SME
Principles of Biology II
Plant form and function
Use this for “A plant cell holds 0.15 M sucrose at 295 K with Ψₚ = 0.20 MPa. It sits in a solution at Ψ = −0.10 MPa. Which way does water move?”
Diagram
Ψ outside −0.1 MPa, inside −0.168 MPa: water moves into the cell, toward the lower Ψ.
Inside: Ψ = Ψₛ + Ψₚ = −0.368 + 0.2 = −0.168 MPa
Each solute dot stands for 0.025 MPa of solute potential.
This is an example. Type your own values to start a new problem.
Ψₛ (MPa)
=
−
i
×
C (M)
×
R
×
T (K)
Ψ (MPa)
=
Ψₛ (MPa)
+
Ψₚ (MPa)
Ψ(sol)
Solution water potential
example · MPa
ΔΨ
Water potential difference
calculated · MPa
Formulas
Ψₛ
=
−
i
×
C
×
0.00831
×
T
−0.3677 = −1 × 0.15 × 0.00831 × 295
Ψ
=
Ψₛ
+
Ψₚ
−0.1677 = −0.3677 + 0.2
ΔΨ
=
Ψ
(sol)
−
Ψ
+0.06772 = −0.1 − (−0.1677)
Assumptions
•
Ψₛ = −iCRT with C in mol/L and R = 0.00831 L·MPa/(mol·K); i is 1 for sucrose, 2 for NaCl.
•
Ψ = Ψₛ + Ψₚ: the wall’s push (Ψₚ) raises Ψ, and tension in xylem makes Ψₚ negative.
•
Water moves from higher Ψ to lower Ψ, so ΔΨ = Ψ(sol) − Ψ above 0 means into the cell.
•
The solution is in an open beaker: its Ψₚ is 0, so its Ψ is its solute potential.
Step-by-step
WE KNOW
i = 1, C = 0.15 M, T = 295 K, Ψₚ = 0.2 MPa, Ψ(sol) = −0.1 MPa
FIND
solute potential (Ψₛ), cell water potential (Ψ), water potential difference (ΔΨ)
Step 1 · Find solute potential (Ψₛ)
Use Ψₛ = −i × C × 0.00831 × T
Dissolved
particles
lower
the
water
potential:
multiply
i
,
C
,
R
and
T
,
then
make
it
negative.
Ψₛ = −1 × 0.15 × 0.00831 × 295
Ψₛ = −0.15 × 0.00831 × 295
Ψₛ = −0.0012465 × 295
Ψₛ = −0.3677 MPa
Step 2 · Find cell water potential (Ψ)
Use Ψ = Ψₛ + Ψₚ
Add the wall’s pressure to the solute potential.
Ψ
=
−0.3677
+
0.2
Ψ
=
−0.1677
MPa
Step 3 · Find water potential difference (ΔΨ)
Use ΔΨ = Ψ(sol) − Ψ
Take
the
cell’s
Ψ
from
the
solution’s
Ψ
;
water
moves
toward
the
lower
one.
ΔΨ = −0.1 − (−0.1677)
ΔΨ
=
+0.06772
MPa
→
ΔΨ
>
0:
the
solution’s
Ψ
is
higher,
so
water
moves
into
the
cell.
Check
Put the numbers back in. Both sides should match.
−0.3677 = −1 × 0.15 × 0.00831 × 295 ✓
−0.1677 = −0.3677 + 0.2 ✓
+0.06772 = −0.1 − (−0.1677) ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.