Problem 99 - Chemistry: The Central Science

Question

The standard free energy of formation of solid glycine is \(-369 \mathrm{~kJ} / \mathrm{mol}\), whereas that of solid glycylglycine is \(-488 \mathrm{kl} / \mathrm{mol}\). What is \(\Delta G^{4}\) for the condensation of glycine to form glycylglycine?

Step-by-Step Solution

Answer

The change in Gibbs free energy, ΔG, for the condensation of glycine to form glycylglycine can be calculated using the formula ΔG = ΔG(products) - ΔG(reactants). Given the standard free energy of formation for solid glycine (-369 kJ/mol) and solid glycylglycine (-488 kJ/mol), the change in Gibbs free energy is calculated as follows: ΔG = [(-488)] - [2 * (-369)] = 250 kJ/mol.

Step 1: Identify the reactants and products in the condensation reaction

In the condensation of glycine to form glycylglycine, the reaction can be represented as: 2 Glycine → Glycylglycine + H2O Reactants: 2 moles of Glycine Product: 1 mole of Glycylglycine

Step 2: Write down the formula for calculating ΔG for the reaction

To calculate ΔG for the condensation reaction, we will use the following formula: ΔG = ΔG(products) - ΔG(reactants) ΔG = [(ΔG(Glycylglycine) + ΔG(H2O)] - [2 * ΔG(Glycine)] Note that the standard free energy of formation for water (∆G°(H2O)) is considered negligible in this context, as it is constant for both sides of the equation.

Step 3: Plug in the given ΔG values into the formula

We know the values of ΔG for solid glycine and solid glycylglycine: ΔG(Glycine) = -369 kJ/mol ΔG(Glycylglycine) = -488 kJ/mol Now, plug in the values into the formula we derived in Step 2: ΔG = [(-488)] - [2 * (-369)]

Step 4: Calculate ΔG for the condensation reaction

To find the change in Gibbs free energy, ΔG, for the condensation of glycine, perform the calculations: ΔG = -488 + (2 * 369) ΔG = -488 + 738 ΔG = 250 kJ/mol The change in Gibbs free energy, ΔG, for the condensation of glycine to form glycylglycine is 250 kJ/mol.

Key Concepts

Condensation Reaction

Condensation reactions are a kind of chemical process where two molecules combine to form a larger molecule while releasing a smaller molecule, typically water. This occurs often among biomolecules to form complex structures such as proteins from amino acids, as seen in our example where glycine molecules come together to form glycylglycine.

During condensation, chemical bonds are formed, and the process is crucial in biological systems. One of the key aspects of these reactions is that they often require energy and can be influenced by environmental conditions such as temperature and pH. Understanding how energy is transferred during these reactions is part of the field of chemical thermodynamics.

Enthalpy

Enthalpy, denoted by the symbol H, is a measure of the total heat content of a system at constant pressure. It reflects the energy needed to form a compound from its elements in their standard states. Although enthalpy cannot be measured directly, changes in enthalpy (∆H) during a reaction can be. These changes indicate if a reaction is exothermic (releases heat) or endothermic (absorbs heat).

For instance, in a condensation reaction, the enthalpy change tells us whether the reaction will release heat to the surroundings or absorb heat from them. This concept is important because it helps predict the spontaneity of a reaction along with Gibbs free energy.

Chemical Thermodynamics

Chemical thermodynamics deals with the relationship between chemical reactions and energy changes involving heat. It's a cornerstone of physical chemistry that helps us understand the energy balance in a reaction. Key principles of thermodynamics, such as the first and second laws, elucidate how energy is conserved in chemical processes and the direction of spontaneous reactions.

These principles allow chemists to predict whether reactions will occur spontaneously based on thermodynamic quantities like enthalpy, entropy (a measure of disorder or randomness), and Gibbs free energy. The interplay between these quantities reveals much about a reaction's characteristics and feasibility.

Gibbs Free Energy Calculation

Gibbs free energy (G) is a thermodynamic potential used to predict the direction of chemical reactions and whether or not they are spontaneous at constant temperature and pressure. It's calculated by the equation G = H - TS, where H is the enthalpy, T is the temperature, and S is the entropy of the system.

The change in Gibbs free energy (∆G) during a reaction can be computed via the formula ∆G = ∆G(products) - ∆G(reactants), as exemplified in the step-by-step solution of our exercise. If ∆G is negative, the reaction is spontaneous; if positive, it's non-spontaneous; and if zero, the system is in equilibrium. This calculation is pivotal in chemical thermodynamics, as it incorporates both enthalpic and entropic considerations, providing a comprehensive picture of reaction spontaneity.