Question

The standard free energy of formation of solid maltose is \(-1334.42 \mathrm{~kJ} / \mathrm{mol},\) whereas that of solid glucose is \(-910.56 \mathrm{~kJ} / \mathrm{mol}\). What is \(\Delta G^{\circ}\) for the condensation of two glucose molecules to form maltose?

Short answer

The standard free energy change for the condensation of two glucose molecules to form a maltose molecule is \(\Delta G^{\circ} = 486.70 \mathrm{~kJ/mol}\).

Step-by-step solution

Write the chemical equation for the condensation reaction.

The condensation reaction of two glucose molecules to form a maltose molecule can be represented by the following chemical equation: 2 C6H12O6 (s) → C12H22O11 (s) + H2O (l) This shows that two glucose molecules (C6H12O6) combine to form one maltose molecule (C12H22O11) and one water molecule (H2O).

Write the equation for calculating the standard free energy change (∆G°) for the reaction.

The standard free energy change (∆G°) for the condensation reaction can be calculated using the following equation: ∆G°(reaction) = ∆G°(products) - ∆G°(reactants) For this equation, we need to consider the free energy of formation for maltose and glucose molecules.

Substitute the given values of the standard free energy of formation for maltose and glucose.

We are given the following values for the standard free energy of formation: - Maltose: ∆G°(maltose) = -1334.42 kJ/mol - Glucose: ∆G°(glucose) = -910.56 kJ/mol Now we will substitute these values into the equation from Step 2: ∆G°(reaction) = ∆G°(maltose) - 2 * ∆G°(glucose)

Calculate the standard free energy change for the condensation reaction.

Using the information from Step 3, we can calculate the standard free energy change for the condensation reaction: ∆G°(reaction) = (-1334.42 kJ/mol) - 2 * (-910.56 kJ/mol) ∆G°(reaction) = (-1334.42 kJ/mol) + 1821.12 kJ/mol ∆G°(reaction) = 486.70 kJ/mol Thus, the standard free energy change for the condensation of two glucose molecules to form a maltose molecule is 486.70 kJ/mol.

Key concepts

Standard Free Energy

Thermodynamics is an important part of chemistry. It helps predict how chemical reactions will behave. One central concept is the standard free energy (\( \Delta G^{\circ} \)). This value tells us if a reaction can happen on its own. If \( \Delta G^{\circ} \) is negative, the reaction is said to be spontaneous, meaning it can occur without needing energy from outside sources. If \( \Delta G^{\circ} \) is positive, like in our exercise, the reaction won't happen on its own. Additional energy input is needed.

To figure out \( \Delta G^{\circ} \) for a reaction, you use a specific equation: \[\Delta G^{\circ}(\text{reaction}) = \Delta G^{\circ}(\text{products}) - \Delta G^{\circ}(\text{reactants})\]Using this equation, we understand how much energy is associated with forming the products and breaking down the reactants.

It's also key to know that these values are usually given for specific conditions: 1 atm pressure, 298K (about 25°C) temperature. This allows scientists to calculate and compare values consistently, using under the same conditions ("standard state"). Learning to calculate and understand \( \Delta G^{\circ} \) not only helps solve problems like our exercise but also provides insight into how reactions occur in the real world.

Chemical Equations

Chemical equations are vital in chemistry. They use symbols to represent what happens in a reaction. They help us understand the details of what reactants are used and what products are formed.

For example, in our exercise, the chemical equation given is:

• 2 C₆H₁₂O₆ (s) → C₁₂H₂₂O₁₁ (s) + H₂O (l)

This describes a condensation reaction where two glucose molecules (C₆H₁₂O₆) join to form maltose (C₁₂H₂₂O₁₁) and water (H₂O). Here's how to interpret it:

• The left side includes the reactants, showing you what goes into the reaction. In this case, it is two glucose molecules.
• The right side shows the products, representing what's produced. In this case, maltose and water are made.

Balanced chemical equations ensure that the same number of each type of atom appears on both sides, aligning with the Law of Conservation of Mass. This means atoms are neither created nor destroyed during the reaction. It may seem simple but this principle is crucial for accurate reactions and calculations in chemistry.

Condensation Reaction

Condensation reactions are specific types of chemical reactions. They often involve two smaller molecules joining together to form a larger molecule, while losing a small molecule such as water. In our exercise, two glucose molecules condense to form maltose. This produces one water molecule in the process.

These reactions are important because they are common in many biological processes. For instance, they’re essential in forming biomolecules like carbohydrates and proteins.

Key features of a condensation reaction include:

• Joining of two or more molecules
• Formation of a new larger molecule
• Release of a small molecule (commonly water)

In learning about condensation reactions, it's clear they play a crucial role in both synthetic and natural processes. Additionally, understanding these reactions helps in grasping larger concepts in biochemistry and molecular biology. In practical terms, knowing how to predict and control condensation reactions is valuable in fields like medicine and materials science.