a gas mixture of methane and steam at atmospheric pressure and 400Cis fed to a reactor where the following reactions occur CH4+H2O give CO2+4H2 and CH4+H2O give CO+3H2 the product steam leaves the reactor at 850C its composition( mole fraction)is:CO2=0.0275 and CO=0.1725 and H2O=0.1725 and H2=0.6275 determine the quantity of heat added to the reactor per mole of product gas.
Question
a gas mixture of methane and steam at atmospheric pressure and 400Cis fed to a reactor where the following reactions occur CH4+H2O give CO2+4H2 and CH4+H2O give CO+3H2 the product steam leaves the reactor at 850C its composition( mole fraction)is:CO2=0.0275 and CO=0.1725 and H2O=0.1725 and H2=0.6275 determine the quantity of heat added to the reactor per mole of product gas.
Solution
To determine the quantity of heat added to the reactor per mole of product gas, we need to calculate the heat of reaction for each reaction and then use the mole fractions to determine the total heat added.
Step 1: Calculate the heat of reaction for each reaction
The heat of reaction (ΔH) can be calculated using the equation ΔH = Σ ΔHf (products) - Σ ΔHf (reactants), where ΔHf is the heat of formation.
For the first reaction: CH4 + H2O -> CO2 + 4H2 ΔH1 = [ΔHf (CO2) + 4ΔHf (H2)] - [ΔHf (CH4) + ΔHf (H2O)]
For the second reaction: CH4 + H2O -> CO + 3H2 ΔH2 = [ΔHf (CO) + 3ΔHf (H2)] - [ΔHf (CH4) + ΔHf (H2O)]
Step 2: Use the mole fractions to determine the total heat added
The total heat added to the reactor per mole of product gas can be calculated by multiplying the heat of reaction for each reaction by the mole fraction of the product of that reaction and then summing these values.
Total heat added = (ΔH1 * mole fraction of CO2) + (ΔH2 * mole fraction of CO)
Please note that the heat of formation values (ΔHf) for each compound can be found in thermodynamic tables. Also, the heat capacity of the gas mixture should be considered when calculating the heat added to the reactor, especially since the temperature changes from 400C to 850C.
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