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.

Step-by-step explanation:

The given data is as follows.

Ions to be transported =
`(10 mM) * (100 \mu^(3))(N)`

=
`0.010 mol * 10^(-13) L * 6.02 * 10^(23) ions/mol`

=
`6.02 * 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 * 10^(6) ions * (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.