Thermodynamics of Membrane Diffusion: Uncharged Molecule: Videos & Practice Problems

The study of thermodynamics in the context of membrane diffusion focuses on how uncharged molecules move across biological membranes. This process can be understood through the lens of Gibbs free energy, specifically the change in Gibbs free energy associated with membrane transport, referred to as ΔG_transport.

To analyze this, we utilize the equation for Gibbs free energy under any conditions, which is expressed as:

$$\Delta G = \Delta G^{\circ} + RT \ln Q$$

In this equation, ΔG^° represents the change in Gibbs free energy under standard conditions, R is the gas constant (8.315 J/(mol·K)), T is the temperature in Kelvin, and Q is the reaction quotient, defined as the ratio of the concentration of products to the concentration of reactants.

For membrane diffusion, it is crucial to note that ΔG^° is equal to zero because membrane transport does not involve the formation or breaking of chemical bonds; the molecule remains unchanged as it crosses the membrane. Therefore, the equation simplifies to:

$$\Delta G_transport = RT \ln Q$$

In this context, Q is defined as the ratio of the concentration of the uncharged molecule on the final side of the membrane (symbolizing the product) to its concentration on the initial side (symbolizing the reactant):

$$Q = \frac{[C]_{final}}{[C]_{initial}}$$

This formulation allows us to calculate the thermodynamic favorability of the diffusion process for any uncharged molecule by substituting the appropriate concentration values into the equation. Understanding these principles is essential for predicting how uncharged molecules will behave in biological systems, particularly in terms of their movement across membranes driven by concentration gradients.

As we progress, practical examples will illustrate how to apply this equation effectively, enhancing our grasp of membrane diffusion thermodynamics.

To calculate the change in Gibbs free energy (ΔG) for the transport of glucose across a cell membrane, we can follow a systematic four-step process. In this example, we have a glucose concentration of 10 millimolar (mM) outside the cell and 0.1 mM inside the cytosol, with a temperature of 20 degrees Celsius.

First, we identify the nature of the diffusing molecule. Glucose is an uncharged molecule, which allows us to use a specific equation for calculating ΔG transport. This step is crucial as the approach differs for charged molecules.

Next, we determine the direction of diffusion. In this case, glucose is moving from the outside of the cell (initial side) to the inside (final side). Visualizing this with a sketch can be helpful, as it clarifies the flow of molecules across the membrane.

In the third step, we check the units of the given values. The concentrations of glucose are already in compatible units (mM), but we need to convert the temperature from degrees Celsius to Kelvin. The conversion formula is:

T(K) = T(°C) + 273.15

For our example, 20 °C converts to 293.15 K.

Finally, we plug the values into the appropriate equation for ΔG transport:

ΔG = R * T * ln([C_final]/[C_initial])

Where:

• R = 8.315 J/(mol·K)
• T = 293.15 K
• [C_final] = 0.1 mM
• [C_initial] = 10 mM

Substituting these values into the equation gives:

ΔG = 8.315 * 293.15 * ln(0.1/10)

Calculating this yields:

ΔG ≈ 2437.54 J/mol * (-4.605) ≈ -11225.3 J/mol

The negative value of ΔG indicates that the transport of glucose is an exergonic process, meaning it occurs spontaneously without the need for additional energy input. This systematic approach can be applied to similar problems, ensuring a clear understanding of the principles governing molecular transport across cell membranes.