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7 July, 13:59

What volume of PFR (report in m3) is required for steady state removal of 95% of a substance that decays according to first order kinetics with a rate constant of 0.07 d-1

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  1. 7 July, 15:46
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    The volume of the PFR is 4.28m3

    Explanation: A Plug Flow Reactor (PFR) is a type of reactor that has a steady state flow. Therefore the flow rate is a constant, which is always measured in liters.

    In a PFR, the rate of conversion is always dependent on the rate of flow.

    For any PFR to have a conversion rate of 90% and above, that means the flow rate should be 100l/min or 100l/day depending on the rate constant.

    Therefore since our conversation is 95% and our rate constant is 0.07per day, that means our flow rate is 100liters/day

    The equation for a first order PFR is

    dFa/dV = Ra ... (1)

    To calculate volume, the equation becomes

    (R/K) ln (Cao/Ca) = V ... (2)

    R = flow rate = 100l/day = 0.1m3/day

    K = rate constant = 0.07/day

    Cao = initial conversion rate

    Ca = conversion rate = 95%

    V = volume

    STEP 1: FIND Cao,

    Cao + Ca = 100%

    Cao = 100% - 95% = 5% = 0.05

    Therefore

    0.05 = Ca / Cao

    Ca = 0.05Cao ... (3)

    STEP3 : Find the volume.

    Using equation 2 and substituting equation 3 in equation 2.

    (0.1m3/day : 0.07/day) ln (Cao/0.05Cao) =

    1.43m3 * ln20 = 4.98m3

    Therefore the volume of the PFR is

    4.98m3
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