Q.38 The concentration of Mg2+ ions outside a cell is twice the concentration inside.
If the transmembrane potential of the cell is −60 mV (inside negative),
the free energy change of transporting Mg2+ ions across the membrane
against the concentration gradient at 37 °C is
________ kJ/mol.
Faraday constant: 96.5 kJ V−1 mol−1
Faraday constant: 96.5 kJ V−1 mol−1
Given Data
- Outside concentration = 2 × inside concentration
- Membrane potential = −60 mV (inside negative)
- Temperature = 37 °C = 310 K
- Charge on Mg2+, z = +2
- Faraday constant, F = 96.5 kJ V−1 mol−1
Concept: Electrochemical Free Energy Change
The free energy change for ion transport across a membrane is given by:
ΔG = RT ln(Cfinal/Cinitial) + zFΔψ
Step 1: Direction of Transport
Since the concentration of Mg2+ is higher outside than inside,
transport against the concentration gradient occurs from inside to outside.
Step 2: Concentration Term
ln(Coutside/Cinside) = ln(2)
RT = 8.314 × 310 = 2577 J mol−1
RT ln 2 = 2577 × 0.693 = 1786 J mol−1 = 1.79 kJ mol−1
Step 3: Electrical Potential Term
Δψ = ψoutside − ψinside = 0 − (−0.06) = +0.06 V
zFΔψ = 2 × 96.5 × 0.06 = 11.58 kJ mol−1
Step 4: Total Free Energy Change
ΔG = 1.79 + 11.58 = 13.37 kJ mol−1
Final Answer
The free energy change for Mg2+ transport is
+13.4 kJ mol−1.
The positive value indicates that the process is energetically unfavorable
and requires active transport.
Common Mistakes to Avoid
- Using the wrong direction of ion transport
- Ignoring the electrical potential term
- Forgetting the +2 charge on Mg2+
- Using temperature in °C instead of Kelvin
Conclusion
When both concentration gradient and membrane potential are considered,
transporting Mg2+ ions against the gradient requires energy.
The calculated free energy change of +13.4 kJ mol−1 confirms
that the process is not spontaneous and must be driven by active transport mechanisms.
