How many ATP will be required to transport three N ions from inside (5mM) to outside (150mM) at 37 C at standard physiological conditions

Number of ATP molecules required  = 1.34 ATP molecules

Explanation:

The free energy change for moving an ion is given by the following formula:

ΔG = RT㏑(C₂/C₁) + ΖЭψ

where R is molar gas constant = 8.315 J/mol; T = 273 +37 = 310 K; C₂ is concentration outside = 150 mM or 0.15 M; C₁ is concentration inside = 0.005 M; Ζ is charge on ion = +1 ;Э is Faraday's conatant = 96500 J/V; ψ is standard transmembrane potential = 0.05 V

ΔG = (8.315 J/mol * 310 K) ㏑(0.15/0.005) + 1 *(96500 J/V * 0.05 V)

ΔG = 13592.10 J/mol

Since three Na⁺ ions are to be transported, total free energy change will be;

ΔG = 3 * 13592 J = 40776.3 = 40.8 kJ/mol

Energy obtained from the hydrolysis of an ATP molecule is 30.5 kJ/mol

Therefore, number of ATP molecules required = 40.8 / 30.5

Number of ATP molecules required  = 1.34 ATP molecules