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. `1.0`
B. `10.0`
C. `24.5`
D. `51.4`

Answer

A

Explanation

Let the heat capacity of insulated beaker be C.
Mass of aqueous content in expt.` 1=(100 + 100) xx 1 =200`g
`implies` Total heat capacity `=(C+200 xx 4.2) J//K`
Moles of acid , base neutralised in expt.`1=0.1xx1=0.1`
`implies ` Heat released in expt. `1= 0.1xx57 = 5.7 KJ " "implies 5.7xx1000=(C+200xx 4.2)xxDeltaT.`
`5.7 xx1000 =(C+200+4.2)xx5.7" "implies (C+200xx 4.2)= 1000`
In second experiment, `n_(CH_(3)COOH) = 0.2, n_(NaOH) =0.1`
Total mass of aqueous content `=200`g
`implies` Total heat capacity `=(C+200xx4.2) = 1000 implies` Heat released `=1000xx5.6= 5600 J`
Overall, only `0.1` mol of `CH_(3)COOH` undergo neutralization.
`implies DeltaH_("neutrialization")` of `CH_(3)COOH = -(5600)/(0.1) =-56000 J//mol =-56 KJ//mol.`
`implies DeltaH_("ionization")` of `CH_(3)COOH = 57 - 56 = 1 KJ//mol`