question_answer 25)

Enthalpies of formation of \[CO(g),C{{O}_{2}}(g),{{N}_{2}}O(g)\]and\[{{N}_{2}}{{O}_{4}}(g)\] are\[-110,-393,+81\]and\[+9.7kJ\,mo{{l}^{-1}}\]respectively. Find the value of\[{{\Delta }_{r}}H\] for the reaction:  

Answer:

Information shadow: The reaction is: \[{{N}_{2}}{{O}_{4}}(g)+3CO(g)\to {{N}_{2}}O(g)+3C{{O}_{2}}(g)\] \[{{\Delta }_{f}}H_{Co(g)}^{{}^\circ }=-110kJ\,mo{{l}^{-1}}\] \[{{\Delta }_{f}}H_{C{{O}_{2}}}^{{}^\circ }=-393kJmo{{l}^{-1}}\] \[{{\Delta }_{f}}H_{{{N}_{2}}O(g)}^{{}^\circ }=+81kJ\,mo{{l}^{-1}}\] \[{{\Delta }_{f}}H_{{{N}_{2}}{{O}_{4}}(g)}^{{}^\circ }=+9.7kJ\,mo{{l}^{-1}}\] Problem solving strategy: \[{{\Delta }_{r}}{{H}^{{}^\circ }}=\Sigma {{\Delta }_{f}}H_{\text{Products}}^{{}^\circ }-\Sigma {{\Delta }_{f}}H_{\text{Reactants}}^{{}^\circ }\] Working it out: \[{{\Delta }_{r}}{{H}^{{}^\circ }}=[{{\Delta }_{f}}H_{{{N}_{2}}O(g)}^{{}^\circ }+3{{\Delta }_{f}}H_{C{{O}_{2}}(g)}^{{}^\circ }]\] \[-[{{\Delta }_{f}}H_{{{N}_{2}}{{O}_{4}}(g)}^{{}^\circ }+3{{\Delta }_{f}}H_{CO(g)}^{{}^\circ }]\] \[=[81+3(-393)]-[9.7+3(-110)]=-777.7kJ\]