Please show work and answer to the questions. Thank you for your help. A protein
ID: 73649 • Letter: P
Question
Please show work and answer to the questions. Thank you for your help.
A protein complex called the sodium/potassium pump uses the free energy of hydrolysis of ATP to pump sodium ions Na out of the cell and potassium ions K^+ into the cell. The net reaction for active transport of sodium and potassium ions is thought to be: The diagram below shows the concentrations of sodium and potassium ions inside and outside a cell. The electrical potential E inside and outside the cell is also given. Calculate the change in the electrochemical potential involved in transporting 1 mole of sodium ion out of the cell. Assume the activity coefficients of sodium ion inside and outside the cell are unity. Assume the temperature is 310K. Calculate the free energy change involved in transporting 1 mole of potassium ion into the cell. Assume the activity coefficients of potassium ion inside and outside the cell are unity. Assume the temperature is 310K. Calculate the total free energy change involved in transporting 3 moles of sodium ion out of the cell and two moles of potassium into the cell at T=310K. Assume, as in parts a and b, that all activity coefficients are unity. The standard free energy change for the hydrolysis of ATP i.e. concentration of inorganic phosphate is 0.01M, calculate the ratio of ATP to ADP (i.e. in the reaction quotient Q) which will furnish the work required to accomplish the transport described in part c.Explanation / Answer
a)
GNa+(in to out) = GNa+(out) - GNa+(in)
= RT In [Na+out / Na+in] + zF (ENa+(out) - ENa+(in))
= (8.31 J / mol K) x (310 K) In [140 / 10] + (+1)(96485 C / mol)[0 - (-0.07 V)]
= 13552 J / mol
Endergonic because G>0 so work is required for this transport.
b)
GK+(out to in) = RT In [Na+in / Na+out] + zF (ENa+in - ENa+out)
= (8.31 J / mol K) x (310 K) In [100 / 5] + (+1)(96485 C / mol)[-0.07)]
= 963.0 J / mol
c)
Gtotal = 3G(Na+out) + 2G(K+in)
= 3 (13,600 J / mol) + 2 (1000 J / mol)
= 42,800 J / mol (Work)
d)
Gtotal = Gtransport total + GATPto ADP 0
Gtransport total + GATP to ADP = 42,800 + GoATPto ADP + R InQ 0
= 42,800 - 31,300 + (8.31)(310) In[(Pi)(ADP) / ATP] 0
= 11,500 + (2576) In[(Pi)(ADP) / ATP] 0
In[(Pi)(ADP) / ATP] -4.464
[(Pi)(ADP) / ATP] e-4.464 = 0.01152
[(Pi)(ADP) / ATP] 0.01152
[(0.01)(ADP) / ATP] 0.01152
[ADP] / [ATP] 1.152
Therefore, [ATP] / [ADP] 0.868