Q.A certain mass of a gas occupies 250 mL at 750 mm pressure. What will be its volume if the pressure gas is changed to 540 mm at the same temperature?
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🔒 Start your 14-day free trial to unlock the full solution →Concept understanding — Gas Laws — Boyle's, Charles's and Avogadro's Law
Before the kinetic theory explained why gases behave as they do, three empirical laws, established from careful
experimental measurement, described precisely how they behave — each by fixing one variable and studying the
relationship between the remaining two.
Boyle's law (pressure-volume relationship) states that, at constant temperature and for a fixed amount of gas,
volume is inversely proportional to pressure: V∝1/P, giving P1V1=P2V2 for two states of the same
sample. Compressing a gas to half its volume doubles its pressure, and vice versa — a direct consequence, in
kinetic-theory terms, of particles striking a smaller wall area more frequently when confined to less space.
Charles's law (temperature-volume relationship) states that, at constant pressure and for a fixed amount of
gas, volume is directly proportional to the absolute (Kelvin) temperature: V∝T, giving
T1V1=T2V2. Heating a gas at constant pressure makes it expand; cooling it makes it
contract, consistent with the kinetic theory's link between temperature and average particle speed.
A closely related law, Gay-Lussac's law (pressure-temperature relationship), states that at constant volume,
pressure is directly proportional to temperature: P∝T. Heating a gas sealed in a rigid container raises
its pressure, since faster particles strike the fixed walls harder and more often.
Avogadro's law (volume-amount relationship) states that, at the same temperature and pressure, equal volumes …
This is a Boyle's Law problem: at constant temperature, pressure and volume of a fixed mass of gas are inversely related. …
Applying Boyle's Law (P1V1 = P2V2) at constant temperature gives a new volume of about 347.2 mL.
At constant temperature, for a fixed mass of gas, Boyle's Law states:
P1 V1 = P2 V2
Given:
- P1 = 750 mm, V1 = 250 mL
- P2 = 540 mm, V2 = ?
Rearranging:
V2 = (P1 V1) / P2 …
Showing the 12 most recent of 14 on this concept.
- CBSE 2023Set ANNUAL1 markMCQQ.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 …
- CBSE 2023Set ANNUAL1 markMCQQ.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)
…
- CBSE 2022Set TERM11 markMCQQ."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. …
- CBSE 2022Set TERM11 markMCQQ.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.
…
- CBSE 2022Set TERM11 markMCQQ.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.
…
- CBSE 2022Set TERM11 markMCQQ.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).
…
- CBSE 2022Set TERM11 markMCQQ.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).
…
- CBSE 2022Set ANNUAL1 markMCQQ.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 = …
- CBSE 2022Set ANNUAL1 markQ.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) ⟹ P1V1 = P2V2
…
- CBSE 2022Set ANNUAL1 markQ.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 ⟹ V1/T1 = V2/T2
…
- CBSE 2022Set ANNUAL1 markQ.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 …
- CBSE 2021Set ANNUAL1 markQ.What is Charle's Law?
›Reveal solutionSolution
Charles's Law: at constant pressure, gas volume is directly proportional to absolute temperature (V∝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∝T(at constant P, n)orT1V1=T2V2
where T must be expressed in kelvin (absolute temperature), not Celsius.
…
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