Question

Suppose that initially there are 100 na and 25 k ions inside the cell, near the sodium-potassium pump. a. use the expressions for n and k to determine how many ions of each kind are inside the cell in the region near the pump after 10, 30, and 40 cycles. show your work. Explain how these values relate to the results.

Answer 1

The question is about the change in Na+ and K+ ion concentrations inside a cell after several cycles of the sodium-potassium pump. After 10 cycles, there would be 70 Na+ and 45 K+. After 30 cycles, there would be 10 Na+ and 85 K+. 40 cycles cannot complete due to Na+ depletion.

Step-by-step explanation:

The student is asking about the sodium-potassium pump and its effect on Na+ and K+ ion concentrations after several cycles. The sodium-potassium pump moves three Na+ ions out of the cell and two K+ ions into the cell per cycle, using energy from ATP. Starting with 100 Na+ and 25 K+ ions inside the cell, after one cycle, you would have 97 Na+ and 27 K+ ions (since 3 Na+ are pumped out and 2 K+ are pumped in).

Let's calculate the ion concentrations after 10, 30, and 40 cycles:

• After 10 cycles, 100 Na+ - (3 Na+ × 10) = 70 Na+, and 25 K+ + (2 K+ × 10) = 45 K+.
• After 30 cycles, 100 Na+ - (3 Na+ × 30) = 10 Na+, and 25 K+ + (2 K+ × 30) = 85 K+.
• After 40 cycles, 100 Na+ - (3 Na+ × 40) = -20 Na+ (which is not possible, as you cannot have a negative number of ions; this indicates that there cannot be 40 full cycles with the starting amount of Na+), and 25 K+ + (2 K+ × 40) = 105 K+ (but we cannot consider this number of K+ ions accurate since the Na+ ions are already depleted before 40 cycles are complete).

These calculations illustrate that the electrochemical gradient is maintained by the action of the sodium-potassium pump which is vital for various cellular functions, including maintaining the electrical gradient necessary for nerve function.