[Four-digit Integer] The heat of total cracking of hydrocarbons, ΔHTC is defined as ΔH at 298.15 K a — Thermodynamics and Thermochemistry Chemistry Question
Question
[Four-digit Integer] The heat of total cracking of hydrocarbons, ΔHTC is defined as ΔH at 298.15 K and 101.325 kPa for the process: CnHm + (2n - m/2) $H_2$ → n $CH_4$. The values of ΔHTC is -65.2 kJ for $C_2H_6$ and -87.4 kJ for $C_3H_8$. Calculate ΔH (in kJ) for: $CH_4$(g) + $C_3H_8$(g) → 2 $C_2H_6$(g)
💡 Solution & Explanation
The reaction is $CH_4$(g) + $C_3H_8$(g) → 2 $C_2H_6$(g). Using the ΔHTC values:<br>Reaction for $C_2H_6$ cracking: $C_2H_6$ + $H_2$ → 2 $CH_4$; ΔH = -65.2 kJ.<br>Reaction for $C_3H_8$ cracking: $C_3H_8$ + 2 $H_2$ → 3 $CH_4$; ΔH = -87.4 kJ.<br>Combining these to get target reaction: $CH_4$ + $C_3H_8$ → 2 $C_2H_6$.<br>ΔH = ΔH($C_3H_8$ cracking) - 2 × ΔH($C_2H_6$ cracking) = -87.4 - 2 × (-65.2) = -87.4 + 130.4 = +43.0 kJ.<br>Thus, ΔH = 43 kJ.