How to Determine the Molar Mass of Nitrogen Gas (N) in a Teaching Lab
The experiment most commonly used to find nitrogen's molar mass relies on generating pure N in a closed system and measuring its mass, volume, temperature, and pressure. A typical undergraduate procedure decomposes sodium azide, NaN, using a balanced equation of 2 NaN 2 Na + 3 N. From the mass of sodium azide consumed, you calculate the theoretical yield of nitrogen, then confirm that number experimentally by collecting the gas and applying the ideal gas law. The resulting molar mass should land very close to 28.02 g/mol, which is the accepted value for N. The reason this experiment works at all is that nitrogen is remarkably inert and behaves nearly ideally under standard lab conditions. At 1 atm and 25°C, the compressibility factor Z for N is approximately 0.9995, meaning the deviation from ideal behavior is about 0.05%. That makes N one of the best candidates for a straightforward PV = nRT calculation, especially compared to gases like CO or ammonia, which require van der Waals corrections to stay within acceptable error margins. For nitrogen, the ideal gas approximation is sufficient for most teaching lab precision levels. Here is the practical procedure I use. Weigh an empty, dry gas collection bulb with a stopcock. Record the mass to at least 0.001 g precision. Attach a known mass of sodium azide powder into a side arm or reaction chamber that can be thermally activated without opening the system. The reaction chamber connects to the bulb through tubing and a water displacement trap. When the azide is heated—typically around 300°C in a controlled oven—the nitrogen gas evolves and displaces water in the collection bulb. Once the reaction is complete, allow the entire apparatus to return to room temperature before taking measurements.
Measure the volume of collected gas by reading the water level inside the bulb or by weighing the displaced water and converting that mass to volume using the density of water at the measured temperature. Record the temperature of the water bath, the barometric pressure in the lab, and the water vapor pressure at that temperature from a standard table. The total pressure inside the bulb equals the barometric pressure plus or minus the hydrostatic head from the water column. Subtract the water vapor pressure from the total pressure to get the partial pressure of dry nitrogen. That correction is critical and is where most student calculations go wrong. I once ran this experiment and got a molar mass of 27.1 g/mol instead of the expected 28.0 g/mol. The discrepancy was 3.2% too low. After two days of checking the math and the equipment, I traced the error to the water vapor correction. The temperature sensor was measuring the air around the bath, not the water itself, and the water had cooled to about 18°C while the sensor read 22°C. The vapor pressure of water at 18°C is 15.5 mmHg, but at 22°C it is 19.8 mmHg. That 4.3 mmHg difference meant I was subtracting too much vapor pressure, which lowered my calculated partial pressure of nitrogen, which in turn lowered the number of moles and inflated the molar mass calculation in the wrong direction. The fix was simple: I submerged the temperature probe directly into the water bath and waited ten minutes for equilibrium before proceeding. The corrected result was 27.9 g/mol, within 0.4% of the accepted value. The calculation itself is straightforward. From the ideal gas law, n = PV / RT. Use the corrected pressure in atmospheres, the volume in liters, the temperature in kelvin, and R = 0.08206 L·atm·mol¹·K¹. Divide the mass of nitrogen by the calculated moles to get the molar mass. The mass of nitrogen comes from the stoichiometry of the decomposition: every mole of NaN produces 1.5 moles of N, and the molar mass of NaN is 65.01 g/mol. So 5.00 g of sodium azide should produce approximately 0.115 mol of N, which at STP occupies about 2.58 L.
There are real limitations to this method that are worth stating plainly. The hydrostatic correction for the water column in the displacement setup is often ignored, but if your water level inside the bulb is 5 cm higher than the outside level, that adds roughly 3.7 mmHg to the internal pressure, which shifts the result by about 0.5%. For a teaching lab where the goal is ±2% accuracy, this is acceptable, but it is a real source of error. Another limitation is that sodium azide is highly toxic. Even small amounts can be absorbed through the skin, and the reaction produces solid sodium metal as a byproduct, which reacts violently with moisture. The procedure must be done in a fume hood with proper PPE, and the waste sodium must be quenched with isopropanol before disposal. A less common but more precise alternative uses a gas syringe and a pre-weighed reaction vessel. You seal the system, initiate the reaction, and measure the volume change directly on the syringe. This eliminates the water displacement step and the associated vapor pressure correction entirely. The trade-off is that gas syringes have friction and stiction issues that introduce their own variability, especially at low volumes below 10 mL. For nitrogen generation from sodium azide, the volumes are typically large enough that the syringe method works reasonably well, but the water displacement method remains the standard in most teaching labs because the equipment is simpler and the corrections are better documented. One detail that rarely gets mentioned is the effect of gas solubility. A small fraction of the generated nitrogen dissolves in the water used for displacement. At 25°C and 1 atm, the Bunsen absorption coefficient for N in water is about 0.015, meaning roughly 1.5% of the gas volume dissolves per atmosphere of contact. In practice, this means your measured volume will be slightly lower than the true evolved volume, which biases the molar mass slightly high. Saturated salt water reduces this effect by about a factor of three, but it does not eliminate it. If you need sub-1% accuracy, you either correct for solubility using published coefficients or use a non-aqueous displacement fluid.
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Another source of systematic error is the assumption that the collected gas is pure nitrogen. If the sodium azide contains impurities or if air was not fully purged from the system before the reaction, trace amounts of oxygen or argon will remain in the collection bulb. Argon is particularly problematic because its molar mass is 39.95 g/mol, which is far from nitrogen's 28.02 g/mol. Even 1% argon contamination would shift the apparent molar mass by about 0.2 g/mol. A proper purge with an inert gas before starting the reaction eliminates this issue, but many lab protocols skip it to save time. For calibration purposes, I sometimes run the same procedure with a known gas like argon from a cylinder. The measured molar mass should be 39.95 g/mol within experimental error. If it is not, the deviation points directly to a systematic issue in the pressure, volume, or temperature measurement chain. This calibration step is something I add to my lab sessions because it gives students a concrete reference point instead of asking them to trust the textbook value. The key numbers to remember for nitrogen are simple. The molar mass of atomic nitrogen is 14.01 g/mol. The molar mass of molecular nitrogen, N, is 28.02 g/mol. Standard temperature and pressure give one mole of an ideal gas a volume of 22.414 L. At 25°C and 1 atm, that volume increases to about 24.47 L. These are the reference points your experiment should converge toward, and the size of the deviation tells you which correction to revisit.
