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. The density of final solution is ${1gm ml}^{-1}$ . Initially, both solutions are at $21^{\circ} C$ . Select correct statement $[G i v e n : Δ H_{N e u t r a l i z a t i o n}^{\circ} = - 56.2 k J m o l^{- 1}]$
Specific heat of $H_{2} O = 4.184 J g m^{- 1}$ .

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

Final temperature is ${25.76}^{\circ} C$

Some HCl is left unreacted

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

answer is A, C.

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Detailed Solution

$M o l e o f H C l = \frac{200 \times 0.9}{1000} = 0.18 M o l e o f O H^{-} = \frac{200 \times (0.45 \times 2)}{1000} = 0.18 T h u s, [H^{+}] = [O H^{-}] h e n c e n o r e a c \tan t i s l e f t u n r e a c t e d Δ_{f} H^{\circ} = (0.18) (- 56.2 k J m o l^{- 1}) = - 10.116 k J Δ H_{c a l o r i m e t e r} = C_{p} Δ T = 450 \times Δ T Δ H_{s o l u t i o n} = m . s . Δ T = 400 \times 4.184 \times Δ T Δ H_{t o t a l} = 450 Δ T + 1673.6 Δ T 10.116 \times 10^{3} = 2123.6 Δ T Δ T = \frac{10116}{2123.6} = 4.7636 K ≃ 4.76 T_{2} = 4.76 + 21 = {25.76}^{\circ} C$