-6.8955
kJ/mol
-6.754
kJ/mol
-13.6495
kJ/mol
71.47
mV
-141.47
mV
14.5
-6.8955
kJ/mol
-6.754
kJ/mol
-13.6495
kJ/mol
71.47
mV
-141.47
mV
14.5
The Electrochemical Gradient Calculator determines the total free energy change for transporting an ion across a biological membrane. The electrochemical gradient has two components: the chemical gradient (driven by concentration difference) and the electrical gradient (driven by membrane potential). Together, they determine whether ion transport is thermodynamically favorable or requires energy input.
This calculation is fundamental to understanding active and passive transport, nerve impulse propagation, muscle contraction, and ATP synthesis in mitochondria. The sign and magnitude of the total ΔG determine which direction ion flow is spontaneous and how much energy is needed for transport against the gradient.
The electrochemical free energy change for moving an ion from outside to inside the cell has two terms:
ΔG = RT × ln(Cin/Cout) + zFVm
The chemical component: ΔG_chem = RT × ln(Cin/Cout)
The electrical component: ΔG_elec = zFVm
Where R = 8.314 J/(mol·K), T is temperature in Kelvin, z is the ion charge, F = 96,485 C/mol, and Vm is the membrane potential in volts. Negative total ΔG means inward movement is spontaneous.
Inputs
Results
For Na⁺ entering a neuron, both the concentration gradient (high outside) and electrical gradient (negative inside attracts cations) favor inward movement. Total ΔG = -13.2 kJ/mol, highly favorable.
Inputs
Results
For K⁺ moving inward, the concentration gradient opposes entry (ΔG_chem positive) but the electrical gradient favors it. The net ΔG is slightly positive, meaning K⁺ entry requires slight energy input. K⁺ outflow is spontaneous.
A negative total ΔG means the inward transport of the ion is thermodynamically spontaneous and can occur passively through ion channels without energy input. A positive ΔG means inward transport requires energy, typically provided by ATP hydrolysis via active transport pumps like the Na⁺/K⁺-ATPase.
In mitochondria, the electron transport chain pumps protons (H⁺) out of the matrix, creating a large electrochemical gradient (proton motive force). When protons flow back down this gradient through ATP synthase, the stored energy drives the phosphorylation of ADP to ATP. The proton motive force is approximately 200 mV, providing about 20 kJ/mol per proton.
By convention, the calculation considers the energy change for moving an ion from outside to inside the cell. Negative ΔG means inward movement is favorable. If you want the energy for outward movement, simply reverse the sign. This convention aligns with standard physiology texts and the Goldman equation framework.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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