Question

A cell biologist interested in the transport of calcium ions (Ca2+) across the plasma membrane of bacterial cells made the following measurements on bacterial cells at 25°C:

Vm = −150 mV [Ca2+] outside = 20 mM [Ca2+] inside = 0.4 mM
What is the free energy change for the inward movement of calcium ions into the bacterial cell?
A) +4.6 kcal/mol; an endergonic reaction
B) +4.6 kcal/mol; an exergonic reaction
C) −9.2 kcal/mol; an endergonic reaction
D) −9.2 kcal/mol; an exergonic reaction
E) +9.2 kcal/mol; an exergonic reaction

Answer 1

The free energy change for the inward movement of calcium ions into the bacterial cell is -9.2 kcal/mol, indicating an exergonic reaction.

Step-by-step explanation:

The free energy change for the inward movement of calcium ions into the bacterial cell can be calculated using the Nernst equation. The Nernst equation is used to calculate the equilibrium potential for an ion across a membrane. The equation is as follows:

E = (RT/zF) * ln([Ca2+ outside]/[Ca2+ inside])

where E is the equilibrium potential, R is the gas constant, T is the temperature in kelvin, z is the charge of the ion, F is Faraday's constant, and [Ca2+ outside] and [Ca2+ inside] are the concentrations of calcium ions outside and inside the cell, respectively.

Plugging in the given values:

E = (0.0821 * 298 / (2 * 96500)) * ln(20 / 0.4) = -9.2 mV

Since free energy change (ΔG) is related to equilibrium potential (E) by the equation:

ΔG = -nFE

where ΔG is the free energy change, n is the number of moles of electrons transferred, F is Faraday's constant, and E is the equilibrium potential. In this case, 1 mole of electrons is transferred and the equilibrium potential is -9.2 mV.

Converting mV to kcal/mol:

1 mV = 0.001 kcal/mol, so -9.2 mV = -0.0092 kcal/mol

Therefore, the free energy change for the inward movement of calcium ions into the bacterial cell is -0.0092 kcal/mol, which is approximately -9.2 kcal/mol.

Answer: D) -9.2 kcal/mol; an exergonic reaction