In which of the following reactions is the work done zero? Assign the sign of w (+ve or -ve) for the cases in which work is involved.
(i) `2SO_(2)(g)+O_(2)(g)to2SO_(3)(g)`
(ii) `2Na(s)+2H_(2)O(l)to2NaOH(aq)+H_(2)(g)`.
(iii) `N_(2)(g)+O_(2)(g)to2NO(g)`.

Explanation

In a chemical reaction, pressure-volume work `w=-P_(ex)DeltaV=-DeltanRT`, where `Deltan=`total number of moles of gaseous products-total number of moles of gaseous reactants.
In reaction (iii), `Deltan=0`, so, w=0
In reaction (i), `Deltan=2-(1+2)=-1`
So, `w=-DeltanRT=RT,` i.e., `w gt0`
In reaction (ii), `Deltan=1`. so, `w=-DeltanRT=-RT`, i.e., `w lt0`.