Question

(a) For the following conditions, calculate the change in the Gibbs energy associated with transporting 1 mole of sodium ions from inside to outside the cell. Is work required or produced? Outside: [Na+] = 130 mM [K+] 5 mM Electrical potential = 0 mV [Na+]= [K 110 mM Electrical potential =-70 mV Temperature 25 °C Inside: 10 mM (b) For the same conditions, calculate the change in the Gibbs energy associated with transporting 1 mole of potassium ions from outside to inside the cell. Is work required or produced? Why is the answer to (b) so different from the answer to (a)? (c) As shown in the animation of the sodium/potassium pump, three sodium ions are transported out of the cell and two potassium ions are transported into the cell for each ATP hydrolyzed. How much total energy is required to accomplish this under the conditions given above? (d) If the standard Gibbs energy change for the hydrolysis of ATP at 25°C and pH 7 is-30.5 kJ mol, and if the total concentration of inorganic phosphate, [P] is 0.01 M, what is the ratio of ATP to ADP required to provide the work required to achieve the transport in (c)?

Answer 1

$\Delta G=RT ln [Xo]/[Xi]$

Where,

R= Gas constant = 8.3145 Joule / Kelvin mol

T= Temperature in Kelvin = 25^oC = 25+273 = 298K

a). For the transport of the Sodium ions

$\Delta G_{Na}=RT ln [Na^{+}_{o}]/[Na^{+}_{i}]$

[Na⁺]_o = Sodium ion concentration outside of the cell = 130mM

[Na⁺]_i = Sodium ion concentration inside of the cell = 10mM

$\Delta G_{Na}=8.315 X 298 ln [130/10]$

$\Delta G_{Na}=2477.709 ln [13]$

$\Delta G_{Na}=2477.709 X 2.565$

$\Delta G_{Na}=6355.198$

Delta G is positive which means the energy would be consumed.

b). For the transport of the Potassium ions

$\Delta G_{K}=RT ln( [K^{+}_{o}]/[K^{+}_{i}])$

[K⁺]_o = Pottasium ion concentration outside of the cell = 5mM

[K⁺]_i = Potassium ion concentration inside of the cell = 110mM

$\Delta G_{K}=8.315 X 298 ln [5/110]$

$\Delta G_{K}=2477.709 ln [0.45455]$

$\Delta G_{K}=2477.709 X (-309104)$

$\Delta G_{K}=-7658.8$