In a constant pressure calorimeter with heat capacity of $450 J K^{- 1},$ 200 ml of 0.9 M HCl and 200 ml of 0.45 M $B a {(O H)}_{2}$ are mixed. (density of final solution $= 1 g m m l^{- 1}$ ). Initially, both solutions are at $21^{o} C .$ Select correct statement
[Given: $Δ H_{N e u t r a l i z a t i o n}^{o} = - 56.2 k J m o l^{- 1}$ ]
Specific heat of $H_{2} O = 4.184 J o u l e g m^{- 1} .$

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Final temperature is ${25.76}^{0} C$

Some HCl is left unreacted

$Δ H^{o}$ of reaction is $- 10.116 \times 10^{3} J$

Some $B a {(O H)}_{2}$ is left unreacted

answer is A, C.

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Detailed Solution

Ans: AC
Moles of $H^{+} = \frac{200 \times 0.9}{1000} = 0.18$
Moles of $O H^{-} = \frac{200 \times (0.45 \times 2)}{1000} = 0.18$
Thus, $[H^{+}] = [O H^{-}]$ hence no reactant is left unreacted.
$Δ_{r} H^{0} = (0.18) (- 56.2 k J m o l^{- 1})$
$= - 10.116 k J$
$Δ H_{s o l u t i o n} = m . s . Δ T = 400 \times 4.184 \times Δ T$
$Δ H_{t o t a l} = 450 Δ T + 1673.6 Δ T$
$10.11 \times 10^{3} = 2123.6 Δ T$
$Δ T = \frac{10116}{2123.6} = 4.7636 \approx 4.76$
$T_{2} = 4.76 + 21 = {25.76}^{0} C$