Question

When 100 $mL$ of 1.0 $M$ $HCl$ was mixed with 100 $mL$ of 1.0 $M$ $NaOH$ in an insulated beaker at constant pressure, a temperature increase of ${5.7}^{\circ }C$ was measured for the beaker and its contents (Expt 1). Because the enthalpy of neutralization of a strong acid with a strong base is a constant (-57.0 $kJmo{l}^{-1}$), this experiment could be used to measure the calorimeter constant. In a second experiment (Expt 2), 100 $mL$ of 2.0 $M$ acetic acid $(K_a=2.0\times {10}^{-5})$ was mixed with 100 $mL$ of 1.0 $M$ $NaOH$ (under identical conditions to Expt 1) where a temperature rise of ${5.6}^{\circ }C$ was measured.
(Consider heat capacity of all solutions as $4.2J{g}^{-1}{K}^{-1}$ and density of all solutions as $1.0gm{L}^{-1}$)

Enthalpy of dissociation (in $kJ$ $mo{l}^{-1}$) of acetic acid obtained from the Expt. 2 is:

• A. 1
• B. 10
• C. 24.5
• D. 51.4

Answer 1

The correct option is A 1

Let the heat capacity of insulated beaker be C
Mass of aqueous content in expt. 1 $=(100+100)\times 1$
$=200\text{g}$
$\Rightarrow$ Total heat capacity $=(C+200\times 4.2)J/K$
Moles of acid, base neutralised in expt. 1 $=0.1\times 1=0.1$
$\Rightarrow$ Heat released in expt. 1 $=0.1\times 57=5.7kJ$
$\Rightarrow 5.7\times 1000=(C+200\times 4.2)\times \Delta T$
$5.7\times 1000=(C+200+4.2)\times 5.7$
$\Rightarrow (C+200\times 4.2)=1000$
In second experiment,
$n_{C{H}_{3}COOH}=0.2$, $n_{NaOH}=0.1$
Total mass of aqueous content = 200 g
$\Rightarrow$ Total heat capacity $=(C+200\times 4.2)=1000$
$\Rightarrow$ Heat released $=1000\times 5.6=5600J$
Overall, only 0.1 mol of $C{H}_{3}COOH$ undergo neutralization.
$\Rightarrow \Delta H_{neutralization}$ of $C{H}_{3}COOH=\frac{-5600}{0.1}=-56000J/mol$
$=-56kJ/mol$
$\Rightarrow \Delta H_{ionization}$ of $C{H}_{3}COOH=57-56=1kJ/mol$