Calculate gas volume from mass at RTP

Quantitative chemistry • Volumes of gases

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When to use molar volume of 24.0 dm3

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Use 24.0 dm3 per mole only at room temperature (≈20 °C) and pressure (1 atm) with near-ideal gas behaviour.

Key concepts

What you'll likely be quizzed about

Definition of RTP and molar volume

Room temperature and pressure (RTP) denotes a standard set of conditions used for simple gas volume calculations. RTP corresponds to an approximate temperature of 20 °C and a pressure of 1 atmosphere. Under these conditions, one mole of an ideal gas occupies about 24.0 dm3; this value is the molar volume at RTP and provides a direct link between moles and volume. The molar volume value applies only at the specified temperature and pressure and assumes near-ideal gas behaviour. Significant deviations from RTP or high pressures cause the molar volume to change and require use of the ideal gas equation or experimental data.

Converting mass to amount (moles)

The amount of substance in moles equals mass divided by relative formula mass (Mr). The formula is: moles = mass (g) ÷ Mr. The relative formula mass is the sum of relative atomic masses for all atoms in the formula and is dimensionless. Mass must be in grams for the formula to give moles directly. The calculation produces the amount of substance, which is the required intermediate step before converting amount into gas volume at RTP.

Calculating gas volume from moles at RTP

The gas volume at RTP equals the amount in moles multiplied by the molar volume: volume (dm3) = moles × 24.0 dm3. Combining the two steps gives: volume (dm3) = (mass (g) ÷ Mr) × 24.0. Units must remain consistent: mass in grams, Mr unitless, and volume returned in cubic decimetres (dm3). Conversion to other units requires appropriate factors (1 dm3 = 1 L = 1000 cm3).

Worked numerical example

Example: 10.0 g of carbon dioxide (CO2) has Mr = 44.0. Amount in moles = 10.0 ÷ 44.0 = 0.227 mol (3 s.f.). Volume at RTP = 0.227 × 24.0 = 5.45 dm3. The calculation shows cause → effect: known mass leads to moles via division by Mr; moles lead to volume via multiplication by the molar volume. The result depends on RTP conditions and correct unit usage.

Limitations and significant figures

The method assumes RTP and near-ideal gas behaviour; significant departures require the ideal gas equation (PV = nRT) or experimental molar volumes. Accuracy depends on the precision of mass measurements and the chosen value for the molar volume. Final answers require appropriate significant figures based on input data. Units must be stated with the answer, and any conversions performed in intermediate steps must preserve numerical precision.

Key notes

Important points to keep in mind

RTP corresponds to approximately 20 °C and 1 atm; molar volume = 24.0 dm3 per mole.

Always convert mass to grams before calculating moles.

Moles = mass (g) ÷ Mr; volume (dm3) = moles × 24.0.

State final units (dm3 or L) and include units in intermediate steps as needed.

Use PV = nRT if temperature or pressure differ from RTP.

Convert units correctly: 1 dm3 = 1000 cm3 = 1 L.

Round only the final answer to the correct significant figures.

Check whether gases behave ideally; high pressure or low temperature causes deviation.

Show full working: mass → moles → volume to avoid arithmetic errors.

Mr is unitless; include correct atomic masses for accurate Mr calculation.