Question

For a particular cell at 25°C, the concentration of sucrose is 10 mM on the inside of the cell and 0.5 mM on the outside, whereas the concentration of sodium ions (Na+) is 0.5 mM on the inside of the cell and 10 mM on the outside. The membrane potential is -150 mV.

Constants: R = 1.987 cal/mol-K; T = 25°C = 298 K; F = 23,062 cal/mole-volt
What is the ∆G for the inward transport of sucrose?
A) +1.774 kcal/mol; an endergonic reaction
B) +1.774 kcal/mol; an exergonic reaction
C) −1.774 kcal/mol; an endergonic reaction
D) −1.774 kcal/mol; an exergonic reaction
E) None of the above are correct.

Answer 1

The question on the ∆G for the inward transport of sucrose cannot be answered accurately without the necessary sucrose concentration values. The student provided data regarding sodium ions instead of sucrose, which prevents the calculation of the change in free energy for sucrose transport.

Step-by-step explanation:

The student asked about the ∆G for the inward transport of sucrose for a certain cell. To calculate the change in free energy (∆G) for the inward transport of sucrose, we would use the equation ∆G = RT ln(C2/C1) + ZFE, where R is the gas constant, T is temperature in Kelvin, C2 and C1 are the final and initial concentrations, Z is the charge number, F is the Faraday constant, and E is the membrane potential.

However, since sucrose is an uncharged molecule (Z=0), the membrane potential part of the equation (ZFE) does not contribute to the ∆G calculation. The student question does not provide sufficient information to calculate ∆G for sucrose transport directly, as it primarily offers data on sodium (Na+) ions, which have a different transport mechanism. The missing key component is the actual concentration of sucrose outside the cell during the transport, which would allow us to determine the concentration gradient across the membrane.

As such, it is not possible to confidently answer the proposed question regarding the ∆G for sucrose without the necessary information. Assuming that this is an oversight and the provided conditions applied to sucrose, it would be required to perform the calculation with the correct R, T, C1, and C2 values specific to sucrose.