Question

g Consider a uniport system where a carrier protein transports an uncharged substance A across a cell membrane. Suppose that at a certain ratio of [ A ] inside to [ A ] outside , the Δ G for the transport of substance A from outside the cell to the inside, A outside → A inside , is − 14.1 kJ/mol at 25°C. What is the ratio of the concentration of substance A inside the cell to the concentration outside?

Answer 1

Answer : The ratio of the concentration of substance A inside the cell to the concentration outside is, 296.2

Explanation :

The relation between the equilibrium constant and standard Gibbs free energy is:

`\Delta G^o=-RT* \ln Q\\\\\Delta G^o=-RT* \ln (([A]_(inside))/([A]_(outside)))`

where,

`\Delta G^o` = standard Gibbs free energy = -14.1 kJ/mol

R = gas constant = 8.314 J/K.mol

T = temperature =
`25^oC=273+25=298K`

Q = reaction quotient

`[A]_(inside)` = concentration inside the cell

`[A]_(outside)` = concentration outside the cell

Now put all the given values in the above formula, we get:

`-14.1* 10^3J/mol =-(8.314J/K.mol)* (298K)* \ln (([A]_(inside))/([A]_(outside)))`

`([A]_(inside))/([A]_(outside))=296.2`

Thus, the ratio of the concentration of substance A inside the cell to the concentration outside is, 296.2