a gas mixture of methane and steam at atmospheric pressure and 500C is 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. the Cp of CO=30.3 and CH4=49.1 and H2O=35.3 and CO2=45.1 and H2=29.1 Answer question
Question
a gas mixture of methane and steam at atmospheric pressure and 500C is 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. the Cp of CO=30.3 and CH4=49.1 and H2O=35.3 and CO2=45.1 and H2=29.1 Answer question
Solution
To solve this problem, we need to calculate the heat added to the reactor per mole of product gas. We can do this by using the heat capacity (Cp) values given and the formula for heat transfer, which is q = nCpΔT, where n is the number of moles, Cp is the heat capacity, and ΔT is the change in temperature.
First, we need to calculate the number of moles for each component in the product gas using the given mole fractions:
n(CO2) = 0.0275 mol n(CO) = 0.1725 mol n(H2O) = 0.1725 mol n(H2) = 0.6275 mol
Next, we calculate the change in temperature (ΔT) for the process. The initial temperature is 500C and the final temperature is 850C, so ΔT = 850C - 500C = 350C.
Then, we calculate the heat added (q) for each component using the formula q = nCpΔT:
q(CO2) = 0.0275 mol * 45.1 J/molC * 350C = 432.7125 J q(CO) = 0.1725 mol * 30.3 J/molC * 350C = 1826.0875 J q(H2O) = 0.1725 mol * 35.3 J/molC * 350C = 2123.8375 J q(H2) = 0.6275 mol * 29.1 J/molC * 350C = 6393.8625 J
Finally, we add up the heat added for each component to get the total heat added to the reactor:
q(total) = q(CO2) + q(CO) + q(H2O) + q(H2) = 432.7125 J + 1826.0875 J + 2123.8375 J + 6393.8625 J = 10776.5 J
So, the quantity of heat added to the reactor per mole of product gas is 10776.5 J/mol.
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