Question

The oxidising power of chlorine in aqueous solution can be determined by the parameters indicated below: $ \dfrac{1}{2}C{l_{2(g)}} $ to $ Cl_{(aq)}^ - $
(using the data, $ {\Delta _{diss}}{H_{C{l_2}}} = 240kJ/mol,{\Delta _{eq}}{H_{C{l^ - }}} = - 349kJ/mol,{\Delta _{hyd}}{H_{C{l^ - }}} = - 381kJ/mol $ ) will be:
A) $ - 850kJ/mol $
B) $ + 120kJ/mol $
C) $ + 152kJ/mol $
D) $ - 610kJ/mol $

Answer 1

Hint :The oxidising power of Chlorine is equal to the total enthalpy of the reaction of Converting $ \dfrac{1}{2}C{l_{2(g)}} $ to $ Cl_{(aq)}^ - $ . This problem can be solved using Hess's Law which states that the overall enthalpy of a reaction is equal to the sum of all enthalpies in its proceeding steps.

Complete Step By Step Answer:
The conversion of $ \dfrac{1}{2}C{l_{2(g)}} $ to $ Cl_{(aq)}^ - $ involves three steps. First is the Dissociation, Second is the electron gaining step and last is the conversion from gaseous form to aqueous form. Finding the enthalpy for the first step of Dissociation of Chlorine molecule to chlorine atom. The reaction that occurs is:
 $ \dfrac{1}{2}C{l_{2(g)}} \to C{l_{(g)}}(\Delta {H_1}) $
 $ \Delta {H_1} = \dfrac{1}{2}{\Delta _{diss}}{H_{C{l_2}}} = \dfrac{1}{2} \times 240 = + 120kJ/mol $
The second step is the electron gaining step. Chlorine atom gains an electron and converts into Chloride ion. The reaction that occurs is:
 $ C{l_{(g)}} \to Cl_{(g)}^ - (\Delta {H_2}) $
 $ \Delta {H_2} = {\Delta _{eg}}{H_{C{l^ - }}} = - 349kJ/mol $
The third step is the Hydration step of converting gaseous chloride ion to aqueous chloride ion. The reaction that occurs is:
 $ Cl_{(g)}^ - \to Cl_{(aq)}^ - (\Delta {H_3}) $
 $ \Delta {H_3} = {\Delta _{hyd}}{H_{C{l^ - }}} = - 381kJ/mol $
The overall enthalpy of the reaction $ \Delta H $ can be given as the sum of all enthalpies. The overall enthalpy $ \Delta H $ $ = \Delta {H_1} + \Delta {H_2} + \Delta {H_3} $
The overall enthalpy $ = (120 - 349 - 381)kJ/mol = - 610kJ/mol $
The correct Option is Option D).

Note :
The Hess Law, proposed by Henry Hess, states that the overall enthalpy of a reaction is independent of the pathway it follows. The overall enthalpy is the sum of all the enthalpies of the intermediate reactions, into which the main reaction is divided into, provided the temperature remains constant. Mathematically it can be given as:
 $ \Delta {H_{\operatorname{Re} action}} = \sum {\Delta {H_r}} $ ,where $ \sum {\Delta {H_r}} $ is the enthalpy change in all the intermediate reactions involved in the overall conversion.
The Hess Law is primarily used to determine the enthalpy of the reactions that cannot be found experimentally.