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?

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Alleei Alleei · Answer 1 · 2020-03-30T08:15:47+02:00

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:

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

where,

[tex]\Delta G^o[/tex] = standard Gibbs free energy = -14.1 kJ/mol

R = gas constant = 8.314 J/K.mol

T = temperature = [tex]25^oC=273+25=298K[/tex]

Q = reaction quotient

[tex][A]_{inside}[/tex] = concentration inside the cell

[tex][A]_{outside}[/tex] = concentration outside the cell

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

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

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

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