Can someone help me please Thank you Ethane is burned in pur

Can someone help me please? Thank you

Ethane is burned in pure oxygen in a continuous flow furnace. The produced heat is used to reform methane with steam to produce \"synthesis gas in a continuous- flow reactor. Ethane combustion: 2 C2H6 (g) 7 O2 (g) 4 CO2 (g) 6 H20 (g) Catalytic Reforming: CH4 (g) H20 (g) CO (g) 3 H2 (g) A 2:7 molar mixture of ethane and oxygen enters the furnace at TJ25 C, P-1 bar, and 27 mol/s flow rate. After a complete combustion, the product gas leaves the furnace at P-1 bar and T-1000 K. 30 percent of the heat generated is lost to the surroundings and the remaining heat produced is transferred to the reactor. A 1:3 molar mixture of methane and water enters the reactor at T 400 K and P 1 bar. The reaction proceeds to completion and the products exit the reactor at T 800 K and P-1 bar. Find the molar flow rate of the \"synthesis gas\" when it exits the reactor. Assume all gases to be ideal.

Solution

It is given that a 2:7 molar mixture of ehtane and oxygen enters the chamber for combustion. This is the stoichiometric mixture. Hence no excess oxygen or ethane enters and it undergoes complete combustion.

It is given that the molar flow rate into the combustion chamber is 27 mol/sec.

If I assume the molar flow rate of ethane as 2x, then the molar flow rate of oxygen is 7x

Hence total flow rate is the sum of individual flow rates 2x + 7x = 9x = 27 mol/sec

=> x = 3 mol/sec

Hence, molar flow rate of ethane is 6 mol/sec

We know that enthalpy of combustion of ethane is 1560 kJ/mol (taken from wiki)

Assuming that there is no ethane unburnt, the heat produced is given as = enthalpy* flow rate

= 1560*6 = 9360 kJ/sec = 9360 kW

It is given that 30% of the heat is lost to the surroundings. Hence the heat utilized is 9360*70%= 6552 kW

Given that the heat is used to generate synthesis gas through catalytic reforming.

From the equation given above, one mole of methane reacts with one mole of water to produce one mole of CO and 3 moles of hydrogen (i.e. 4 moles of output gas)

But the inflow of gases is 1:3 molar mixture of methane and water.

Assuming the molar flow rate of methane as x, the molar flow rate of water is 3x

For syngas production, it is an endothermic process consuming a heat of 206 kJ/mol

Hence, total heat absorbed by the syngas production is 206*x= 206x kW

We know that the heat generated is = 6552 kW = heat absorbed by the syngas production

Solving for x, we get x= 31.80 mol/sec

By consulting the equation of production, we get that for every one mole of methane flow, you get 4 moles of gases. Hence, for 31.80 mol of methane, we get 127.2 mol/sec of flow of syngas

Hence, the molar flow rate of syntehsis gas is 127.2 mol/sec