Gas Laws (College Board AP® Chemistry): Flashcards

The partial pressure of gas A in a mixture is given by PA = XA × P_T, where X_A is the mole fraction of A.

The gas collected is a mixture of the target gas and water vapor. By Dalton's law, PT = Pdry gas + P_H₂O. To find the pressure (and therefore the moles) of the dry gas alone, subtract the vapor pressure of water at that temperature from the total pressure.

True.

Mole fraction is the ratio of moles of one component to total moles. Since a component cannot contribute more moles than the total, X_A is always between 0 (absent) and 1 (pure gas).

Mole fraction of N₂: XN₂_ = 0.40 / (0.40 + 0.10) = 0.40 / 0.50 = 0.80

PN₂ = XN~2~ × P_T = 0.80 × 2.50 = 2.00 atm

At constant temperature and fixed amount of gas, the volume of a gas is inversely proportional to its pressure: PV = constant, or P₁V₁ = P₂V₂. A plot of V vs P gives a curve; a plot of V vs 1/P gives a straight line.

False.

Boyle's Law shows an inverse relationship (V ∝ 1/P), so a V vs P plot gives a hyperbolic curve, not a straight line. A straight line through the origin is obtained only when V is plotted against 1/P.

At constant pressure and fixed amount of gas, the volume of a gas is directly proportional to its absolute temperature: V/T = constant, or V₁/T₁ = V₂/T₂. Temperature must be in Kelvin. A V vs T (K) plot gives a straight line through the origin.

Extrapolating a volume–temperature (Celsius) graph to zero volume gives a temperature intercept of −273.15°C, which corresponds to 0 K — defined as absolute zero.

Avogadro's Law states that at constant temperature and pressure, the volume of a gas is directly proportional to its number of moles: V/n = constant, or V₁/n₁ = V₂/n₂. A plot of V vs n gives a straight line through the origin.

True.

Charles's Law relies on the direct proportionality V ∝ T. This only holds when T is the absolute (Kelvin) temperature. Using Celsius temperatures would give incorrect results because the Celsius zero is arbitrary, not a true zero of energy.

Using Boyle's Law: P₁V₁ = P₂V₂

V₂ = P₁V₁ / P₂ = (1.00 × 20.0) / 2.00 = 10.0 L

Doubling the pressure halves the volume, consistent with the inverse relationship.

A model that explains gas behavior at the molecular level using five key assumptions:

• gas molecules are negligibly small points with no significant volume

• molecules move randomly in straight lines

• intermolecular forces are negligible except during collisions

• collisions are elastic — total kinetic energy is conserved

• average kinetic energy is proportional to absolute temperature

True.

Elastic collisions conserve total kinetic energy. This means gas molecules continue to move with the same average kinetic energy unless energy is added or removed — the total kinetic energy of the gas is preserved across every collision.

Compressing the gas reduces the volume, so molecules collide with the container walls more frequently. At constant temperature, their average speed (and hence force per collision) is unchanged, but the increased collision frequency produces a higher pressure.

The average kinetic energy of a gas molecule is given by KE = ½mv², where m is molecular mass and v is average speed.

False.

At the same temperature, gases share the same average kinetic energy (KE ∝ T), but average speed depends on molecular mass (KE = ½mv²) — so lighter molecules move faster even though their kinetic energies are equal.

Absolute zero is 0 K (equivalent to −273.15 °C) — the lowest possible temperature, at which gas molecules would have minimum kinetic energy. The Kelvin scale is anchored at this point, with 1 K equal in magnitude to 1 °C.

Gas law equations require an absolute temperature scale because they are based on direct proportionalities — doubling the Kelvin temperature genuinely doubles the average kinetic energy, whereas Celsius temperatures are relative and would give physically incorrect results in ratio-based equations.

To convert a temperature from Celsius to Kelvin, use the relationship: K = °C + 273.15.

A mathematical description of the spread of molecular speeds (or kinetic energies) in a gas at a given temperature. It shows that molecules move at a range of speeds, with most clustered near the most probable speed and fewer at very low or very high speeds.

The curve shifts to the right (higher speeds), the peak lowers and moves to a higher most probable speed, and the curve broadens. More molecules have higher kinetic energies, reflecting the increased average kinetic energy at higher temperature.

False.

The Maxwell-Boltzmann distribution shows that molecules move at a wide range of speeds at any temperature. The curve gives the fraction of molecules at each speed — from near zero to very high values — with the peak representing only the most probable speed.

On a Maxwell-Boltzmann distribution curve, the peak of the curve corresponds to the most probable speed, which is the speed possessed by the largest number of molecules.

True.

At lower temperature, molecules have less kinetic energy on average. The most probable speed decreases (curve shifts left), and more molecules are concentrated near that lower speed, so the peak is higher and narrower.

Because kinetic energy (KE = ½mv²) is directly related to speed, the effects of temperature on both quantities are equivalent. The examiner may use either label — the shape of the distribution and how it shifts with temperature are identical in both cases.

The deviation of a real gas from the predictions of the ideal gas equation, caused by the existence of intermolecular forces and the finite volume of gas molecules. Deviations are most significant at high pressure and low temperature.

False.

Real gases deviate most from ideal behavior at low temperature and high pressure. At low temperature, molecules lack the kinetic energy to overcome intermolecular attractions; at high pressure, molecules are crowded together so their own volumes become significant.

At high temperature, molecules have sufficient kinetic energy to overcome intermolecular attractions, so forces between molecules become negligible. At low pressure, molecules are widely spaced, so their individual volumes are negligible relative to the container — both key assumptions of the ideal gas model are satisfied.

For one mole of an ideal gas, the quantity PV/RT equals 1 at all pressures. A real gas deviates from this when plotted as PV/RT against pressure.

True.

At high pressure, molecules are packed closely together. Their own finite volume is no longer negligible compared to the container volume, so the real gas occupies more volume than the ideal gas equation (which assumes zero molecular volume) would predict.

At lower temperature, molecules have less kinetic energy and cannot overcome the intermolecular attractive forces between them. Instead of bouncing off each other elastically, molecules tend to stick together momentarily, reducing the pressure and volume below what the ideal gas equation predicts.