= Solution
\b[At the same temperature and pressure, one volume of HCl corresponds to $\tfrac12$ volume of hydrogen and $\tfrac12$ volume of chlorine; one of steam to one of hydrogen and $\tfrac12$ of oxygen; one of $\mathrm{N_2O}$ to one of nitrogen and $\tfrac12$ of oxygen; one of NO to $\tfrac12$ of each element; and one of ammonia to $\tfrac12$ of nitrogen and $\tfrac32$ 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 $\mathrm{H_2}$, $\mathrm{Cl_2}$, $\mathrm{N_2}$ 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.
* For gaseous <hydrogen chloride>, $\mathrm{H_2+Cl_2\rightarrow2HCl}$. Thus $\boxed{V_{\mathrm{HCl}}:V_{\mathrm{H_2}}:V_{\mathrm{Cl_2}}=2:1:1}$. There is no change in total <gas volume> in this idealized combination.
* For <water vapor>, $\mathrm{2H_2+O_2\rightarrow2H_2O(g)}$. Thus $\boxed{V_{\mathrm{H_2O(g)}}:V_{\mathrm{H_2}}:V_{\mathrm{O_2}}=2:2:1}$: three reactant <volumes> give two product <volumes>.
* “Protoxide of nitrogen” is <nitrous oxide>, $\mathrm{N_2O}$. The composition equation $\mathrm{2N_2+O_2\rightarrow2N_2O}$ gives $\boxed{V_{\mathrm{N_2O}}:V_{\mathrm{N_2}}:V_{\mathrm{O_2}}=2:2:1}$. This equation expresses composition; it does not assert that direct mixing gives an easy preparative reaction.
* “Binoxide of nitrogen” in the historical equivalent nomenclature is <nitric oxide>, modern $\mathrm{NO}$, rather than modern <nitrogen dioxide>. The equation $\mathrm{N_2+O_2\rightarrow2NO}$ gives $\boxed{V_{\mathrm{NO}}:V_{\mathrm{N_2}}:V_{\mathrm{O_2}}=2:1:1}$. Older $\mathrm{NO_2}$ notation with <oxygen> equivalent 8 describes the same oxygen-to-nitrogen mass ratio as modern $\mathrm{NO}$ with <oxygen> atomic weight 16; reading its subscript by modern rules changes the substance.<Review of Chemistry for Students by John G. Murphy>[Nitrogen, p.115, “Binoxide of Nitrogen; Nitric Oxide”, older formula and equal elemental volumes]{ref}
* For <Ammonia>, $\mathrm{N_2+3H_2\rightarrow2NH_3}$ gives $\boxed{V_{\mathrm{NH_3}}:V_{\mathrm{N_2}}:V_{\mathrm{H_2}}=2:1:3}$: four reactant <volumes> correspond to two product <volumes>.
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>.
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