A vessel of $2\ ext{L}$ nitrogen gas and a vessel of $2\ ext{L}$ oxygen gas are both at the same temperature and pressure. Using Avogadro's law, compare the number of molecules present in the two vessels.

Question

A vessel of $2\ 	ext{L}$ nitrogen gas and a vessel of $2\ 	ext{L}$ oxygen gas are both at the same temperature and pressure. Using Avogadro's law, compare the number of molecules present in the two vessels.

Accepted Answer

Avogadro's law states that, at the same temperature and pressure, equal volumes of any gas contain equal numbers of molecules — the identity of the gas is irrelevant, only the number of particles present under those conditions matters. Here, both vessels hold the same volume ( $2\ \text{L}$ each) at the same temperature and pressure, even though one contains nitrogen molecules and the other contains oxygen molecules, which have different molar masses ( $28\ \text{g mol}^{-1}$ versus $32\ \text{g mol}^{-1}$ ) and different chemical identities. By Avogadro's law, these differences do not matter for the count of molecules present: since $V \propto n$ at fixed $T,P$ , and both volumes are equal, the number of moles — and he …

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Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

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CBSE 2023Set ANNUAL1 markMCQ
$Q. A gas which obeys gas laws at all ranges of temperature and pressure is called$
(a) Real gas
(b) Ideal gas
(c) Noble gas
(d) None of these
›Reveal solutionSolution

An ideal gas is defined as one that obeys the gas laws exactly under all conditions of temperature and pressure; real gases only approximate this, especially deviating at high pressure and low temperature.

The gas laws (Boyle's law, Charles's law, and their combination PV = nRT) are derived assuming point-mass gas particles with no intermolecular forces. A gas that follows PV = nRT exactly at ALL temperatures and pressures, with no deviation, is by definition an ideal gas — a useful theoretical model rather than something that truly exists in nature. Real gases deviate especially at high pressure (molecules have finite volume) and low temperature (intermolecular attractions become significant), w …

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CBSE 2023Set ANNUAL1 markMCQ
$Q. What will be the minimum pressure required to compress 500 dm^3 of air at 1 bar pressure to 200 dm^3 at 30 degrees C?$
(a) 3.5 bar
(b) 2.5 bar
(c) 700 bar
(d) 900 bar
›Reveal solutionSolution

Since both states are at the same temperature (30°C), this is an isothermal (constant-T) compression, so Boyle's Law applies directly: P1V1 = P2V2.

Given: P1 = 1 bar, V1 = 500 dm3, V2 = 200 dm3, T constant at 30°C throughout (compression only, no temperature change between the two states).

Boyle's Law: P1V1 = P2V2

(1 bar)(500 dm3) = P2 (200 dm3)

…

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CBSE 2022Set TERM11 markMCQ
$Q. "Equal volumes of all the gases under same conditions of pressure and temperature contain equal number of molecules" is known as$
(a) Charles' law
(b) Boyle's law
(c) Avogadro's law
(d) none of these
›Reveal solutionSolution
This is the textbook statement of Avogadro's law, a gas law from the (now removed) States of Matter chapter.

Boyle's law relates pressure and volume at constant temperature (PV = constant).

Charles' law relates volume and temperature at constant pressure (V/T = constant).

Avogadro's law states that equal volumes of any gas, under the same conditions of temperature and pressure, contain equal numbers of molecules -- exactly the statement quoted in the question. …
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CBSE 2022Set TERM11 markMCQ
$Q. PV = nRT is$
(a) Ideal gas equation
(b) Real gas equation
(c) Elementary gas equation
(d) none of these
›Reveal solutionSolution

PV = nRT is the combined form of Boyle's, Charles', and Avogadro's laws, known as the ideal gas equation.

Combining Boyle's law (V proportional to 1/P), Charles' law (V proportional to T), and Avogadro's law (V proportional to n) gives PV = nRT, where R is the universal gas constant. This single equation describes the behaviour of an ideal (hypothetical, non-interacting) gas.

…

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CBSE 2022Set TERM11 markMCQ
$Q. What will be the minimum pressure required to compress 500 dm3 of air at 1 bar to 200 dm3 at 30°C ?$
(a) 3.5 bar
(b) 2.5 bar
(c) 700 bar
(d) 900 bar
›Reveal solutionSolution

Apply Boyle's law (P1V1 = P2V2) since the compression happens at constant temperature.

Given: P1 = 1 bar, V1 = 500 dm3, V2 = 200 dm3 (temperature stated as 30 degrees C throughout, so it is constant -- an isothermal process, which is exactly Boyle's law's condition).

Boyle's law: P1V1 = P2V2

1 x 500 = P2 x 200

P2 = 500 / 200 = 2.5 bar.

