PV=nRT Units: What Units to Use in the Ideal Gas Law
Choosing the right units for PV=nRT is the most common source of errors in gas law calculations. This guide shows you exactly which units to use and how to match them with the correct R value.
Variable Units Reference
| Variable | Symbol | Common Units | SI Unit | Notes |
|---|---|---|---|---|
| Pressure | P | atm, kPa, mmHg, psi, bar | Pa (Pascal) | 1 atm = 101.325 kPa = 760 mmHg |
| Volume | V | L, mL, cm³ | m³ | 1 L = 1000 mL = 0.001 m³ |
| Moles | n | mol | mol | n = mass / molar mass |
| Gas Constant | R | See table below | 8.314 J/(mol·K) | Must match P and V units |
| Temperature | T | K | K (Kelvin) | ALWAYS Kelvin. K = °C + 273.15 |
R Values for Each Unit Combination
| R Value | Units | Pressure Unit | Volume Unit |
|---|---|---|---|
| 0.08206 | L·atm/(mol·K) | atm | L |
| 8.314 | J/(mol·K) = Pa·m³/(mol·K) | Pa | m³ |
| 8.314 | kPa·L/(mol·K) | kPa | L |
| 62.36 | L·mmHg/(mol·K) | mmHg | L |
| 1.987 | cal/(mol·K) | Energy calculations | |
For detailed R values, see Gas Constant R Values.
How to Match R to Your Units
- Look at the pressure unit in your problem (atm, kPa, mmHg, Pa).
- Look at the volume unit (L, mL, m³).
- Find the R value in the table above that matches both.
- If your units don't match any R directly, convert them. It's easier to convert units than to find an obscure R value.
Common Unit Mistakes
- Using °C instead of K: Always convert. K = °C + 273.15. This is the #1 error in gas law problems.
- Using mL instead of L: If R uses liters, convert mL to L by dividing by 1000.
- Mismatching R with units: If P is in kPa, you cannot use R = 0.08206 (that's for atm). Use R = 8.314 kPa·L/(mol·K) instead.
- Forgetting unit conversions: Always check that ALL units are consistent before plugging into the formula.
Unit Conversion Quick Reference
| Conversion | Formula |
|---|---|
| °C to K | K = °C + 273.15 |
| °F to K | K = (°F + 459.67) × 5/9 |
| atm to kPa | kPa = atm × 101.325 |
| atm to mmHg | mmHg = atm × 760 |
| atm to Pa | Pa = atm × 101325 |
| atm to psi | psi = atm × 14.696 |
| L to mL | mL = L × 1000 |
| L to m³ | m³ = L / 1000 |
Try the PV=nRT Calculator — it handles unit conversions automatically.
Frequently Asked Questions
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Temperature must be in Kelvin. Pressure is commonly in atm, kPa, mmHg, or Pa. Volume is in L, mL, or m³. Moles are always in mol. The key is choosing an R value that matches your pressure and volume units.
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R is the same physical constant but expressed in different unit systems. R = 0.08206 L·atm/(mol·K) uses liters and atmospheres, while R = 8.314 J/(mol·K) uses the SI system (Pa and m³). The numerical value changes because the units change.
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The most common mistake is forgetting to convert temperature to Kelvin. Using °C or °F directly will give completely wrong answers. Another common error is mismatching pressure/volume units with the R value.