1) If the capacitance of a mitochondrion is 3.6×1011F and the potential differen

Question

1) If the capacitance of a mitochondrion is 3.6×1011F and the potential difference between the interior and exterior is 0.16 V, how much electrical energy does it store?

2)If a mitochondrion were to use all of its stored electrical energy to produce ATP molecules, and each ATP molecule requires 9.5×1020J, how many molecules could it produce? (In reality, ATP molecules are produced by the flow of protons caused by the proton motive force, and not by the direct conversion of electrical energy stored by the capacitance of mitochondria.)

Express your answer to two significant figures and include appropriate units.

Explanation / Answer

(1) Expression for the electrical energy inside a capacitor is given by -

E = (1/2)*C*V^2

Here we have -

C = 3.6 x 10^-11 F

V = 0.16 Volt

Therefore, stored electrical energy, E = (1/2)*(3.6 x 10^-11)*(0.16)^2

= 4.608 x 10^-13 J

(2) Now, given that one ATP molecule requires 9.5 x 10^-20 J energy.

So, no. of molecules produced, n = E / (9.5 x 10^-20) = (4.608 x 10^-13) / (9.5 x 10^-20)

= 4.85 x 10^6

In two significant digits our answer = 4.9 x 10^6.

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