Past exam of the medicine course of the University of Oxford / 1864 / First examination / Chemistry / 8 / Solution

At the same temperature and pressure, one volume of HCl corresponds to $\frac{1}{2}$ volume of hydrogen and $\frac{1}{2}$ volume of chlorine; one of steam to one of hydrogen and $\frac{1}{2}$ of oxygen; one of ${\mathrm{N}}_2\mathrm{O}$ to one of nitrogen and $\frac{1}{2}$ of oxygen; one of NO to $\frac{1}{2}$ of each element; and one of ammonia to $\frac{1}{2}$ of nitrogen and $\frac{3}{2}$ of hydrogen. All elemental volumes here refer to their ordinary diatomic gases.

The simplest way to avoid an erroneous factor of two is to balance each chemical reaction using ${\mathrm{H}}_2$, $\mathrm{C}{\mathrm{l}}_2$, ${\mathrm{N}}_2$ and ${\mathrm{O}}_2$. Under Avogadro's law, their stoichiometric coefficients are also gas volume ratios, provided all gases are compared at the same temperature and pressure and ideal gas behaviour is a good approximation.

If the common chosen volume of each compound is $V$, the corresponding ordered elemental volumes are therefore $(V/2,V/2)$, $(V,V/2)$, $(V,V/2)$, $(V/2,V/2)$ and $(V/2,3V/2)$. The ratios concern molecular counts and hypothetical free elemental gases, not separate compartments of elemental gas still present inside a compound.

“Hydrochloric acid” must here mean gaseous hydrogen chloride, rather than its aqueous chemical solution; water must remain as steam. If water condenses or Ammonia dissolves in the collecting liquid, measured volumes no longer show these simple ratios. For an experimental comparison, dry-gas and hydrostatic pressure corrections are those discussed in 3.