3 mol of Mg(g) is reacted in a fixed volume bomb calorimeter with excess $N_{2}$ at 298 K and 1 atm into $M g_{3} N_{2} (s)$ . During this reaction, temperature increases from 298.0 K to 325.3 K. If heat capacity of the bomb calorimeter and enthalpy of atomization of Mg(s) are 30.00 kJ and $148 k J m o l^{- 1}$ , respectively, the calculated standard molar enthalpy of formation of $M g_{3} N_{2} (s)$ at 298 K is $Y k J m o l^{- 1}$ . The value of |Y| is _____.
[Given $R = 8.3 J K^{- 1} m o l^{- 1}$ ]

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answer is 383.9.

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Detailed Solution

$\begin{array}{l} 3 M g (s) + N_{2} (g) \overset{}{\to} M g_{3} N_{2} (s); Δ_{f} H ° = ? \\ 3 M g (g) + N_{2} (g) \overset{}{\to} M g_{3} N_{2} (s) - - - - (i) \\ Δ U ° = - (325.3 - 298.00) \times 30 k J = - 819 \\ Δ H ° = Δ U ° + R T Δ n_{g} = - 819 + \frac{8.3 \times 298 \times (- 4)}{1000} = - 828.89 k J \\ 3 M g (s) \overset{}{\to} 3 M g (g); Δ H ° = 3 \times 148 = 444 - - - - - (i i) \\ (i) + (i i) g i v e s \\ 3 M g (s) + N_{2} (g) \overset{}{\to} M g_{3} N_{2} (s); Δ_{f} H ° = - 828.89 + 444 = - 384.89 \end{array}$