SME
Chemical Reaction Engineering · Problem type
Energy balance with a cooling jacket
Use this for “A CSTR is fed 2 mol/s of A at 300 K, ΣθCₚ = 250 J/(mol·K), ΔHRx = −60 kJ/mol, with UA = 1000 W/K and coolant at 300 K. What X holds it at 360 K?”
Chart
XEB(360) = 0.75
This is an example. Type your own values to start a new problem.
X
=
(
ΣθᵢCₚᵢ (J/(mol·K))
×
(
T (K)
−
T₀ (K)
)
+
UA (W/K)
×
(
T (K)
−
Tₐ (K)
)
÷
FA0 (mol/s)
)
÷
(−(
ΔHRx (kJ/mol)
))
Formulas
X
=
(ΣθᵢCₚᵢ
×
(
T
−
T₀
)
+
UA
×
(
T
−
Tₐ)
÷
FA0)
÷
(−ΔHRx)
0.75 = (250 × (360 − 300) + 1,000 × (360 − 300) ÷ 2) ÷ (−(−60,000))
Formulas are worked in J/mol. The step-by-step shows the conversions.
Assumptions
•
Steady CSTR with ΔCₚ = 0, so ΔHRx stays the same at every temperature.
•
The coolant stays near Tₐ: its flow is large, so it hardly warms.
•
UA = 0 gives the adiabatic line (dashed); the jacket makes the line steeper.
Step-by-step
WE KNOW
FA0 = 2 mol/s, ΣθᵢCₚᵢ = 250 J/(mol·K), T₀ = 300 K, UA = 1,000 W/K, Tₐ = 300 K, ΔHRx = −60 kJ/mol, T = 360 K
FIND
conversion (X)
Step 1 · Convert to the formula’s units
The formulas don’t work directly in the units you chose, so convert first (to J/mol).
ΔHRx = −60 kJ/mol = −60,000 J/mol (1 kJ/mol = 1000 J/mol)
Step 2 · Find conversion (X)
Use X = (ΣθᵢCₚᵢ × (T − T₀) + UA × (T − Tₐ) ÷ FA0) ÷ (−ΔHRx)
At steady state the heat the reaction releases per mole of A fed warms the feed and leaves through the jacket.
X
=
(250
×
(360
−
300)
+
1,000
×
(360
−
300)
÷
2)
÷
(−(−60,000))
X
=
250 × 60 + 1,000 × 60 ÷ 2
−(−60,000)
X
=
15,000 + 60,000 ÷ 2
−(−60,000)
X
=
15,000 + 30,000
−(−60,000)
X
=
45,000
−(−60,000)
X
=
45,000
60,000
X
=
0.75
Check
Put the numbers back in. Both sides should match.
0.75 = (250 × (360 − 300) + 1,000 × (360 − 300) ÷ 2) ÷ (−(−60,000)) ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Related lessons
Nonisothermal reactors
Main lesson
Adiabatic CSTR steady states
Use this for “E = 80 kJ/mol, k = 5 × 10⁻⁵ per min at 300 K, τ = 10 min, fed at 300 K with ΔTad = 240 K. Compare XMB and XEB at 360 K.”
Equilibrium conversion and temperature
Use this for “A ⇌ B has ΔHRx = −60 kJ/mol and K = 50 at 300 K. What is the equilibrium conversion at 350 K?”