SME
Chemical Reaction Engineering
Catalysis
Use this for “KA = 2 atm⁻¹ at 1.5 atm of A, with k = 0.04 mol/(kg·s). What are the coverage and the rate?”
Chart
Horizontal asymptote θA = 1
θA(2) = 0.5
This is an example. Type your own values to start a new problem.
θA
=
KA (atm⁻¹)
×
PA (atm)
÷
(1
+
KA (atm⁻¹)
×
PA (atm)
)
rA (mol/(kg·s))
=
k (mol/(kg·s))
×
θA
Formulas
θA
=
KA
×
PA
1 + KA × PA
0.5
=
0.5
×
2
1 + 0.5 × 2
rA
=
k
×
θA
0.05 = 0.1 × 0.5
Assumptions
•
Langmuir adsorption: one molecule of A per site, all sites alike, no pull between neighbors.
•
The surface reaction limits the rate (Langmuir–Hinshelwood, single site), so the rate is kθA.
•
Coverage θA is the share of sites holding A; KA is its adsorption equilibrium constant.
Step-by-step
WE KNOW
KA = 0.5 atm⁻¹, PA = 2 atm, k = 0.1 mol/(kg·s)
FIND
fractional coverage (θA), rate per kg of catalyst (rA)
Step 1 · Find fractional coverage (θA)
Use θA = KA × PA ÷ (1 + KA × PA)
Adsorbing and leaving balance: KA PA over 1 + KA PA is the share of sites taken.
θA
=
0.5
×
2
1 + 0.5 × 2
θA
=
0.5
×
2
1 + 1
θA
=
0.5
×
2
2
θA
=
1
2
θA = 0.5
Step 2 · Find rate per kg of catalyst (rA)
Use rA = k × θA
Only
adsorbed
A
reacts,
so
the
rate
is
k
times
the
share
of
sites
it
holds.
rA = 0.1 × 0.5
rA = 0.05 mol/(kg·s)
Check
Put the numbers back in. Both sides should match.
0.5
=
0.5
×
2
1 + 0.5 × 2
✓
0.05 = 0.1 × 0.5 ✓
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Instantaneous selectivity of parallel reactions
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Effectiveness factor of a pellet
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