When a student mixed `50mL` of `1M HCI` and `50mL` of `1M NaOH` in a coffee cup calorimeter, the temperature of the resultant solution increases from `21^(@)C` to `27.5^(@)C`. Assuming that the calorimeter absorbs only a negligible quantity of heat, that the total volume of solution is `100mL`, its density `1gmL^(-1)` and that its specific heat is `4.18 J g^(-1)`. calculate:
a. The heat change during mixing.
b. The enthalpy change for the reaction
`HCI(aq) +NaOH(aq) rarr NaCI(aq) +H_(2)O(aq)`

Explanation

Number of moles of `HCI` and `NaOH` added
`= (MV)/(1000) = (1xx150)/(1000) = 0.15`
Miss of mixture `= V xx d = 1000 xx 1 = 100 g`
Heat evolved, `q = ms DeltaT = 100 xx 4.18 xx (27.5 - 21.0)`
`= 100 xx 4.18 xx 6.5J = 2717J = 2.717 kJ`
The involved reaction is
`HCI(aq) +NaOH(aq)rarr NaCI(aq) +H_(2)O`
`DeltaH^(Theta) =` Heat evolved per mol `= (-2.717)/(0.15) =- 18.11 kJ`