Final answer:
To calculate the concentration ratio of substance A inside the cell to the concentration outside, the equation ΔG = -RT ln([A]_inside/[A]_outside) is used, substituting the given ΔG value, universal gas constant, and temperature.
Step-by-step explanation:
The problem involves calculating the ratio of the concentration of substance A inside the cell to the concentration outside, given the free energy changeΔG for the transport of substance A from outside to inside the cell at a specific temperature. The relationship between ΔG and the concentrations of reactants and products (in this case substance A inside and outside the cell) is given by the equation ΔG = -RT ln([A]inside/[A]outside), where R is the universal gas constant and T is the absolute temperature in Kelvin.
In the given scenario, the ΔG is -14.3 kJ/mol (which is -14,300 J/mol), and the temperature (T) is 25°C or 298 K. The universal gas constant (R) is 8.314 J/(mol*K). By rearranging the equation to solve for the ratio [A]inside/[A]outside, we can calculate the desired concentration ratio.
To find the concentration ratio, we use the formula:
ΔG = -RT ln([A]inside/[A]outside)
Replacing ΔG with -14,300 J/mol, R with 8.314 J/(mol*K), and T with 298 K, and solving for the ratio [A]inside/[A]outside yields:
-14,300 J/mol = -(8.314 J/(mol*K) * 298 K) ln([A]inside/[A]outside)
Dividing -14,300 J/mol by -(8.314 J/(mol*K) * 298 K) and taking the exponential of both sides of the equation:
ln([A]inside/[A]outside) = 14,300 / (8.314 * 298)
[A]inside/[A]outside = e (14,300 / (8.314 * 298))
By calculating the above expression, one can determine the concentration ratio of substance A inside the cell to outside.