= Vapor-density molar mass measurement
An <ideal gas law> measurement obtains <amount of substance> without knowing the <chemical formula> in advance:
$$
n=\frac{pV}{RT},\qquad M_{\rm inferred}=\frac{mRT}{pV}.
$$
Here $p$ is vapor <pressure>, $V$ is its occupied <volume (thermodynamics)>, $T$ is absolute <temperature>, $R$ is the <molar gas constant>, and $m$ is the <mass> of vapor occupying that <volume (thermodynamics)> at those conditions.
Santa Monica College's teaching experiment uses a $125\,\mathrm{mL}$ <Erlenmeyer flask> with a pinhole foil cap, a $600\,\mathrm{mL}$ water bath on a hot plate, a <thermometer>, and a barometer. Excess volatile liquid displaces air. A dissolved dye loses its colour and deposits when the liquid evaporates; three more minutes of heating follow. Cooling condenses retained vapor. Subtracting the dry assembly <mass> from the cooled assembly <mass> supplies $m$. The flask <volume (thermodynamics)> comes from brim-full <water> <mass> and <mass density> at its measured <temperature>. Controls include a dry exterior, excluding bath <water>, and three trials.<11B: The Dumas Method (Experiment) by Santa Monica College>[Santa Monica College, 11B, Experimental Set-up steps 1–6; Trials 1–3 steps 1–4: apparatus, dye endpoint, heating, drying and repetition]{ref}
The inference assumes vapor <pressure> equals atmospheric <pressure>, vapor and bath reach <thermal equilibrium>, the retained vapor <mass> is recovered on cooling, and the vapor obeys the <ideal gas law>. Residual air, <thermal expansion> of the flask, and vapor <temperature> below bath <temperature> are explicit error questions in the teaching experiment. Repeating trials assesses repeatability; it does not remove a shared bias.<11B: The Dumas Method (Experiment) by Santa Monica College>[Lab Report, questions 1–4: residual air, glass expansion, nonideal vapor and incomplete thermal equilibration]{ref}
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