the same.

Dalton's law

p_i=x_iP=\frac{n_i}{n_{\text{total}}}\,P

Worked example

A mixture of

16

g of

\mathrm{O_2}

and

7

g of

\mathrm{N_2}

has a total pressure of

1.5

atm. Find the partial pressure of

\mathrm{O_2}

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

JEE Mains · 2023 · 31 January 2023 · Q58Moderate

Example 3 · Some Basic Concepts of Chemistry · Gas Laws and Gas Volumes

The total pressure of a mixture of non-reacting gases

X(0.6\text{ }g)

and

Y(0.45\text{ }g)

in a vessel is

740\text{ }mm

Hg

. The partial pressure of the gas

X

mm

Hg

. (Nearest Integer) (Given: molar mass

X = 20

and

Y = 45\text{ }g{\text{ }mol}^{- 1}

)

Mass fraction is not mole fraction

A mixture that is

40\%

hydrogen by mass is over

90\%

hydrogen by moles, because

\mathrm{H_2}

is so light. Convert to moles first.

Moist gas: only the dry part changes

When the volume changes, the water vapour pressure stays fixed as long as liquid remains. Apply Boyle's law to the dry gas, then add the vapour pressure back.

Drill 6 more on partial pressures and gas mixtures

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (3)

The ideal gas equation and its special cases
Ideal gas equation
$PV=nRT=\frac{m}{M}RT\quad\Rightarrow\quad M=\frac{dRT}{P}$
Gas volumes in reactions
Volume from moles
$V_{\text{gas}}=n\,V_m,\qquad\frac{V_A}{V_B}=\frac{\nu_A}{\nu_B}$
Partial pressures and gas mixtures
Dalton's law
$p_i=x_iP=\frac{n_i}{n_{\text{total}}}\,P$

Watch out for (5)

Celsius in the gas equation
→ The ideal gas equation and its special cases
Match R to the units
→ The ideal gas equation and its special cases
Only gases count
→ Gas volumes in reactions
Mass fraction is not mole fraction
→ Partial pressures and gas mixtures
Moist gas: only the dry part changes
→ Partial pressures and gas mixtures

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