Question

9) How long would it take 100 molecules of valinomycin to transport enough K+ to change the concentration inside an erythrocyteof volume 100um3by10 mM? (Assume that valinomycin does not also transport any K+ out of the cell, which it really does, and that valinomycin molecules outside the cell are always saturated with K+.)

Answer 1

Answer: Time required for 100 molecules of valinomycin to transport enough $K^{+}$ to change the concentration inside an erythrocyte is 10 minutes.

Explanation:

The given data is as follows.

 Ions to be transported = $(10 mM) \times (100 \mu^{3})(N)$

            = $0.010 mol \times 10^{-13} L \times 6.02 \times 10^{23} ions/mol$

             = $6.02 \times 10^{6}$ ions

Here, there are 100 ionophores are present and each one of ionophores are required to transport a value of  ions.

Therefore, the time required for 100 molecules of valinomycin to transport enough $K^{+}$ to change the concentration inside an erythrocyte is as follows.

   $6.02 \times 10^{6} ions \times \frac{1 sec}{10^{4} ions}$

              = 602 sec

or,          = 10 minutes        (as 1 min = 60 sec)

Thus, we can conclude that time required for 100 molecules of valinomycin to transport enough $K^{+}$ to change the concentration inside an erythrocyte is 10 minutes.