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Enthalpy

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What will be the final temperature attained if all the heat released in neutralization of $1$ L of $0.2$ M $N H_{4} O H$ with $2$ L of $0.1$ M HCl increases the temperature of the final solution having density $0.95$ gm/ml and specific heat capacity = $13 J / g^{0} C$ , if original temperature was $27^{0} C$ ? Assume weak base to be completely unionized.

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Solution

$N H_{4} O H + H C l \to N H_{4} C l + H_{2} O$
Number of mole of $N H_{4} O H = 1 L \times 0.2 M$
$n_{N H_{4} O H} = 0.2 m o l e$
Number of mole of $H C l = 2 L \times 0.1 M$
$n_{H C l} = 0.2 m o l e$
Total volume of final solution = $2 L + L = 3 L$
Mass = $0.95 \times 3 L \times 1000 = 2850 g m$
total heat released = $2850 \times 13 J \times Δ T = 37.05 k J Δ T$
$37.05 Δ T = 51.46 k J$
$Δ T = \frac{51.56}{37.05} = 1.4$
$T_{2} - T_{1} = 1.4$
$T_{2} - 300 = 1.4$
$T_{2} = 301.4 k$

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