Use R = 0.0821 when pressure is in atmospheres and volume in liters; use R = 8.314 when you work in SI/energy units (pressure in Pa or kPa and volume in m³, or when R must be in joules).
Explanation
- The gas constant appears in the ideal gas law $PV = nRT$. You must choose the R value whose units match the units of $P$ and $V$ you use.
- Common forms:
- $R = 0.082057\ \text{L·atm·mol}^{-1}\text{·K}^{-1}$ (often rounded to 0.0821) — use if $P$ is in atm and $V$ is in L.
- $R = 8.314462\ \text{J·mol}^{-1}\text{·K}^{-1}$ (often rounded to 8.314 or 8.31) — use if you need energy units (J) or if $P$ is in Pa and $V$ in m³ (SI).
- Other forms: $R = 8.314\ \text{kPa·L·mol}^{-1}\text{·K}^{-1}$ or $0.08314\ \text{bar·L·mol}^{-1}\text{·K}^{-1}$, etc.
You can convert between them because they are the same constant expressed with different unit combinations:
$$8.314\text{ J·mol}^{-1}\text{·K}^{-1}=8.314\text{ kPa·L·mol}^{-1}\text{·K}^{-1}=0.082057\text{ L·atm·mol}^{-1}\text{·K}^{-1}.$$
Quick rule of thumb
- Use 0.0821 when PV is in (atm·L).
- Use 8.314 when PV is in (J) or when P is in Pa (or kPa) and V in m³ (or convert to kPa·L).
Always keep units consistent; otherwise your numeric answer will be wrong.
Short example
Find n from $PV = nRT$ with $P=2.00\ \text{atm}$, $V=10.0\ \text{L}$, $T=300\ \text{K}$:
$$n=\frac{PV}{RT}=\frac{2.00\times10.0}{0.0821\times300}\approx0.81\ \text{mol}.$$