SME
General Chemistry II · Problem type
Molar mass from osmotic pressure
Use this for “0.500 g of a protein in 100 mL of solution has an osmotic pressure of 5.20 torr at 25 °C. Find its molar mass.”
Diagram
Molarity is moles per liter: 2.797 × 10⁻⁵ mol in 100 mL is 0.0002797 mol/L.
Each dot is 1 × 10⁻⁶ mol of protein: 28 dots, about.
This is an example. Type your own values to start a new problem.
Π
Osmotic pressure
example · torr
T
Temperature
example · K
i
Van ’t Hoff factor
example
c
Molarity
calculated · M
V
Solution volume
example · mL
n
Moles of solute
calculated · mol
m
Solute mass
example · g
M
Molar mass
calculated · g/mol
Formulas
Π
760
=
i
×
c
×
0.08206
×
T
5.2
760
=
1
×
(2.797
×
10
-4
)
×
0.08206
×
298.15
n
=
c
×
V
1,000
2.797 ×
10
-5
=
2.797 ×
10
-4
×
100
1,000
M
=
m
n
1.788 ×
10
4
=
0.5
2.797 ×
10
-5
Assumptions
•
The solution is ideal and dilute, so Π = i × c × R × T with Π in atm (torr ÷ 760) and R = 0.08206 L·atm/(mol·K).
•
The membrane lets only the solvent through, and Π is read once the flow has stopped (at equilibrium).
•
Temperatures are in kelvins (°C + 273.15): 25 °C is 298.15 K.
Step-by-step
WE KNOW
Π = 5.2 torr, T = 298.15 K, i = 1, V = 100 mL, m = 0.5 g
FIND
molarity (c), moles of solute (n), molar mass (M)
Step 1 · Find molarity (c)
Use Π ÷ 760 = i × c × 0.08206 × T
Turn
the
pressure
into
atm
(÷
760),
then
divide
by
i
×
R
×
T
.
c
=
Π
760 ×
i
× 0.08206 ×
T
c
=
5.2
760 × 1 × 0.08206 × 298.15
c
=
5.2
62.3656 × 298.15
c
=
5.2
18,594
c
=
2.797 ×
10
-4
M
Step 2 · Find moles of solute (n)
Use n = c × V ÷ 1,000
Molarity
times
the
volume
in
liters
(
mL
1000
)
counts
the
moles
of
solute.
n
=
2.797 ×
10
-4
×
100
1,000
n
=
0.02797
1,000
n
=
2.797 ×
10
-5
mol
Step 3 · Find molar mass (M)
Use M = m ÷ n
Grams of solute over its moles is the molar mass.
M
=
0.5
2.797 ×
10
-5
M
=
1.788 ×
10
4
g/mol
Check
Put the numbers back in. Both sides should match.
5.2
760
=
1
×
(2.797
×
10
-4
)
×
0.08206
×
298.15
✓
2.797 ×
10
-5
=
2.797 ×
10
-4
×
100
1,000
✓
1.788 ×
10
4
=
0.5
2.797 ×
10
-5
✓
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Solutions and colligative properties
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Molarity to molality and mass percent
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