Unit 6 explains how gases behave by picturing them as tiny, fast-moving particles, then turns that picture into equations that link pressure, volume, temperature, and moles. By the end, you should be able to predict how a gas responds to a change and calculate the missing variable with the right gas law.
Read the overview for the big picture, work through the two review notes and their examples, then use the common mistakes and key terms to check yourself before a quiz or test.
Gases are the one state of matter you can describe almost entirely with a few simple equations. This unit starts with the particle model of a gas and builds up to the ideal gas law. It leans hard on unit conversions and algebra, so expect plenty of calculation practice.
Honors Chemistry Unit 6 covers gases. You learn kinetic molecular theory (KMT), which models a gas as widely spaced particles in constant random motion. From there you use Boyle's law (pressure and volume), Charles's law (volume and temperature), Gay-Lussac's law (pressure and temperature), and the combined gas law to solve before-and-after problems. The unit then introduces the ideal gas law, PV = nRT, which brings in moles so you can connect gases to stoichiometry. It also covers Dalton's law of partial pressures for gas mixtures and explains why real gases stop acting ideally at high pressure and low temperature.
More frequent collisions, or collisions that transfer more momentum, mean higher pressure. Shrinking the container makes particles hit the walls more often. Heating makes particles move faster and, in a rigid container, raises the pressure.
Boyle's law keeps temperature fixed, so pressure and volume move in opposite directions. Charles's and Gay-Lussac's laws show that volume or pressure rises directly with Kelvin temperature. The combined gas law handles pressure, volume, and temperature changing together for a fixed amount of gas.
PV = nRT lets you solve for moles, which you can turn into grams or particles. That makes it the bridge between gas measurements and the mole calculations from earlier units. It works best when the gas is hot and at low pressure.
If you can picture what the particles are doing, you can predict which way a variable will move before you calculate anything. Faster particles push harder, and crowded particles hit the walls more often. Use that picture to sanity-check every answer you get from an equation.
Kinetic molecular theory (KMT) pictures a gas as tiny particles moving rapidly in straight lines between collisions.
The ideal gas law, PV = nRT, adds the amount of gas (n, in moles) to pressure, volume, and temperature.
Kinetic molecular theory (KMT) pictures a gas as tiny particles moving rapidly in straight lines between collisions. The particles are far apart, don't attract each other, and collide elastically. Their average kinetic energy is proportional to Kelvin temperature, and pressure is the combined push of particles hitting the container walls.
Every gas law follows from that picture. Squeeze a gas into half the space at the same temperature, and particles hit the walls twice as often, so pressure doubles (Boyle's law). Heat a gas, and particles move faster. The volume then grows to keep pressure steady (Charles's law), or, in a rigid container, the pressure rises (Gay-Lussac's law). The combined gas law, , covers all three, and you cross out whatever stays constant.
Temperature must be in kelvins. Convert with , often rounded to 273. The Kelvin scale starts at absolute zero, so doubling the Kelvin temperature really does double the average particle energy.
Worked example. A balloon holds 2.0 L of air at 27°C and is warmed to 127°C at constant pressure. Find the new volume. Convert first, so K and K. Then L. Plugging in Celsius would give 9.4 L, which is far too big. The temperature went up and so did the volume, which matches the particle picture.
Check yourself. A sealed rigid can of gas at 300 K and 1.5 atm is heated to 600 K. What is the new pressure? The answer is 3.0 atm. At constant volume, pressure is directly proportional to Kelvin temperature, so doubling T doubles P.
| Law | Held constant | Relationship | Equation |
|---|---|---|---|
| Boyle's law | Temperature and moles | P and V are inverse | $P_1V_1 = P_2V_2$ |
| Charles's law | Pressure and moles | V and T are direct | $\frac{V_1}{T_1} = \frac{V_2}{T_2}$ |
| Gay-Lussac's law | Volume and moles | P and T are direct | $\frac{P_1}{T_1} = \frac{P_2}{T_2}$ |
| Combined gas law | Moles only | P, V, and T all change | $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$ |
The ideal gas law, , adds the amount of gas (n, in moles) to pressure, volume, and temperature. Use it when a problem gives one set of conditions instead of a before and after. The value of R depends on your units. With atm and liters, use L·atm/(mol·K). With kPa and liters, use 8.314 L·kPa/(mol·K). At 0°C and 1 atm, a common classroom definition of STP, one mole of an ideal gas occupies about 22.4 L. Some sources define STP with 100 kPa, so check the conditions given in the problem.
