Final answer:
Each ATP molecule hydrolyzed provides 7.3 kcal/mol of energy, which is enough to transport approximately three sodium ions across a cell membrane, considering 2.1 kcal/mol is needed to transport one sodium ion.
Step-by-step explanation:
The question relates to the amount of energy needed to actively transport sodium ions through a cell membrane using ATP. The energy provided by the hydrolysis of one ATP molecule releases 7.3 kcal/mol, which is equivalent in strength to -7.3 kcal/mol of energy, indicating that it is energetically favorable (exergonic reaction).
If the energy cost of moving one sodium ion (Na+) across the membrane is 2.1 kcal/mol, as indicated by a ΔG of +2.1 kcal/mol, making it an energetically unfavorable (endergonic) process, we can calculate the number of ions moved by one molecule of ATP.
To find the number of sodium ions one ATP molecule can move, divide the total available energy per ATP molecule by the energy required to move one ion:
7.3 kcal/mol ATP per hydrolysis / 2.1 kcal/mol energy per Na+ ion = 3.476 sodium ions.
This indicates that for each ATP molecule hydrolyzed, approximately three Na+ ions can be transported across the cell membrane. However, since we can't move a fraction of an ion, we can safely say that each ATP molecule can move three sodium ions.