Answer: The enthalpy of the reaction is coming out to be -361.86 kJ.
Step-by-step explanation:
Enthalpy change is defined as the difference in enthalpies of all the product and the reactants each multiplied with their respective number of moles. It is represented as
![\Delta H](https://img.qammunity.org/2020/formulas/chemistry/middle-school/bqomo6yvpcq2ti7z3rpzjmrzpghnoys7hh.png)
The equation used to calculate enthalpy change is of a reaction is:
![\Delta H^o_(rxn)=\sum [n* \Delta H^o_f_((product))]-\sum [n* \Delta H^o_f_((reactant))]](https://img.qammunity.org/2020/formulas/chemistry/high-school/5c7vs79qepq19tdktywtbtker28hpuplvy.png)
For the given chemical reaction:
![2Al^(3+)(aq.)+3Cl_2(g)\rightarrow 2AlCl_3(s)](https://img.qammunity.org/2020/formulas/chemistry/college/jgwpc2lh11ggww53s9fblm64xfn1l10fjo.png)
The equation for the enthalpy change of the above reaction is:
![\Delta H^o_(rxn)=[(2* \Delta H^o_f_((AlCl_3(s))))]-[(2* \Delta H^o_f_((Al^(3+)(aq.))))+(3* \Delta H^o_f_((Cl_2(g))))]](https://img.qammunity.org/2020/formulas/chemistry/college/e305at8dzodgeyf9znnecqr1ibkl4fslbk.png)
We are given:
![\Delta H^o_f_((AlCl_3(s)))=-705.63kJ/mol\\\Delta H^o_f_((Al^(3+)(aq.)))=-524.7kJ/mol\\\Delta H^o_f_((Cl_2))=0kJ/mol](https://img.qammunity.org/2020/formulas/chemistry/college/hhn6ywhy9riy942vn4umeijpwmptf778rz.png)
Putting values in above equation, we get:
![\Delta H^o_(rxn)=[(2* (-705.63))]-[(2* (-524.7))+(3* (0))]\\\\\Delta H^o_(rxn)=-361.86kJ](https://img.qammunity.org/2020/formulas/chemistry/college/wwgnyqbpsfqsip2hlu5ts42r10wyoxtwab.png)
Hence, the enthalpy of the reaction is coming out to be -361.86 kJ.