What the keyword means
The phrase iupac stp 1 bar 273.15 k molar volume 22.711 l refers to the standard molar volume of an ideal gas at IUPAC STP, where the standard conditions are: \(T = 273.15\,\mathrm{K}\) and \(P = 1\,\mathrm{bar}\).
Goal: Find the molar volume \(V_m\) (volume per 1 mole) at IUPAC STP and explain why it differs from the older “STP at 1 atm” value.
Step 1: Start from the ideal gas equation
For an ideal gas,
The molar volume is \(V_m = \frac{V}{n}\), so dividing both sides by \(n\) gives
Step 2: Use IUPAC STP values and consistent units
IUPAC STP uses \(T = 273.15\,\mathrm{K}\) and \(P = 1\,\mathrm{bar}\). Choosing the gas constant in matching units,
Step 3: Compute the molar volume at IUPAC STP
Small differences in the last digits can appear if \(R\) is rounded differently; the standard reported value is \(22.711\,\mathrm{L\cdot mol^{-1}}\) at IUPAC STP.
Step 4: Compare with “traditional STP” at 1 atm
Many textbooks historically used STP as \(T=273.15\,\mathrm{K}\) and \(P=1\,\mathrm{atm}\), where \(1\,\mathrm{atm}=1.01325\,\mathrm{bar}\). Using the same formula,
The IUPAC value is larger because \(1\,\mathrm{bar}\) is slightly lower pressure than \(1\,\mathrm{atm}\), and at fixed \(T\), lower pressure implies larger volume for the same amount of gas.
| Condition label | \(T\) | \(P\) | Ideal-gas molar volume \(V_m\) |
|---|---|---|---|
| IUPAC STP | \(273.15\,\mathrm{K}\) | \(1\,\mathrm{bar}\) | \(22.711\,\mathrm{L\cdot mol^{-1}}\) |
| Traditional STP | \(273.15\,\mathrm{K}\) | \(1\,\mathrm{atm}=1.01325\,\mathrm{bar}\) | \(22.414\,\mathrm{L\cdot mol^{-1}}\) |
Visualization: molar volume at 1 bar vs 1 atm (same temperature)
Final result
At IUPAC STP (\(1\,\mathrm{bar}\), \(273.15\,\mathrm{K}\)), the ideal-gas molar volume is \(V_m \approx 22.711\,\mathrm{L\cdot mol^{-1}}\), and it is larger than the traditional \(1\,\mathrm{atm}\) STP value because \(1\,\mathrm{bar} < 1\,\mathrm{atm}\).