 Solution

The nineteenth-century phrase “impure air” mixed several different mechanisms. Irritant smoke and dust can damage the respiratory system; toxic gases can poison without causing an infection; crowded, poorly ventilated rooms can increase exposure to infectious material. The historical miasma theory treated foul emanations much more broadly as generators of disease. In particular, the smell of sewage does not itself establish the cause of typhoid fever, cholera or malaria.

For the first part, important real consequences include the following:

For the second part, ordinary outdoor air already contains nitrogen, oxygen, a small amount of carbon dioxide, and variable water vapour. Their presence alone is not evidence of pollution. In a smoky industrial town, soot, mineral dust, products of fuel combustion and sulfur dioxide would be particularly relevant. In occupied rooms, expired carbon dioxide, water vapour and suspended biological material increase unless removed. Decomposing wastes may contribute Ammonia, hydrogen sulfide and other volatile products. The actual mixture depends on sources, ventilation and weather.

For the third part, begin with a defined sampling site and time, record occupancy or industrial activity, and compare with a suitable reference. A volume of air, not simply an unrecorded sniff or a discoloured paper, is the basis of quantitative comparison. Methods available by 1867 include:

The chemical equations underlying two of these qualitative tests areHere the precipitates are barium carbonate and lead sulfide. For the baryta absorption method, in an ideal, fully captured sample with no interfering acid gases, the difference between blank and sample acid requirements satisfieswhere $c_{{\mathrm{H}}^{+}}$ is the amount concentration of titratable acid equivalents and the volumes refer to titration of the entire corresponding absorbent portions; any aliquot requires its scale factor. The factor two follows from the two acid equivalents neutralized per mole of barium hydroxide. This calculation assumes that the barium carbonate precipitate is excluded from the residual-base determination; dissolving it again with the titrant would invalidate the inference.

Odour, visible smoke and room stuffiness are useful prompts to investigate, but no single smell, carbon dioxide value, microscopic field or chemical colour test establishes that air is free of harmful impurities. Specify which material was measured and which uncertainty remains.