Final answer:
ATP hydrolysis releases energy used for cellular processes such as the sodium-potassium pump through energy coupling and phosphorylation. The energy released in a cell exceeds what is needed for the pump's cycle, making 1 ATP molecule sufficient for the function.
Step-by-step explanation:
The question revolves around the energy requirements for cellular processes, specifically how 1 ATP is sufficient to power a pump when the hydrolysis of ATP yields 31 kJ/mol, which seems to be less than the value needed for the function of the pump.
The energy produced during ATP hydrolysis is used for cellular processes through a mechanism called energy coupling. This is where the exergonic reaction (energy-releasing) of ATP hydrolysis is paired with the endergonic reaction (energy-consuming) of another process, such as the sodium-potassium pump. Essentially, ATP hydrolysis involves the transfer of a phosphate group onto another molecule - such as a pump protein - through phosphorylation, leading to a conformational change that allows the pump to function.
The hydrolysis of ATP, which is an exothermic reaction, does indeed result in the release of energy, and part of this energy is lost as heat. However, the amount of energy released (-57 kJ/mol under cellular conditions) is more than what is needed for a single cycle of the sodium-potassium pump, confirming that one ATP molecule's hydrolysis is sufficient to power the pump.