Final answer:
The precise free energy change for the inward movement of calcium ions into a bacterial cell cannot be determined without specific data on gradients and membrane potential. It may be endergonic or exergonic, depending on the direction of the gradient.
Step-by-step explanation:
The free energy change for the inward movement of calcium ions into a bacterial cell cannot be accurately determined without specific information about the concentration gradients and the potential difference across the membrane. However, typically, the movement of ions across a cell membrane depends on electromotive forces and concentration gradients. If the movement of calcium ions is against the concentration gradient (from a region of lower concentration to higher concentration) and/or against the electrochemical gradient, it will require energy and thus be an endergonic reaction. If the movement is with the gradient (from a region of higher concentration to lower concentration), it could be an exergonic reaction (energy-releasing). Without detailed information, one cannot precisely determine the actual free energy change for calcium ions entering a bacterial cell.