You are checking the performance of a reactor in which acetylene is produced from methane in the reaction 2 CH₄ (g) ? C₂H₂ (g) + 3 H₂ (g) an undesired side reaction is the decomposition of acetylene: C₂H₂ (g) ? 2 C (s) + H₂ (g) methane is fed to the reactor at 1500CC at a rate of 10.0 mol CH₄/s. Heat is transferred to the reactor at a rate of 975 kW. The product temperature is 1500?C and the fractional conversion of methane is 0.600. A flowchart of the process and an enthalpy table are shown below.

(a) Using the heat capacities given below for enthalpy calculations, write and solve material balances and an energy balance to determine the product component flow rates and the yield of acetylene (mol C₂H₂ produced/mo! CH₄ consumed).

CH₄ (g): ? ? ? ? ??C_p?? 0.079 kJ/(mol??C)

C₂H₂ (g) ? ? ? ? ?C_p?? 0.052 kJ/(mol??C)

H₂ (g): ?? ? ? ? ? ??C_p?? 0.031 kJ/(mol??C)

C (s):? ?? ? ? ? ? ??C_p?? 0.022 kJ/(mol??C)

For example, the specific enthalpy of methane at 1500?C relative to methane at 25?C is [0.079 kJ/ (mol??C)] (1500?C ?25?C) = 116.5 kJ/mol.

(b) The reactor efficiency may be defined as the ratio (actual acetylene yield/acetylene yield with no side reaction). What is the reactor efficiency for this process?

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Feed at 1500°C 10.0 mol CH₂/s CH₂ C₂H₂ H₂ с 975 kW Product at 1500°C REACTOR (mol CH₂/s) gimol C₂H₂/s) (mol H₂/s) (mol C(s)/s) References: C(s). H₂(g), at 25°C, 1 atm nin Substance (mol/s) (kJ/mol) 10.0 41.65 nout (mol/s) n n₂ n3 n₁ Ĥout (kJ/mol) Ĥ₁ Ĥ₂ Ĥ₂ Ĥ₁