Convert moles to volume for a gas at STP or your own pressure and temperature, convert volume to moles, or use molarity for a solution volume.
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| Calculator Operations | Required Inputs |
|---|---|
| Gas volume from moles | Moles and gas conditions (STP preset or custom pressure and temperature) |
| Gas moles from volume | Gas volume and gas conditions (STP preset or custom pressure and temperature) |
| Solution volume from moles | Moles and molarity |
| Solution moles from volume | Final solution volume and molarity |
Mole to Volume Formula
The following formula is used to convert the number of moles into volume.
All 1 atm examples below state their temperature explicitly. IUPAC standard conditions for gases use 0°C and 100 kPa (1 bar), giving about 22.711 L/mol for an ideal gas. They differ from the historical 0°C, 1 atm convention. See IUPAC standard conditions.
- Where V is the volume
- n is the number of moles
- Vm is the molar volume (volume per mole, e.g., L/mol) at the specified conditions
To calculate volume from moles, multiply the number of moles by the molar volume. For ideal gases, Vm = RT/P, where R = 8.31446 J/(mol·K). Because molar volume scales directly with absolute temperature, every 1% increase in Kelvin temperature (at constant pressure) increases gas volume by 1%.
| Moles (mol) | Volume (L) at 0°C and 1 atm (22.414 L/mol) | Volume (L) at 25°C and 1 atm (24.465 L/mol) |
|---|---|---|
| 0.001 | 0.022 | 0.024 |
| 0.005 | 0.112 | 0.122 |
| 0.010 | 0.224 | 0.245 |
| 0.020 | 0.448 | 0.489 |
| 0.050 | 1.121 | 1.223 |
| 0.075 | 1.681 | 1.835 |
| 0.100 | 2.241 | 2.447 |
| 0.125 | 2.802 | 3.058 |
| 0.200 | 4.483 | 4.893 |
| 0.250 | 5.603 | 6.116 |
| 0.500 | 11.207 | 12.233 |
| 0.750 | 16.810 | 18.349 |
| 1.000 | 22.414 | 24.465 |
| 1.250 | 28.017 | 30.582 |
| 1.500 | 33.621 | 36.698 |
| 2.000 | 44.828 | 48.931 |
| 2.500 | 56.035 | 61.164 |
| 3.000 | 67.242 | 73.396 |
| 4.000 | 89.656 | 97.862 |
| 5.000 | 112.070 | 122.327 |
| Assumes ideal gas behavior. V = n × Vm; entries use R = 8.31446261815324 J/(mol·K) before rounding. Vm ≈ 22.414 L/mol at 0°C and 1 atm; Vm ≈ 24.465 L/mol at 25°C and 1 atm. Values rounded to 3 decimals. | ||
Molar Volume vs. Temperature (Ideal Gas at 1 atm)
Because Vm = RT/P, molar volume is directly proportional to absolute temperature. The table below shows how Vm changes across the temperature range relevant to chemistry and engineering. Furnace exhaust at 500°C holds 2.83 times the volume per mole that the same gas would at 0°C and 1 atm, which directly affects flow rates, duct sizing, and catalyst bed design.
| Temperature (°C) | Temperature (K) | Vm (L/mol) | Relative to 0°C and 1 atm |
|---|---|---|---|
| -100 | 173.15 | 14.21 | 0.634x |
| -50 | 223.15 | 18.31 | 0.817x |
| 0 | 273.15 | 22.41 | 1.000x |
| 25 | 298.15 | 24.47 | 1.092x |
| 50 | 323.15 | 26.52 | 1.183x |
| 100 | 373.15 | 30.62 | 1.366x |
| 200 | 473.15 | 38.83 | 1.732x |
| 300 | 573.15 | 47.03 | 2.098x |
| 500 | 773.15 | 63.44 | 2.830x |
| 1000 | 1273.15 | 104.47 | 4.661x |
| Vm = RT/P. R = 8.31446 J/(mol·K), P = 101,325 Pa. Note the linear relationship: doubling absolute temperature exactly doubles molar volume at constant pressure. | |||
Illustrative Gas Z Inputs at 0°C and 1 atm: Conditional Molar Volumes
| Gas | Z at 0°C and 1 atm | Vm (L/mol) |
|---|---|---|
| Hydrogen (H₂) | 1.0006 | 22.427 |
| Helium (He) | 1.0005 | 22.425 |
| Nitrogen (N₂) | 0.9995 | 22.403 |
| Oxygen (O₂) | 0.9990 | 22.392 |
| Argon (Ar) | 0.9982 | 22.374 |
| Carbon Dioxide (CO₂) | 0.9934 | 22.266 |
| Ammonia (NH₃) | 0.9844 | 22.064 |
These inherited Z values are illustrative inputs, not an independently verified gas-property dataset. The displayed volumes are conditional calculations using Vm = ZRT/P at 0°C and 1 atm. Z above 1 gives a larger volume than the ideal model; Z below 1 gives a smaller volume. Use verified Z data for the actual substance and conditions.
