How does a concentration gradient provide energy?

[sameeralord]

Ok hydrogen ion gradient drives ATP synthase. In secondary active transport the preexisting concentration gradient drives the molecules.

My question is what do they mean when they say concentration gradient provides energy to do this. Is it the movement of ions like hyrdogen from high to low that results in energy.

When the concentration on each side is the same why is there no energy!

Thanks!

 

[chemisttree]

DeltaG = RTln(c₁/c₂)
or
DeltaG = 2.303RTlog₁₀(c₁/c₂)

You must also consider the fact that these species are charged. This generates an electric potential in addition to the gibbs energy for concentration.

DeltaG = 2.303RTlog₁₀(c₁/c₂) + ZFdeltaV

where deltaV is the potential in volts across the membrane, Z is the charge and F is the faraday.

What happens when c₁ is equal to c₂ and deltaV = 0?

 

[somasimple]

This response may be true if these ions were free.
There are unfortunately hydrated.

 

[alxm]

Yeah you have to take into account the difference in chemical activities, in ionic strength, etc. It's not a trivial thing.

That said, the aforementioned Nernst Equation is sufficient to explain where the energy's coming from, just not accurately give a number for it.

 

[somasimple]

The Nernst Equation was created for chemical redox reactions for battery cells.
http://en.wikipedia.org/wiki/Nernst_equation
That has nothing to see with biology. The ions gradients are coming from the same specie and do not implie a redox reaction of any kind.
Of course Biology took the original theory and tried to apply it to cell.