Hydrogen Collected over Water: Vapor Pressure and Real-Gas Reasoning
A group reacts mossy zinc with excess 3 M HCl and collects the hydrogen over water in an inverted graduated cylinder. When bubbling stops they adjust the cylinder so the water level inside matches the level in the beaker, then read 42.5 mL at 22.0 °C with a barometer reading of 748 mmHg. They compute moles using P = 748 mmHg, V = 42.5 mL, and T = 22.0 °C and get 1.73 × 10^-3 mol, which they convert to 0.113 g of zinc. Their zinc sample weighed 0.115 g before the reaction, and a small piece remained undissolved at the end. The vapor pressure of water at 22.0 °C is 19.8 mmHg. On the report sheet the group writes that no correction is needed because "the ideal gas law already accounts for everything in the cylinder." The instructor asks them to justify that claim and to state how confident the 0.113 g figure should be.
1. Carry out the calculation with the proper correction, and quantify the error introduced by the group's approach.
Read the worked answer
The gas in the cylinder is a mixture of hydrogen and water vapor, so Dalton's law sets the hydrogen partial pressure:
P(H2) = 748 mmHg - 19.8 mmHg = 728.2 mmHg, and 728.2/760 = 0.9582 atm.
Temperature must be in kelvin: 22.0 + 273.15 = 295.15 K, and volume is 0.0425 L.
n(H2) = PV/RT = (0.9582 × 0.0425) / (0.08206 × 295.15) = 0.04072 / 24.22 = 1.68 × 10^-3 mol.
Mass of zinc consumed = 1.68 × 10^-3 mol × 65.38 g/mol = 0.110 g.
The group's uncorrected value was 1.73 × 10^-3 mol, or 0.113 g, so ignoring water vapor inflated the answer by about 2.7% - small but systematic, and always in the same direction.
The conceptual point: the ideal gas law is being applied to a mixture, and it holds for each component's partial pressure, not for the total pressure assigned to hydrogen. The correction needed is a partial-pressure correction, not a fudge factor.
2. The sample weighed 0.115 g and a residue remained undissolved. Assess whether the corrected result is consistent with that observation, and identify which additional experimental factors would bias the mass high or low.
Read the worked answer
The two numbers are consistent. If the sample was 0.115 g and a piece survived, less than 0.115 g of zinc actually reacted; the corrected 0.110 g falls just below that, which is exactly the ordering the residue requires. The uncorrected 0.113 g is also below 0.115 g, so this single check cannot distinguish the two calculations - the vapor pressure correction must be justified on principle rather than by fit to a coarse mass measurement.
Direction of each bias:
- A cylinder not leveled with the beaker: gas pressure inside exceeds atmospheric, so calculated moles come out high.
- Reading while the gas is still warm from the exothermic zinc-acid reaction, or while holding the cylinder: volume too large, moles high.
- A leak or an opening that lets gas escape before the reading: moles low.
- Dissolved H2: the solubility of hydrogen in water at 22 °C is only about 0.8 mM, a few micromoles in 42 mL, negligible here and it would bias low anyway.
- Acid mist or droplets carried into the cylinder: negligible, but it would bias the collected gas volume slightly.
The best next step is a repeat with a longer equilibration time and a leveled cylinder, not a recalculation.
3. A student argues the result is uncertain because hydrogen is not an ideal gas. Evaluate that objection and rank it against the vapor-pressure correction.
Read the worked answer
The objection is directionally correct but quantitatively trivial here. Nonideality is captured by the compressibility factor Z, where PV = ZnRT. For hydrogen near 0.96 atm and 295 K, Z differs from 1 by well under 0.1%, because the pressure is low and hydrogen has weak intermolecular attractions and a small molecular volume. Applying the correction would shift 1.68 × 10^-3 mol by a few millionths of a mole - far below the balance's readability and far below the roughly 2.7% systematic error from water vapor.
The sizes of the corrections differ because they arise from different causes. Nonideality is a property of H2 interacting with itself, and at about one atmosphere hydrogen behaves almost perfectly. Water vapor is not a deviation from ideality at all; it is an additional substance present at a partial pressure of nearly 20 mmHg, about 2.6% of the total. It must be subtracted before the ideal gas law is applied to hydrogen.
A defensible ranking: water-vapor correction (percent-level, systematic) > thermal and leveling effects (percent-level, variable) > H2 nonideality (parts per thousand at most). The student's objection is scientifically valid but not the controlling error.