Answer : The enthalpy change for the solution is 42.8 kJ/mol
Explanation :
Heat released by the reaction = Heat absorbed by the calorimeter + Heat absorbed by the water
![q=[q_1+q_2]](https://tex.z-dn.net/?f=q%3D%5Bq_1%2Bq_2%5D)
![q=[c_1\times \Delta T+m\times c_2\times \Delta T]](https://tex.z-dn.net/?f=q%3D%5Bc_1%5Ctimes%20%5CDelta%20T%2Bm%5Ctimes%20c_2%5Ctimes%20%5CDelta%20T%5D)
where,
q = heat released by the reaction
= heat absorbed by the calorimeter
= heat absorbed by the water
= specific heat of calorimeter = 
= specific heat of water = 
= mass of water = 100.0 g
= change in temperature = 
Now put all the given values in the above formula, we get:
![q=[(15.8J/^oC\times 8.1^oC)+(100.0g\times 4.18J/g^oC\times 8.1^oC)]](https://tex.z-dn.net/?f=q%3D%5B%2815.8J%2F%5EoC%5Ctimes%208.1%5EoC%29%2B%28100.0g%5Ctimes%204.18J%2Fg%5EoC%5Ctimes%208.1%5EoC%29%5D)
(1 kJ = 1000 J)
Now we have to calculate the enthalpy change for the solution.

where,
= enthalpy change = ?
q = heat released = 3.5138 kJ
m = mass of NaOH = 3.25 g
Molar mass of NaOH = 40 g/mole

Now,

Therefore, the enthalpy change for the solution is 42.8 kJ/mol