question_answer 41)

  \[{{\Delta }_{f}}{{U}^{O-}}\]of formation of \[C{{H}_{4}}\] (g) at certain temperature is\[-393kJ\,mo{{l}^{-1}}\]. The value of \[{{\Delta }_{f}}{{H}^{O-}}\] is: (a) zero                                 (b) \[<{{\Delta }_{f}}{{U}^{O-}}\]                              (c)\[>{{\Delta }_{f}}{{U}^{O-}}\]                                (d) equal to \[{{\Delta }_{f}}{{U}^{O-}}\]

Answer:

  (b)\[C(s)+2{{H}_{2}}(g)\to C{{H}_{4}}(g)\] \[{{\Delta }_{f}}H={{\Delta }_{f}}U+\Delta {{n}_{g}}RT\] \[={{\Delta }_{f}}U+\left\{ 4-\left( \frac{15}{2} \right) \right\}\times RT\] \[={{\Delta }_{f}}U-\frac{7}{2}RT\]                 \[\therefore \]\[{{\Delta }_{f}}H<{{\Delta }_{f}}U\]