Each of the following chemical reaction is carried out at constant temperature and constant pressure. Considering the reaction mixture to be the system, predict the reaction for which `w` is zero?

Options

A. `2 NH_(4) NO_(3) (s) rarr 2 N_(2) (g) + 4 H_(2) O (g) + O_(2) (g)`
B. `2SO_(2) (g) + O_(2) (g) rarr 2SO_(3) (g)`
C. `H_(2) (g) + Cl_(2) (g) rarr 2HCl (g)`
D. `C_(2) H_(5) OH (l) + 2 O_(2) (g) rarr 2 CO_(2) (g) + 2 H_(2) O (l)`

Answer

C

Explanation

For a process at constant pressure, `w = - P Delta V`. By the ideal gas law `(PV = nRT)`, `P Delta V = Delta nRT` at constant temperature. Here, `Delta n` is the change in the number of moles of gaseous substances in the reaction:
`Delta n=` (Number of moles of gaseous products) - (Number of moles of gaseou reactants)
In reaction in which equal numbers of moles of gases are produced and consumed at constant `T` and `P` essentially no work is done as `Deltan = 0`. The work term `w` has a significant value at constant `P` and `T` only when there are different numbers of moles of gaseous products and reactants so that the volume of the system changes.
Because both `R` and `T` (on the Kelvin scale) are positive quantities, the sign of `w` is opposite from that of `Delta n`, it tells whether the work is done on `(w i s + ve)` or by `(w i s - ve)` the system.