#gas law

Ideal Gas Laws and Thermal Properties

A gas occupies 3L at 47∘C and 1.5atm. What will be its volume if the temperature drops to −23∘C and pressure increases t

Given: V1 = 3L, T1 = 47∘C = 320K, P1 = 1.5atm, T2 = −23∘C = 250K, P2 = 3atm. P1V1T1 = P2V2T2. V2 = V1×P1P2×T2T1 = 3×1.53×250320 = 3×0.5×0.78125 = 1.171875L≈1.17L.

Ref: NCBI Bookshelf, Ideal Gas Law: P1V1/T1 = P2V2/T2.

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Latent Heat and Phase Transitions

A gas at 2atm and 47∘C occupies 6L. If the temperature drops to −3∘C and pressure becomes 1.5atm, what is the new volume

Given: P1 = 2atm, T1 = 47∘C = 320K, V1 = 6L, T2 = −3∘C = 270K, P2 = 1.5atm. P1V1T1 = P2V2T2. V2 = V1×P1P2×T2T1 = 6×21.5×270320 = 6×1.3333×0.84375≈6.75L.

Ref: NCBI Bookshelf, Ideal Gas Law: P1V1/T1 = P2V2/T2.

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Latent Heat and Phase Transitions

Which statement is true about the ideal gas equation?

The ideal gas equation (PV = nRT) relates pressure, volume, and temperature for an ideal gas, where R is the universal gas constant and n is the number of moles.

Ref: NCBI Bookshelf, Ideal Gas Law: P1V1/T1 = P2V2/T2.

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Latent Heat and Phase Transitions

A gas at 1.5atm and 77∘C occupies 9L. If the pressure is reduced to 1atm and temperature lowered to 27∘C, what is the ne

Given: P1 = 1.5atm, T1 = 77∘C = 350K, V1 = 9L, P2 = 1atm, T2 = 27∘C = 300K. P1V1T1 = P2V2T2. V2 = V1×P1P2×T2T1 = 9×1.51×300350 = 9×1.5×0.8571≈11.57L.

Ref: NCBI Bookshelf, Ideal Gas Law: P1V1/T1 = P2V2/T2.

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Specific Heat and Calorimetry

A gas at 17∘C and 2.5atm occupies 5L. If the temperature is raised to 67∘C and the volume is adjusted to 7L, what is the

Given: T1 = 17∘C = 290K, P1 = 2.5atm, V1 = 5L, T2 = 67∘C = 340K, V2 = 7L. Ideal gas law: P1V1T1 = P2V2T2. P2 = P1×V1V2×T2T1 = 2.5×57×340290. P2 = 2.5×0.7143×1.1724≈2.09atm.

Ref: NCBI Bookshelf, Ideal Gas Law: P1V1/T1 = P2V2/T2.

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Thermal Expansion of Solids and Liquids

A gas occupies 2.5L at 1.2atm and 37∘C. If the pressure is doubled and temperature increased by 50∘C, what is the new vo

Given: V1 = 2.5L, P1 = 1.2atm, T1 = 37∘C = 310K, P2 = 2.4atm, T2 = 37+50 = 87∘C = 360K. P1V1T1 = P2V2T2. V2 = V1×P1P2×T2T1 = 2.5×1.22.4×360310 = 2.5×0.5×1.1613≈1.45L.

Ref: NCBI Bookshelf, Ideal Gas Law: P1V1/T1 = P2V2/T2.

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Temperature Scales and Triple Point

A gas at 1.9atm and 67∘C occupies 6.5L. If the pressure is increased to 2.5atm and temperature raised to 117∘C, what is

Given: P1 = 1.9atm, T1 = 67∘C = 340K, V1 = 6.5L, P2 = 2.5atm, T2 = 117∘C = 390K. P1V1T1 = P2V2T2. V2 = V1×P1P2×T2T1 = 6.5×1.92.5×390340 = 6.5×0.76×1.1471≈5.66L.

Ref: NCBI Bookshelf, Ideal Gas Law: P1V1/T1 = P2V2/T2.

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Temperature Scales and Triple Point

What happens to the volume of an ideal gas if its temperature is doubled at constant pressure?

For an ideal gas at constant pressure, Charles’ Law states that volume is directly proportional to absolute temperature. If temperature doubles, volume doubles. As per NCERT, applying relevant law/formula with correct units and sign convention leads to It halves. This satisfies dimensional consistency and physical conditions given, so option A is scientifically correct.

Ref: NCBI Bookshelf, Ideal Gas Law: P1V1/T1 = P2V2/T2.

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Temperature Scales and Triple Point

A gas occupies 4.2L at 1.4atm and 47∘C. If the pressure is increased by 0.6atm and temperature decreased by 20∘C, what i

Given: V1 = 4.2L, P1 = 1.4atm, T1 = 47∘C = 320K, P2 = 1.4+0.6 = 2atm, T2 = 47−20 = 27∘C = 300K. P1V1T1 = P2V2T2. V2 = V1×P1P2×T2T1 = 4.2×1.42×300320 = 4.2×0.7×0.9375≈2.76L.

Ref: NCBI Bookshelf, Ideal Gas Law: P1V1/T1 = P2V2/T2.

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Ionic Equilibrium - Acids Bases and pH and Ionization of Weak Acids Bases

For 2HI(g) H₂(g) + I₂(g) , Kp = 0.04 at 500 K. If 1 mole of HI is placed in a 1 L vessel, what is the total pressure at

Initial: PHI = (1 × 0.0831 × 500/1) = 41.55 bar . Let 2x dissociate, PHI = 41.55 - 2x , PH₂ = PI₂ = x , total pressure = 41.55 - 2x + 2x = 41.55 . Kp = (PH₂ PI₂/(PHI)²) = (x²/(41.55 - 2x)²) = 0.04 , (x/41.55 - 2x) = 0.2 , x ≈ 7.58 bar , total = 41.55 bar.

Ref: NCERT Class 11 Chemistry > Chapter 6: Equilibrium > Topic: Ionic Equilibrium - Acids Bases and pH and Ionization of Weak Acids Bases

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