What will be the maximum temperature (≈) attained if the process occurs in adiabatic container? — Thermodynamics and Thermochemistry Chemistry Question
Question
What will be the maximum temperature (≈) attained if the process occurs in adiabatic container?
💡 Solution & Explanation
Reaction: $H_2$(g) + 0.5 $O_2$(g) + 2 $N_2$(g) → $H_2O$(g) + 2 $N_2$(g). Since the vessel is rigid, the process is at constant volume. ΔU = ΔH - ΔngRT. At 298 K, ΔU ≈ ΔH - (-0.5) × 2 × 298 × 10^-3 kcal ≈ -57.8 + 0.3 = -57.5 kcal = -57500 cal.<br>This heat is used to raise the temperature of the products (1 mol $H_2O$(g) and 2 mol $N_2$(g)) at constant volume.<br>$C_{v,m}$($N_2$) = $C_{p,m}$ - R = 8.3 - 2.0 = 6.3 cal/K-mol.<br>$C_{v,m}$($H_2O$) = $C_{p,m}$ - R = 11.3 - 2.0 = 9.3 cal/K-mol.<br>Total $C_v$ of products = $C_v$($H_2O$) + 2 × $C_v$($N_2$) = 9.3 + 2 × 6.3 = 21.9 cal/K.<br>ΔT = Q / $C_v$ = 57500 / 21.9 = 2625 K.<br>Final temperature T = 298 + 2625 = 2923 K ≈ 2940 K.