The Memory Trick
💡 PV = nRT
The Ideal Gas Law connects four properties of a gas into a single equation: Pressure (P) times Volume (V) equals moles (n) times the gas constant (R = 8.314 J/mol·K) times Temperature (T, always in Kelvin). Change any one of these variables, and at least one other must change to keep the equation balanced.
Why It Works
This single equation actually combines three earlier, separately-discovered gas laws (Boyle's, Charles's, and Avogadro's laws) into one relationship — instead of memorizing three separate rules, PV=nRT handles all of them at once.
Step by Step
Applying the Ideal Gas Law
1
Always convert to Kelvin first
T must be in Kelvin for this equation to work correctly — using Celsius directly will give wrong answers, since Kelvin is the only scale where zero actually means zero thermal energy.
25°C must be converted to 298 K (25 + 273) before plugging into PV = nRT.
2
Compressing gas raises pressure
If temperature and moles stay fixed, reducing volume forces pressure to increase proportionally, to keep PV constant.
Pushing down a bicycle pump compresses the air inside, and you feel increasing resistance as pressure rises.
3
Heating gas raises pressure or volume (or both)
With moles fixed, increasing temperature must be balanced by an increase in pressure, volume, or both, to keep the equation balanced.
A sealed can heated over a fire builds internal pressure as temperature rises, since volume can't increase — eventually causing it to burst if pressure exceeds the can's strength.
🏥 Worked Example
A gas sample occupies 2.0 L at a pressure of 3.0 atm and a temperature of 300 K. How many moles of gas are present? (Use R = 0.0821 L·atm/mol·K for these units.)
1
Rearrange PV = nRT to solve for n: n = PV/RT.
2
Plug in values: n = (3.0 × 2.0)/(0.0821 × 300) = 6.0/24.63 ≈ 0.244 mol.
3
Note the units: using R = 0.0821 L·atm/mol·K (rather than the SI 8.314 J/mol·K) matched the given units of L and atm directly, avoiding unnecessary conversion.
📌 Exam Application
Exams test correctly rearranging PV=nRT for any missing variable, converting temperature to Kelvin without fail, and choosing the correct value/units of R to match the given pressure and volume units.
⚠️ Most Common Ideal Gas Law Mistakes
The most common trap is forgetting to convert Celsius to Kelvin before plugging into the equation — even a seemingly small error like using 25 instead of 298 produces a drastically wrong answer, since the equation is not linear in a way that tolerates the offset.
✓ Quick Self-Test
1) Write the Ideal Gas Law. PV = nRT. 2) Why must temperature always be in Kelvin for this equation? Because Kelvin is the only scale where zero represents true zero thermal energy — Celsius has an offset that breaks the proportional relationship. 3) If volume is compressed while temperature and moles stay constant, what happens to pressure? It increases proportionally. 4) What three earlier gas laws does PV=nRT combine into one equation? Boyle's Law, Charles's Law, and Avogadro's Law. 5) What is the value of the gas constant R in SI units? 8.314 J/mol·K.