Ideal Gas Equation — Background
The ideal gas equation combines the simple gas laws (Boyle, Charles, and Avogadro) into a single relationship:
\(PV=nRT\). Here \(P\) is pressure, \(V\) is volume, \(n\) is the amount of gas in moles,
\(T\) is absolute temperature (Kelvin), and \(R\) is the universal gas constant.
Choosing a value of \(R\)
\(R\) has many numerically equivalent forms. Select the form that matches your pressure and volume units so the units
cancel cleanly in the calculation. Common choices:
- \(R=8.314462618\ \mathrm{J\,mol^{-1}\,K^{-1}} = 8.314462618\ \mathrm{Pa\,m^3\,mol^{-1}\,K^{-1}}\)
- \(R=8.314462618\ \mathrm{kPa\,L\,mol^{-1}\,K^{-1}}\)
- \(R=0.08314462618\ \mathrm{bar\,L\,mol^{-1}\,K^{-1}}\)
- \(R=0.082057338\ \mathrm{L\,atm\,mol^{-1}\,K^{-1}}\)
- \(R=62.36367\ \mathrm{L\,mmHg\,mol^{-1}\,K^{-1}}\) (same for torr)
- \(R=8.2057338\times 10^{-5}\ \mathrm{m^3\,atm\,mol^{-1}\,K^{-1}}\)
Temperature must be Kelvin
Always convert to the absolute scale:
\(T_\mathrm{K}=t_{^{\circ}\!\mathrm{C}}+273.15\) or
\(T_\mathrm{K}=(t_{^{\circ}\!\mathrm{F}}-32)\tfrac{5}{9}+273.15\).
Using Celsius or Fahrenheit directly in \(PV=nRT\) gives nonsensical results.
Amount of gas \(n\)
If moles aren’t given explicitly, compute them from a measured mass \(m\) and molar mass \(M\):
\(n=\dfrac{m}{M}\). For particles, \(n=N/N_A\) with Avogadro’s number
\(N_A=6.02214076\times 10^{23}\ \mathrm{mol^{-1}}\).
Rearrangements
Algebraic forms used by the calculator:
- \(P=\dfrac{nRT}{V}\)
- \(V=\dfrac{nRT}{P}\)
- \(n=\dfrac{PV}{RT}\)
- \(T=\dfrac{PV}{nR}\)
Quick unit checks
- With \(R\) in \(\mathrm{kPa\,L\,mol^{-1}\,K^{-1}}\), multiply \(n\) (mol) and \(T\) (K) to get kPa·L; dividing by \(P\) (kPa) leaves L.
- With \(R\) in \(\mathrm{Pa\,m^3\,mol^{-1}\,K^{-1}}\), the product \(nRT\) is Pa·m³; dividing by Pa leaves m³.
- Absolute zero: \(T\to 0\) implies \(V\to 0\) at constant \(P\) (consistent with Charles’s law).
Typical assumptions
The model is best at low to moderate pressures and not-too-low temperatures, where gases behave ideally.
For high precision at high \(P\) or low \(T\), real-gas corrections (e.g., van der Waals) are needed.