Worked example. Find the mass of O₂ in a 5.00 L tank at 2.00 atm and 25°C. Convert the temperature to kelvins, so 25 + 273 = 298 K. Solve for moles with mol. Multiply by the molar mass to get g.
In a mixture, each gas acts as if it were alone. Dalton's law says , so air at 1.00 atm that is 21% oxygen has an O₂ partial pressure of 0.21 atm. Gas collected over water in lab includes water vapor, so subtract the water's vapor pressure to get the dry gas pressure.
Real gases follow closely at high temperature and low pressure. At high pressure, the particles' own volume starts to matter. At low temperature, attractions pull particles together and lower the pressure below the ideal prediction.
Check yourself. A container holds N₂ at 0.60 atm and Ar at 0.25 atm. What is the total pressure, and which gas makes up the larger share of the particles? The total pressure is 0.85 atm. N₂ makes up the larger share because partial pressure is proportional to the number of moles at the same temperature and volume.
| Feature | Ideal gas (KMT model) | Real gas |
|---|---|---|
| Particle volume | Treated as zero | Small but real, and it matters when particles are crowded at high pressure |
| Attractions between particles | None | Present, with strength depending on the substance; their effects increase at low temperature |
| Fits PV = nRT best | Always, by definition | At high temperature and low pressure |
| Typical example | A model, not a real substance | He behaves nearly ideally, and polar NH₃ deviates more |
| Term | Definition |
|---|---|
| Kinetic molecular theory (KMT) | A model describing gases as tiny, widely spaced particles in constant random motion whose average kinetic energy depends on Kelvin temperature. |
| Ideal gas | A hypothetical gas whose particles have no volume and no attractions, so it follows PV = nRT exactly. |
| Pressure | Force per unit area, caused in a gas by particles colliding with container walls and measured in atm, mmHg, kPa, or Pa (1 atm = 760 mmHg = 101.3 kPa). |
| Absolute zero | The temperature of 0 K (-273.15°C), the lowest possible temperature and the starting point of the Kelvin scale. |
| Boyle's law | At constant temperature and moles, the pressure and volume of a gas are inversely proportional, so $P_1V_1 = P_2V_2$. |
| Charles's law | At constant pressure and moles, the volume of a gas is directly proportional to its Kelvin temperature. |
| Gay-Lussac's law | At constant volume and moles, the pressure of a gas is directly proportional to its Kelvin temperature. |
| Ideal gas law | The equation PV = nRT, which relates pressure, volume, moles, and Kelvin temperature for a gas at one set of conditions. |
| Dalton's law of partial pressures | The total pressure of a gas mixture equals the sum of the partial pressures of the individual gases. |
| STP | A standard set of gas conditions. Many high school problems use 0°C and 1 atm, where one mole of an ideal gas occupies about 22.4 L, but some sources use 100 kPa instead of 1 atm. |
Celsius looks normal, so it's easy to forget the conversion. Gas laws need a scale that starts at absolute zero, which is why 0°C would make Charles's law divide by zero. Add 273.15 (often rounded to 273) to every Celsius temperature before you touch an equation.
If pressure is in kPa and you use 0.08206, your answer will be off by a factor of about 101. Look at the units on R first, then convert P to atm or kPa and V to liters to match. A volume in mL needs to be divided by 1000.
Among Boyle's, Charles's, and Gay-Lussac's laws, pressure and volume are inverse when temperature and moles stay constant. Volume or pressure is directly proportional to Kelvin temperature only when the other listed variables and the amount of gas stay constant. Before calculating, predict whether the unknown should go up or down using the particle picture, then check that your number agrees.
Hot, spread-out gases actually behave the most ideally because attractions and particle size barely matter. Deviations show up at high pressure and low temperature, when particles are crowded and slow. That is also the direction that eventually leads to a gas condensing into a liquid.