SME
Material & Energy Balances
Process flow diagrams
Use this for “100 kg/h of 40% benzene and toluene: what are the molar flows and the mole fraction of benzene?”
Diagram
This is an example. Type your own values to start a new problem.
ṅA (kmol/h)
=
×
ṁ (kg/h)
MA (kg/kmol)
ṅB (kmol/h)
=
(1
−
)
×
ṁ (kg/h)
MB (kg/kmol)
xA
=
ṅA (kmol/h)
ṅA (kmol/h)
+
ṅB (kmol/h)
ṅ
Total molar flow
calculated · kmol/h
M̄
Average molar mass
calculated · kg/kmol
Formulas
ṅA
=
wA
×
ṁ
MA
0.5121
=
0.4
×
100
78.11
ṅB
=
(1
−
wA)
×
ṁ
MB
0.6512
=
(1
−
0.4)
×
100
92.14
ṅ
=
ṅA
+
ṅB
1.1633 = 0.5121 + 0.6512
xA
=
ṅA
ṅ
0.4402
=
0.5121
1.1633
M̄
=
ṁ
ṅ
85.9637
=
100
1.1633
Assumptions
•
Two components, benzene (A) and toluene (B); their mass fractions add to 1, and so do their mole fractions.
•
Steady flow: each component’s molar flow is its mass flow ÷ its molar mass.
Step-by-step
WE KNOW
ṁ = 100 kg/h, wA = 0.4, MA = 78.11 kg/kmol, MB = 92.14 kg/kmol
FIND
molar flow of benzene (ṅA), molar flow of toluene (ṅB), total molar flow (ṅ), mole fraction of benzene (xA), average molar mass (M̄)
Step 1 · Find molar flow of benzene (ṅA)
Use ṅA = wA × ṁ ÷ MA
The benzene’s mass flow, divided by its molar mass.
ṅA
=
0.4
×
100
78.11
ṅA
=
40
78.11
ṅA = 0.512098 kmol/h
Step 2 · Find molar flow of toluene (ṅB)
Use ṅB = (1 − wA) × ṁ ÷ MB
The rest of the stream is toluene: its mass flow over its molar mass.
ṅB
=
(1
−
0.4)
×
100
92.14
ṅB
=
0.6
×
100
92.14
ṅB
=
60
92.14
ṅB = 0.651183 kmol/h
Step 3 · Find total molar flow (ṅ)
Use ṅ = ṅA + ṅB
Add the two molar flows.
ṅ
=
0.512098
+
0.651183
ṅ
=
1.1632813
kmol/h
Step 4 · Find mole fraction of benzene (xA)
Use xA = ṅA ÷ ṅ
The benzene’s share of the moles.
xA
=
0.512098
1.1632813
xA = 0.4402
Step 5 · Find average molar mass (M̄)
Use M̄ = ṁ ÷ ṅ
The mass of the mixture per kmol of it.
M̄
=
100
1.1632813
M̄
=
85.9637
kg/kmol
Check
Put the numbers back in. Both sides should match.
0.512098
=
0.4
×
100
78.11
✓
0.651183
=
(1
−
0.4)
×
100
92.14
✓
1.1632813 = 0.512098 + 0.651183 ✓
0.4402
=
0.512098
1.1632813
✓
85.9637
=
100
1.1632813
✓
Topic check
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