SME
Organic Chemistry II · Problem type
Overall yield of a multistep route
Use this for “A four-step route has yields of 92%, 75%, 80% and 64%. What is the overall yield, and how much product do 25 mmol give?”
Chart
This is an example. Type your own values to start a new problem.
Y (%)
=
y₁ (%)
×
y₂ (%)
×
y₃ (%)
×
y₄ (%)
÷
100³
y₁ to y₄ are the four steps’ yields: each is the share of the bar before it that the next bar keeps. Y is the share of the starting moles left at the end.
nₛₜₐᵣₜ
Starting moles
example
nproduct
Product moles
calculated
Formulas
Y
=
y₁
×
y₂
×
y₃
×
y₄
100
3
53.55
=
85 × 70 × 90 × 100
100
3
nproduct
=
nₛₜₐᵣₜ
×
Y
100
5.355
=
10
×
53.55
100
Assumptions
•
Each step’s yield is the moles of its product ÷ the moles of its starting material, as a percent.
•
All of each product goes on to the next step; a step not used is 100%.
•
The overall yield is the product’s moles ÷ the starting moles, with one mole of each made from one of the last.
Step-by-step
WE KNOW
y₁ = 85%, y₂ = 70%, y₃ = 90%, y₄ = 100%, nₛₜₐᵣₜ = 10 mmol
FIND
overall yield (Y), product moles (nproduct)
Step 1 · Find overall yield (Y)
Use Y = (y₁ × y₂ × y₃ × y₄) ÷ 100³
Multiply the step yields; each is a percent, so divide by 100 three times to keep one percent.
Y
=
85 × 70 × 90 × 100
100
3
Y
=
85
×
70
×
90
×
100
1,000,000
Y
=
5,950
×
90
×
100
1,000,000
Y
=
535,500
×
100
1,000,000
Y
=
53,550,000
1,000,000
Y
=
53.55%
→
Each
step’s
yield
multiplies,
so
the
overall
yield
is
never
above
the
worst
step.
Step 2 · Find product moles (nproduct)
Use nproduct = nₛₜₐᵣₜ × Y ÷ 100
Take the overall yield’s share of the starting moles.
nproduct
=
10
×
53.55
100
nproduct
=
535.5
100
nproduct = 5.355 mmol
Check
Put the numbers back in. Both sides should match.
53.55
=
85 × 70 × 90 × 100
100
3
✓
5.355
=
10
×
53.55
100
✓
Topic check
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