3.4 Gas Laws & the Kinetic Molecular Theory

Gases obey their own set of relationships, distinct from the liquids covered in the last sections, but just as central to respiratory physiology — how air moves into the lungs and how oxygen and carbon dioxide are exchanged. Content Category 4B explicitly pairs fluids for circulation with gas movement and gas exchange; this section supplies the gas half of that pairing.

Absolute Temperature and Molar Volume at STP

Every gas law calculation on the MCAT requires temperature in Kelvin (K), the absolute temperature scale where 0 K ("absolute zero") is the theoretical point at which molecular motion stops entirely. Convert from Celsius with:

K = °C + 273

Using Celsius directly in a gas law equation is one of the most common, and easily avoidable, sources of error on this content category. Standard conditions in chemistry are commonly referenced as STP (Standard Temperature and Pressure): 0°C (273 K) and 1 atm. At STP, one mole of any ideal gas occupies 22.4 L — the molar volume of an ideal gas. This number is worth memorizing outright, since it lets you convert between moles and volume instantly without a calculator.

Note a frequent wording trap: standard state conditions in thermodynamics (often 25°C / 298 K and 1 atm or 1 bar) are not the same as STP. When a passage says STP, use 273 K and 22.4 L/mol; when it says 25°C, convert to 298 K and do not assume 22.4 L.

The Ideal Gas Law and Its Three Component Laws

The Ideal Gas Law unifies pressure, volume, moles, and temperature into a single equation:

PV = nRT

where P is pressure, V is volume, n is number of moles, T is absolute temperature, and R is the universal gas constant: R = 0.0821 L·atm/(mol·K), or R = 8.314 J/(mol·K) when working in SI (pascal/meter) units. Three simpler, historically important gas laws are special cases of PV = nRT, each holding one variable constant:

Boyle's Law describes an inverse relationship between pressure and volume at constant temperature and moles — compress a gas, and its pressure rises proportionally. Inspiration and expiration change thoracic volume and therefore alveolar pressure relative to atmosphere (a physiologic cousin of Boyle's idea). Charles' Law describes a direct relationship between volume and absolute temperature at constant pressure — heat a gas at fixed pressure, and it expands proportionally, which is why a helium balloon shrinks in a cold car and expands again in the sun. Avogadro's Law describes a direct relationship between volume and the number of moles at constant temperature and pressure — equal volumes of any ideal gas at the same temperature and pressure contain equal numbers of molecules, regardless of the gas's identity. The combined gas law, P1V1/T1 = P2V2/T2 (n fixed), packs Boyle and Charles together for multi-variable changes.

Kinetic Molecular Theory of Gases

The Kinetic Molecular Theory (KMT) is the conceptual model underlying the Ideal Gas Law. It assumes gas particles: are in constant, random, straight-line motion until they collide; have negligible volume compared to the container; exert no intermolecular forces on one another except during elastic collisions (collisions that conserve total kinetic energy); and have an average kinetic energy directly proportional to absolute temperature, not to the identity or mass of the gas:

KE(avg) per molecule = (3/2) kT and KE(avg) per mole = (3/2) RT

where k is Boltzmann's constant. That temperature–KE link matters: at a given temperature, lighter gas molecules, such as diatomic hydrogen (H2), move faster on average than heavier ones, such as diatomic oxygen (O2), in order to share the same average kinetic energy. Root-mean-square speed scales as v_rms ∝ √(T/M). This is the basis of Graham's Law of effusion and diffusion: the rate of effusion is inversely proportional to the square root of molar mass (rate_A / rate_B = √(M_B / M_A)). Lighter gases effuse and diffuse faster — a fact used in isotope separation historically and tested conceptually on the MCAT.

Heat Capacity at Constant Volume and Constant Pressure

Heat capacity describes how much heat is required to raise a gas's temperature by a given amount. For an ideal gas, heat capacity at constant pressure (Cp) is always greater than heat capacity at constant volume (Cv):

Cp = Cv + R

The reason: at constant volume, all the heat added goes directly into raising the gas's internal energy, and therefore its temperature. At constant pressure, the gas is free to expand as it's heated, so some of the added heat is "spent" doing work on its surroundings (pushing back a piston or the atmosphere) rather than raising temperature — meaning more total heat is required to achieve the same temperature increase.

Boltzmann's constant (k = R/NA ≈ 1.38 × 10⁻²³ J/K, where NA is Avogadro's number) is the per-molecule version of the gas constant, linking a single molecule's average kinetic energy directly to absolute temperature rather than a mole's worth of molecules. On the MCAT, you rarely compute numerical Cp/Cv values, but you should know why Cp > Cv and that monatomic ideal gases have simpler heat capacities than polyatomic gases (more degrees of freedom store energy without raising temperature as quickly).

Deviation of Real Gases from Ideal Behavior

Real gases only approximate the assumptions of the Kinetic Molecular Theory under limited conditions. Deviations from ideal behavior become significant:

• At high pressure, when gas molecules are forced close together, so their own, non-negligible volume starts to matter — the container's "empty space" available for movement is less than assumed.
• At low temperature, when molecules move slowly enough for intermolecular attractive forces, previously assumed negligible, to become significant, pulling molecules together and reducing the pressure or volume they'd otherwise exert.

