Calculate the temperature of a hydrogen-oxygen flame assuming that the gases at are mixed in stoichiometric proportion and react completely to give . \Delta H_{298}^{\circ} \) of combustion of is kcal The reaction is at constant pressure and the values are R \) for each gas. \)

Chemistry · The first law of thermodynamics: Concept of work, heat, internal energy and enthalpy, heat capacity, molar heat capacity

Calculate the temperature of a hydrogen-oxygen flame assuming that the gases at

Calculate the temperature of a hydrogen-oxygen flame assuming that the gases at \( 25^{\circ} \mathrm{C} \) are mixed in stoichiometric proportion and react completely to give \( H_{2} O(g) . \Delta H_{298}^{\circ} \) of combustion of \( \boldsymbol{H}_{2} \) is \( -\mathbf{5 8} \) kcal \( \boldsymbol{m o l}^{-1} \) The reaction is at constant pressure and the \( C_{p} \) values are \( (7 / 2) R \) for each gas. \( (\boldsymbol{R}=\mathbf{2} \boldsymbol{c} \boldsymbol{a} \boldsymbol{l}) \)

A. \( 8583.71 K \)
B. \( 9583.71 K \)
C. \( 4283.71 \mathrm{K} \)
D. None of the above

Step-by-step solution

The reaction is H2 + 1/2 O2 → H2O(g) at constant pressure. ΔH298 = -58 kcal per mole H2, so heat released is 58,000 cal. The product H2O(g) has Cp = (7/2)R = (7/2)*2 = 7 cal/(mol·K). For adiabatic constant pressure, ΔH = 0: ΔH298 + ∫ Cp dT = 0 → 58,000 = 7(T - 298) → T = 298 + 58,000/7 = 8583.71 K.

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Step-by-step solution

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