 Solution

ID: past-exam-of-the-chemistry-course-of-the-year-3-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-4/64/d/iii/solution

For simultaneous competitive adsorption, use the butyric-acid constant inferred in part (c),

b_{b} ≃ 1.21 m^{3} mmo l^{- 1}

, and

C_{b} = 1 0^{6} mmol m^{- 3}

θ_{p} = \frac{0.36 ( 1 0 ^{5} )}{1 + 0.36 ( 1 0 ^{5} ) + 1.21 ( 1 0 ^{6} )} ≃ 0.0289.

The propionic-acid rate is therefore approximately

v_{p} = 2.1 θ_{p} ≃ 0.061 mmol m^{- 3} s^{- 1} .

The abundant, more strongly adsorbing butyric acid occupies most common sites, reducing propionic conversion by roughly a factor of

35

. This calculation follows the requested competitive Langmuir model despite the physical concern about the fitted saturation density noted earlier.

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