…

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CBSE 2022Set TERM11 markMCQ
$Q. V/T = constant (n, P constant) is$
(a) Charles' law
(b) Boyle's law
(c) Avagadro's law
(d) Gay Lussac's law
›Reveal solutionSolution

V/T = constant, with n and P held fixed, is exactly Charles' law.

Charles' law states that at constant pressure, the volume of a fixed amount of gas is directly proportional to its absolute temperature: V proportional to T, i.e. V/T = constant. This matches the relation given in the question (n, P held constant).

…

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CBSE 2022Set TERM11 markMCQ
$Q. The relationship between the three variables P, V and T by combining Boyle's law and Charles' law is$
(a) P1V1T1 = P2V2T2
(b) P1V1/T1 = P2V2/T2
(c) V1T1/P1 = V2T2/P2
(d) none of these
›Reveal solutionSolution

Multiplying/combining Boyle's and Charles' laws gives the combined gas law, PV/T = constant.

Boyle's law: at constant T and n, PV = constant.

Charles' law: at constant P and n, V/T = constant.

Combining both dependencies gives PV/T = constant for a fixed amount of gas, i.e. P1V1/T1 = P2V2/T2 when the gas moves from one state (P1, V1, T1) to another (P2, V2, T2).

…

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CBSE 2022Set ANNUAL1 markMCQ
$Q. The temperature at which the volume of gas is zero ?$
(a) 0°C
(b) 0 K
(c) 0°F
(d) None of these
›Reveal solutionSolution

The V–T graph of a gas, extrapolated to V = 0, meets the temperature axis at −273.15°C, defined as 0 K — absolute zero.

At constant pressure, a real gas's volume decreases linearly as temperature falls (Charles's law, V ∝ T). If this straight-line graph is extrapolated (real gases actually liquefy before this point), it crosses the volume axis at V = 0 when temperature = −273.15°C. This temperature is taken as the zero of the absolute (Kelvin) scale, i.e. 0 K = …

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CBSE 2022Set ANNUAL1 mark
$Q. What is Boyle's Law ?$
›Reveal solutionSolution

Boyle's law: for a fixed amount of gas at constant temperature, PV = constant (V ∝ 1/P).

Robert Boyle observed experimentally that when the temperature and amount (moles) of a gas are held fixed, its pressure and volume are inversely related — compressing a gas to half its volume doubles its pressure, and vice versa. Mathematically:

P ∝ 1/V (at constant T, n) ⟹ PV = k (a constant) ⟹ P $_1$ V $_1$ = P $_2$ V $_2$

…

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CBSE 2022Set ANNUAL1 mark
$Q. What is constant in Charle's Law ?$
›Reveal solutionSolution

Charles's law holds pressure (and amount of gas) constant, and states V/T = constant, i.e. V ∝ T (T in kelvin).

Jacques Charles found that at constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute (Kelvin) temperature:

V ∝ T (at constant P, n) ⟹ V/T = constant ⟹ V $_1$ /T $_1$ = V $_2$ /T $_2$

…

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CBSE 2022Set ANNUAL1 mark
$Q. Each line of V vs. P graph at constant temperature is called .............. .$
›Reveal solutionSolution

A V–P (or P–V) curve plotted at one fixed temperature is called an isotherm, and follows Boyle's law (PV = constant) for an ideal gas.

When a gas's volume is plotted against its pressure while temperature is held fixed, the resulting curve is a rectangular hyperbola (since PV = constant, Boyle's law) called an isotherm. Differen …

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CBSE 2021Set ANNUAL1 mark
$Q. What is Charle's Law?$
›Reveal solutionSolution

Charles's Law: at constant pressure, gas volume is directly proportional to absolute temperature ( $V \propto T$ , so $V/T$ = constant).

Statement: For a fixed mass of gas held at constant pressure, its volume increases in direct proportion to its absolute temperature. Mathematically:

$V \propto T \quad \text{(at constant P, n)} \qquad \text{or} \qquad \dfrac{V_1}{T_1} = \dfrac{V_2}{T_2}$

where T must be expressed in kelvin (absolute temperature), not Celsius.

…

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Q.A vessel of $2\ \text{L}$ nitrogen gas and a vessel of $2\ \text{L}$ oxygen gas are both at the same temperature and pressure. Using Avogadro's law, compare the number of molecules present in the two vessels.

Concept understanding — Gas Laws — Boyle's, Charles's and Avogadro's Law

Q.A vessel of 2 L2\ \text{L}2 L nitrogen gas and a vessel of 2 L2\ \text{L}2 L oxygen gas are both at the same temperature and pressure. Using Avogadro's law, compare the number of molecules present in the two vessels.

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Q.A vessel of $2\ \text{L}$ nitrogen gas and a vessel of $2\ \text{L}$ oxygen gas are both at the same temperature and pressure. Using Avogadro's law, compare the number of molecules present in the two vessels.

Unlock everything free for 14 days