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 o C was measured for the beaker and its contents (Expt.1). Becau

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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 ${5.7}^{o} C$ 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 $(- 57.0 k J m o l^{- 1})$ , 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 ${5.6}^{o} C$ was measured. (Consider heat capacity of all solutions as $4.2 J g^{- 1} K^{- 1}$ and density of all solutions as $1.0 g m L^{- 1}$ )
Enthalpy of dissociation $(i n k J m o l^{- 1})$ of acetic acid obtained from the Expt. 2 is

TestHub · Accepted Answer

Let the heat capacity of insulated beaker be C.
Mass of aqueous content in Expt. 1
$= (100 + 100) \times 1 = 200 g$
$\Rightarrow T o t a l h e a t c a p a c i t y = (C + 200 \times 4.2) J / K$
Moles of acid, base neutralized in Expt. 1 $= 1 \times 0.1 = 0.1$
$\Rightarrow$ Heat absorbed in Expt. 1 $= 0.1 \times 57 = 5.7 k J$
$\Rightarrow 5.7 \times 1000 = (C + 200 \times 4.2) \times Δ T$
$\Rightarrow 5.7 \times 1000 = (C + 200 + 4.2) \times 5.7$
$\Rightarrow (C + 200 \times 4.2) = 1000$
In Second experiment
$n_{C H_{3} C O O H} = 0.2, n_{N a O H} = 0.1$
Total mass of aqueous content = 200 g
$\Rightarrow$ Total heat capacity $= (C + 200 \times 4.2) = 1000$
$\Rightarrow$ Heat released $= 1000 \times 5.6 = 5600 J$
Overall, only 0.1 mol of $C H_{3} C O O H$ undergo neutralization.
$\Rightarrow Δ H_{n e u t r a l i z a t i o n} o f C H_{3} C O O H = \frac{- 5600}{0.1}$
$= - 56,000 J / m o l = - 56 K J / m o l$
$\Rightarrow Δ H_{i o n i z a t i o n} o f C H_{3} C O O H = 57 - 56 = 1 K J / m o l$

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