Flashcards · 9702 · A Level Topic 15

Ideal gases (A Level) flashcards

15 cards on A Level Topic 15, subtopics 15.1 to 15.3. Pick a subtopic or study them all.

Study mode needs JavaScript. Every card is listed below, so you can still cover the answers and test yourself.

All 15 cards

For a quick read-through or printing. Cover the right-hand side to test yourself.

Amount of substance: A fundamental (SI base) quantity, measured in moles (mol).
Avogadro constant: Nₐ = 6.02 × 10²³ mol⁻¹: the number of particles in one mole of any substance.
How many molecules are in 0.50 mol of gas?: N = nNₐ = 0.50 × 6.02 × 10²³ = 3.01 × 10²³.
How is the Boltzmann constant related to the molar gas constant?: k = R ÷ Nₐ = 8.31 ÷ 6.02 × 10²³ = 1.38 × 10⁻²³ J K⁻¹.

Ideal gas: A gas that obeys pV = nRT at all pressures, volumes and temperatures.
pV = nRT and pV = NkT: what do n and N count?: n: number of moles (R = 8.31 J mol⁻¹ K⁻¹). N: number of molecules (k = 1.38 × 10⁻²³ J K⁻¹). T is the thermodynamic temperature, in kelvin.
2.0 mol of an ideal gas at 300 K occupies 0.020 m³. Find its pressure.: p = nRT ÷ V = (2.0 × 8.31 × 300) ÷ 0.020 = 2.49 × 10⁵ Pa.
Boyle’s law, Charles’s law and the pressure law as special cases of pV = nRT: Constant T: p ∝ 1/V. Constant p: V ∝ T. Constant V: p ∝ T. (Fixed mass of gas, T in kelvin.)
A fixed mass of gas at 1.0 × 10⁵ Pa, 2.0 × 10⁻³ m³, 300 K goes to 1.0 × 10⁻³ m³ and 350 K. Find the new pressure.: p₁V₁/T₁ = p₂V₂/T₂, so p₂ = (1.0 × 10⁵ × 2.0 × 10⁻³ × 350) ÷ (1.0 × 10⁻³ × 300) = 2.33 × 10⁵ Pa.

Assumptions of the kinetic theory of gases: Many molecules in random motion; molecular volume negligible compared with the container; no intermolecular forces except during collisions; collisions perfectly elastic; collision time negligible compared with the time between collisions.
How do moving molecules cause gas pressure?: Molecules collide with the walls and rebound, so their momentum changes. The walls exert a force to change it, and the molecules exert an equal and opposite force on the walls. Pressure = total force ÷ area.
Kinetic theory equation for pressure: pV = ⅓Nm⟨c²⟩, where N is the number of molecules, m the mass of one molecule and ⟨c²⟩ the mean-square speed.
Mean translational kinetic energy of a gas molecule: Comparing pV = ⅓Nm⟨c²⟩ with pV = NkT gives ½m⟨c²⟩ = (3/2)kT. It depends only on the thermodynamic temperature, not on the gas: helium and xenon at the same T have equal mean KE.
Find the r.m.s. speed of nitrogen molecules (M = 0.028 kg mol⁻¹) at 300 K.: c_rms = √(3RT ÷ M) = √(3 × 8.31 × 300 ÷ 0.028) = 517 m s⁻¹.
When do real gases deviate most from ideal behaviour, and why?: At high pressure and low temperature: the molecules are close together, so their own volume and the intermolecular attractions are no longer negligible.