We can use the following formula
Q = mc∆T
Q = heat energy (Joules, J), m = mass of a substance (g)
c = specific heat (units J/g∙oC), ∆ is a symbol meaning "the change in"
∆T = change in temperature (oC Celcius)
Heat released by BaBr2 = Heat gained calorimeter + Heat gained by water
Heat gained by calorimeter = (25.93 oC- 22.79oC) x 1.77 J/oC = 5.5578 oC
Heat gained by water = 102.4 gm x 4.184 J/g∙oC x (25.93 oC- 22.79oC) = 1345.3066 Joules
Heat relased by BaBr2 = 5.5578 oC + 1345.3066 Joules = 1,350.8644 Joules = 1.35 Kilo Joules
Moles of BaBr2 = 297.14 g/mol
Moels of BaBr2 = 19.35 gm / 297.14 g/mol = 0.06512 Moles
Enthalpy of dissolution of BaBr2 = 1.35 Kilo Joules / 0.06512 Moles = 20.73 Kilo Joules
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