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:

$\Delta G^o=-RT\times \ln Q\\\\\Delta G^o=-RT\times \ln (\frac{[A]_{inside}}{[A]_{outside}})$

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:

$-14.1\times 10^3J/mol =-(8.314J/K.mol)\times (298K)\times \ln (\frac{[A]_{inside}}{[A]_{outside}})$

$\frac{[A]_{inside}}{[A]_{outside}}=296.2$

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