Illustrative Liquid Density Inputs: Molar Volume via Vm = M/ρ
| Substance | M (g/mol) | ρ (g/mL) | Vm (cm³/mol) | Gas/Liquid Ratio at 0°C and 1 atm |
|---|---|---|---|---|
| Water (H₂O) | 18.015 | 0.997 | 18.07 | 1,240x |
| Methanol | 32.04 | 0.791 | 40.5 | 553x |
| Ethanol | 46.07 | 0.785 | 58.7 | 382x |
| Acetone | 58.08 | 0.784 | 74.1 | 303x |
| Benzene | 78.11 | 0.874 | 89.4 | 251x |
| Glycerol | 92.09 | 1.261 | 73.0 | 307x |
The listed molar masses and densities are approximate illustrative inputs with no verified common temperature. Vm = M/ρ; the gas/liquid ratio compares ideal gas at 0°C and 1 atm with that calculated liquid volume. It does not establish vapor-phase stability or determine storage-vessel size.
Illustrative Solid Density Inputs: Molar Volume via Vm = M/ρ
| Substance | M (g/mol) | ρ (g/cm³) | Vm (cm³/mol) |
|---|---|---|---|
| Aluminum (Al) | 26.98 | 2.70 | 9.99 |
| Iron (Fe) | 55.85 | 7.87 | 7.10 |
| Copper (Cu) | 63.55 | 8.96 | 7.09 |
| Gold (Au) | 196.97 | 19.3 | 10.2 |
| Table salt (NaCl) | 58.44 | 2.165 | 27.0 |
| Silicon (Si) | 28.09 | 2.33 | 12.1 |
These approximate molar masses and density inputs illustrate Vm = M/ρ. Use condition-specific measured data for quantitative material-volume work.
Mole to Volume: Gases, Liquids, and Solids
For ideal gases, equal volumes at the same temperature and pressure contain equal amounts of substance. Their molar volume is approximately 22.414 L/mol at 0°C and 1 atm. Real-gas behavior is described by a condition-specific compressibility factor Z; volume is ZnRT/P. The ideal model alone does not provide a universal error bound.
For liquids and solids, the separate relation Vm = M/ρ uses density at the actual conditions; it is not an ideal-gas or molarity calculation. For example, the stated water inputs give about 18.07 cm³/mol. One kilogram of CO₂ corresponds to about 22.7 mol and about 509 L in the ideal-gas model at 0°C and 1 atm. Actual liquid density, phase stability and storage volume require condition-specific property data. The calculator above provides gas and solution conversions; the density relation is a separate reference calculation.
Molar Volume in Chemical Reactions
The most practical application of mole-to-volume conversion is predicting gas volumes produced or consumed in reactions. Because all ideal gases share the same molar volume at a given temperature and pressure, stoichiometric coefficients translate directly into volume ratios. In the combustion of methane (CH₄ + 2O₂ → CO₂ + 2H₂O), under the ideal-gas, complete-reaction model at common temperature and pressure, each liter of CH₄ corresponds to 2 liters of O₂ and 1 liter of CO₂.
As a stoichiometric illustration, the balanced equation 2NaN₃ → 2Na + 3N₂ gives 3 mol of N₂ per 2 mol of NaN₃. An ideal 60 L gas amount at 25°C and 1 atm is about 2.45 mol, corresponding arithmetically to about 1.63 mol or 106 g of NaN₃ in that equation. This is a simplified reaction calculation, not an airbag design or performance prediction.
Mole to Volume Example
How to calculate mole to volume?
- First, determine the number of moles.
Calculate the number of moles.
- Next, determine the molar volume.
Determine the molar volume (volume per mole, e.g., L/mol) at your temperature and pressure.
- Finally, calculate the total volume.
Calculate the total volume using the equation above.
V = n × Vm = 2.5 mol × 24.47 L/mol = 61.2 L
At 0°C and 1 atm: 2.5 × 22.41 = 56.0 L — about 9% less, from the 25°C temperature difference alone.
FAQ
Molar volume (Vₘ) is the volume occupied by one mole of a substance at a specified temperature and pressure. It is not a universal constant; it varies with conditions for gases, and with density for liquids and solids.
At 0°C and 1 atm, one mole of any ideal gas occupies 22.414 L. At 25°C and 1 atm, the value rises to 24.465 L/mol. Both values follow from PV = nRT with R = 8.31446 J/(mol·K).
Use Vm = M / ρ, where M is the molar mass in g/mol and ρ is the density in g/cm³. For example, ethanol (M = 46.07 g/mol, ρ = 0.785 g/mL) gives Vm = 58.7 cm³/mol.
Yes, especially for gases. For an ideal gas, Vm = RT/P; doubling the absolute temperature at constant pressure doubles molar volume. For liquids and solids, thermal expansion causes small changes but the effect is far smaller than for gases.
Molar volume (L/mol or cm³/mol) is the volume per mole of a pure substance. Molar concentration (mol/L) describes moles of solute per liter of solution. For a pure liquid they are reciprocally related: concentration = ρ / M = 1 / Vm.
For an ideal gas, use Vm = RT/P. At 100°C (373.15 K) and 1 atm: Vm = 8.31446 × 373.15 / 101,325 = 0.03062 m³/mol = 30.62 L/mol. For real gases, multiply by the compressibility factor Z: Vm,real = Z × RT/P. The value of Z depends on gas composition, temperature and pressure; those broad conditions do not guarantee a percentage accuracy. Relative volume error of the ideal estimate against the real volume is |1/Z − 1|.
Moles to volume: V = n × Vm, where V is volume, n is amount in moles, and Vm is molar volume at the specified conditions.