When `100mL` of `1.0M HCl` was mixed with `100 mL` of `1.0 M NaOH` in an insulated beaker at constant pressure, a temperature increase of `5.7^(@)C` was measured for the beaker and its contents (Expt.1). Because the enthalpy of neutralisation of a strong acid with a strong base is constant `(-57.0kJmol^(-1))` this experiment couldbe used to measure the calorimeter constant. In a second experiment (Expt.2), `100mL` of `2.0M` acetic acid `K_(a)=2.0xx10^(-5))` was mixed with `100mL` of `1.0M NaOH` (under identical conditions to Expt. 1) where a temperature rise of `5.6^(@)C` was measured.
Enthalpy of dissociation (in `kJ mol^(-1)`) of acetic acid obtained from the Expt. 2 is

Options

A. 1
B. 10
C. 24.5
D. 51.4

Answer

A

Explanation

Number of moles of HCl and NaOH
`=(MV)/(1000)=(1xx100)/(1000)=0.1`
Heat released in neutralization `=0.1xx57=5.7kJ`
`=5700kJ`
Heat used to increase the temperature of mixed solution
`=msDeltaT`
`=200xx4.2xx5.7`
`=4788J`
Heat used to increase the temperature of calorimeter
`=5700-4788=912J`
i.e., `msDeltaT=912`
`msxx5.7=912`
`ms=160JK^(-1)` for calorimeter
Heat released in neutralization of `CH_(3)COOH and NaOH`
`=(msDeltaT)_("solution")+(msDeltaT)_("calorimeter")`
`=(200xx4.2xx5.6)+(160+5.6)=5600J`
Heat used in the dissociation of `CH_(3)COOH` per mol
`=(5700-5600)/(0.1)`
`=1000J=1kJ" "mol^(-1)`.