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 ΔG for the transport of substance A from outside the cell to the inside, Aoutside→Ainside , is 14.9 kJ/mol at 25°C. What is the ratio of the concentration of substance A inside the cell to the concentration outside? [A]inside[A]outside= Choose the true statement about the transport of A under the conditions described. Increasing [A]outside will cause ΔG for movement of Aoutside to Ainside to become a larger positive number. Because ΔG is positive, the ratio [A]inside/[A]outside must be less than one. Movement of Ainside to Aoutside will be spontaneous. Decreasing the concentration of the uniport protein in the membrane will cause ΔG to become a smaller positive number.

Explanation: Gibbs Free Energy was defined by its developer as the "available energy" in a system. It combines enthalpy (amount of heat, at constant pressure, necessary for a substance to change) and entropy (measurement of the randomness and disorder of molecules based on the number of arrangements available to them) into a single value:

ΔG = ΔH - TΔS

where:

ΔG is Gibbs Free Energy

ΔH is enthalpy

T is temperature

ΔS is entropy

To determine the ratio of concentration of the substance:

ΔG = R.T.ln[tex]\frac{[A]_{inside} }{[A]_{outside} }[/tex]

where

R is the "gas constant" (R=2[tex]\frac{cal}{mol.K}[/tex])

T is temperature in Kelvin (T=25+273)

ln[tex]\frac{[A]_{inside} }{[A]_{outside} }[/tex] = [tex]\frac{G}{RT}[/tex]

ln[tex]\frac{[A]_{inside} }{[A]_{outside} }[/tex] = [tex]\frac{14.9}{2.298}[/tex]

ln[tex]\frac{[A]_{inside} }{[A]_{outside} }[/tex] = 2220.1

[tex]\frac{[A]_{inside} }{[A]_{outside} }[/tex] = [tex]e^{2220.1}[/tex]

[tex]\frac{[A]_{inside} }{[A]_{outside} }[/tex] = 6034.85

The ratio is 6034.85 mM.

Under the conditions described, the transport of substance A from outside to inside has a positive Gibbs free energy. So, when in equilibrium, the inverse trajectory, inside → outside has a negative Gibbs free energy.

With Gibbs free energy, is possible determine if a reaction is spontaneous (happens without external energy being needed) or not. If ΔG > 0 is non-spontaneous.

Since Gibbs free energy from inside to outside is negative, ΔG < 0, the reaction and the transport is spontaneous.

batolisis batolisis · Answer 2 · 2021-11-18T22:45:41+01:00

A) The ratio of concentration of A(inside) to A(outside) is : - 6034.85 mM

B) The true statement about the transport of A under the described conditions is ; ( C ) Movement of Ainside to Aoutside will be spontaneous

Given data :

ΔG for transport of substance A from outside to inside = 14.9 kJ/mol

Temperature = 25°C = 298 K

A) Determine the ratio of concentration A(inside) to A(outside)

applying the formula below

ΔG = R.T. In [ A(inside) / A(outside) ] --- ( 1 )

where ; R = 2 cal / mol.k , T = 298 K,

∴ In [ A(inside) / A(outside) ] = ΔG / RT

= 14.9 kJ/mol / ( 2 * 298 )

= 2220.1

∴ [ A(inside) / A(outside) ] = [tex]e^{2220.1}[/tex] = 6034.85 mM

B) The movement of Ainside to Aoutside will be spontaneous because,

ΔG > 0 from outside to inside the cell which means that the reaction will not require and external energy to kickstart. while ΔG < 0 from inside to outside which makes it

Hence we can conclude that ;The ratio of concentration of A(inside) to A(outside) is : 6034.85 mM, The true statement about the transport of A under the described conditions is, Movement of Ainside to Aoutside will be spontaneous.

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