Rucete ✏ SAT Chemistry In a Nutshell
5. Gases and the Gas Laws
This chapter introduces the nature of gases, how they are measured, and the laws that describe their behavior. Topics include atmospheric gases, kinetic molecular theory, gas pressure, and fundamental gas laws that help solve SAT Chemistry problems.
Composition and Behavior of Atmospheric Gases
- Earth’s atmosphere is mostly nitrogen (78%) and oxygen (21%), with trace gases like argon, CO₂, and water vapor.
- Atmospheric mixing prevents heavier gases from settling below lighter ones.
- Greenhouse effect is linked to rising CO₂ from fossil fuels; ozone depletion is linked to chlorofluorocarbons (CFCs).
Oxygen
- Makes up ~21% of air; crucial for life and combustion.
- Lab preparation: Heat potassium chlorate (KClO₃) with a catalyst (MnO₂).
Reaction: 2KClO₃ → 2KCl + 3O₂ (g) - Physical properties: Colorless, odorless, tasteless, slightly heavier than air, slightly soluble in water.
- Chemical property: Supports combustion but does not burn itself.
- Ozone (O₃) is an allotrope of oxygen. It forms in the upper atmosphere and absorbs harmful UV radiation.
Hydrogen
- First recognized by Henry Cavendish; burns to form water.
- Lab method: React a metal like zinc with dilute acid (e.g., H₂SO₄).
Zn + H₂SO₄ → ZnSO₄ + H₂ (g) - Other production methods: Electrolysis of water, steam over hot metals, or methane + steam.
- Physical properties: Lightest gas, colorless, odorless, diffuses very rapidly, slightly soluble in water.
- Chemical properties: Combusts in air, good reducing agent, but does not support other combustion.
Measuring Gas Pressure
- Atmospheric pressure = force of air molecules pressing on surfaces (about 1 atm at sea level).
- Measured using a barometer (usually mercury).
1 atm = 760 mm Hg = 101.3 kPa = 101,325 Pa = 760 torr - Manometers measure pressure in containers. Read differences in mercury height to calculate internal pressure.
Kinetic Molecular Theory
- Explains gas behavior using three key assumptions:
- Gases consist of tiny particles with mostly empty space between them.
- Particles are in constant, random, straight-line motion.
- Collisions are elastic—no energy is lost during collisions.
- Temperature is a measure of the average kinetic energy of gas particles.
- Gases diffuse (spread out) and effuse (pass through small holes) due to particle motion.
- Faster motion = higher temperature; slower motion = lower temperature.
Graham’s Law of Effusion
- The rate of effusion/diffusion of a gas is inversely proportional to the square root of its molar mass:
Rate₁ / Rate₂ = √(M₂ / M₁) - Light gases (e.g., H₂) move faster than heavier gases (e.g., O₂).
- Example: Hydrogen diffuses 4 times faster than oxygen.
Charles’s Law
- At constant pressure, volume is directly proportional to temperature (in Kelvin):
V₁ / T₁ = V₂ / T₂ - Must convert °C to Kelvin by adding 273.
- If T increases, V increases; if T decreases, V decreases.
Boyle’s Law
- At constant temperature, volume is inversely proportional to pressure:
P₁V₁ = P₂V₂ - If pressure increases, volume decreases and vice versa.
Combined Gas Law
- Combines Charles’s and Boyle’s Laws for changing P, V, and T:
(P₁V₁) / T₁ = (P₂V₂) / T₂ - Use when all three variables change.
Gay-Lussac’s Law
- At constant volume, pressure is directly proportional to temperature:
P₁ / T₁ = P₂ / T₂ - Example: If gas in a sealed tank is heated, its pressure increases.
Dalton’s Law of Partial Pressures
- For a mixture of gases, total pressure = sum of individual partial pressures:
Ptotal = P₁ + P₂ + P₃ + ... - Applies when gases are collected over water—must subtract vapor pressure of water from total pressure.
Collecting Gases Over Water
- When collecting a gas over water, the sample contains both gas and water vapor.
- To find the pressure of the dry gas, subtract the vapor pressure of water from the total pressure:
P(dry gas) = P(total) − P(water vapor) - Vapor pressure of water depends on temperature and must be looked up in a table.
Correcting for Fluid Height in Eudiometers
- In gas collection tubes, the water (or mercury) level may not be equal inside and outside the tube.
- If the liquid level inside is higher, subtract the difference (converted to mm Hg) from outside pressure.
- If the level outside is higher, add the corrected difference to get the total gas pressure.
- For water: divide height difference by 13.6 to convert to mm Hg (since mercury is 13.6 times denser).
Ideal Gas Law
- The Ideal Gas Law combines all gas variables into one equation:
PV = nRT - Where:
- P = pressure (atm)
- V = volume (L)
- n = moles of gas
- R = ideal gas constant (0.0821 L·atm/mol·K)
- T = temperature (K)
- Use to find moles, volume, pressure, or temperature when the other three are known.
- Example: If given mass, convert to moles using molar mass before solving.
Real Gas Deviations
- Ideal Gas Law assumes no volume for molecules and no intermolecular forces—this is only true under ideal conditions.
- Gases behave most ideally at low pressure and high temperature.
- At high pressure or low temperature, real gases deviate from ideal behavior:
- Molecules get closer → attractions matter
- Volume decreases more than expected → PV < nRT
- Deviations are greater for polar gases and larger molecules.
In a Nutshell
Gases behave in predictable ways governed by pressure, volume, and temperature. Their motion is described by the kinetic molecular theory. The gas laws—Boyle’s, Charles’s, Dalton’s, and the Ideal Gas Law—help us quantify gas behavior. Real gases deviate from ideal models under high pressure or low temperature. Mastery of these principles allows accurate predictions and problem solving in SAT Chemistry.