The Van der Waals equation corrects the Ideal Gas Law quantitatively for these two effects:

(P + an²/V²)(V − nb) = nRT

The a term corrects pressure for intermolecular attraction (a larger value of a means stronger attractive forces, common in polar or highly polarizable molecules), and the b term corrects volume for the finite size of the gas molecules themselves. Gases with strong intermolecular forces, such as water vapor or ammonia, and gases made of large molecules deviate from ideal behavior more than small, nonpolar gases such as helium or hydrogen. Ideal behavior is best approached at high temperature and low pressure — the opposite of the high-P, low-T corner of worst deviation.

Partial Pressure, Dalton's Law, and Henry's Law in Gas Exchange

For a mixture of non-reacting gases, Dalton's Law states that the total pressure equals the sum of each gas's individual partial pressure — the pressure that gas would exert if it alone occupied the entire container:

P(total) = P1 + P2 + P3 + ...

Each gas's partial pressure can also be found from its mole fraction (Xi, the fraction of total moles contributed by that gas) multiplied by the total pressure:

Pi = Xi × P(total)

This directly explains respiratory physiology: atmospheric air is roughly 21% oxygen and 78% nitrogen by mole fraction, so at sea level, where P(total) ≈ 760 mmHg, the partial pressure of oxygen in dry inspired air is about 0.21 × 760 ≈ 160 mmHg. After humidification and mixing with residual alveolar gas, alveolar PO2 is lower (classically near 100 mmHg), and oxygen diffuses from alveolar air into pulmonary capillary blood along its own partial pressure gradient, independent of the other gases present — the core physical principle behind gas exchange in the lungs. CO2 moves the opposite way, down its partial pressure gradient from blood to alveolus.

Henry's Law links gas partial pressure to solubility in liquid:

C = k_H × P

The concentration of a dissolved gas is proportional to its partial pressure above the liquid (with a gas-specific solubility constant k_H). Higher PO2 dissolves more O2 in plasma; higher PCO2 dissolves more CO2. This is why hyperbaric oxygen therapy raises dissolved oxygen, why nitrogen narcosis and decompression sickness are depth/pressure phenomena for divers (more N2 dissolves at high pressure and can bubble out on rapid ascent), and why the amount of gas that can leave alveoli into blood depends on both partial pressure gradients (Dalton) and solubility (Henry). Hemoglobin binding of O2 is in addition to the small Henry's-Law dissolved fraction — the MCAT may test that dissolved O2 is partial-pressure driven even though most arterial O2 content is Hb-bound.

Worked Example: Boyle's Law with Mental-Math-Friendly Numbers

A sealed syringe contains 8 L of an ideal gas at a pressure of 2 atm and constant temperature. A researcher compresses the plunger until the volume is 2 L, without changing the temperature or the amount of gas. Find the new pressure.

Since temperature and moles are constant, apply Boyle's Law:

P1V1 = P2V2

(2 atm)(8 L) = P2(2 L)

16 = P2 × 2

P2 = 8 atm

Compressing the gas to one-fourth its original volume quadruples its pressure, consistent with the inverse relationship Boyle's Law describes. As a quick cross-check using the structure of the Ideal Gas Law: since n and T don't change, the product PV must stay constant, and indeed 2 × 8 = 16 = 8 × 2, confirming the answer.

Bonus check with molar volume: if that same gas were instead described as exactly 1 mole at STP (0°C, 1 atm), you should immediately recognize its volume must be 22.4 L without any calculation — a fact worth having memorized cold for Test Day.

Henry's Law add-on: if the syringe gas were pure O2 at 8 atm over water at fixed temperature, the dissolved O2 concentration would be four times what it was at 2 atm, because C ∝ P at constant k_H — the same proportional idea that underlies dissolved-gas loads under elevated partial pressures.

Common MCAT Traps

• Plugging Celsius directly into a gas law equation. Always convert to Kelvin first (K = °C + 273).
• Forgetting which variable is held constant. Boyle's, Charles', and Avogadro's Laws are each special cases with one variable fixed; using the wrong one produces a nonsensical answer.
• Assuming heavier gas molecules move faster or carry more kinetic energy. At the same temperature, all ideal gas molecules have the same average kinetic energy regardless of mass — it's speed, not kinetic energy, that differs, with lighter molecules moving faster.
• Mixing up the a and b corrections in the Van der Waals equation. The a term relates to intermolecular attraction and affects the pressure term; the b term relates to molecular volume and affects the volume term.
• Forgetting that mole fraction is dimensionless and that partial pressures must sum to the total pressure, a quick way to check your own arithmetic in a multi-gas mixture problem.
• Confusing Dalton (partial pressures add) with Henry (dissolved concentration ∝ partial pressure). Gas exchange needs both: gradients from Dalton/partial pressures, solubility from Henry.