Problem 68 - Chemistry The Central Science

Question

(a) What is the value of the standard enthalpy of formation of an element in its most stable form? (b) Write the chemical equation for the reaction whose enthalpy change is the standard enthalpy of formation of sucrose (table sugar), \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(s), \Delta H_{f}^{\circ}\left[\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(s)\right]\)

Step-by-Step Solution

Answer

(a) The standard enthalpy of formation of an element in its most stable form is \(0 \, \text{kJ/mol}\). (b) The balanced chemical equation for the standard enthalpy of formation of sucrose is \(12 C(graphite) + 11 H_{2}(g) + 11 O_{2}(g) \rightarrow C_{12}H_{22}O_{11}(s)\).

Step 1: (a) Standard Enthalpy of Formation Definition

The standard enthalpy of formation, \(\Delta H_{f}^{\circ}\), is the change in enthalpy when one mole of a substance in its standard state is formed from its constituent elements in their standard states. For an element in its most stable form, it is already in its standard state; thus, no change in enthalpy occurs, and its standard enthalpy of formation is zero.

Step 2: (a) Entropy of Formation Value for a Stable Element

Given the definition of standard enthalpy of formation, we conclude that the value of the standard enthalpy of formation of an element in its most stable form is \(0 \, \text{kJ/mol}\).

Step 3: (b) Formation of Sucrose Chemical Equation

We are asked to write a balanced chemical equation representing the enthalpy change for the formation of sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(s)\). Sucrose is formed from its constituent elements, carbon (C), hydrogen (H), and oxygen (O), in their standard states (solid graphite, diatomic hydrogen gas, and diatomic oxygen gas, respectively). We will begin by writing the unbalanced chemical equation: \(C(graphite) + H_{2}(g) + O_{2}(g) \rightarrow C_{12}H_{22}O_{11}(s)\) Next, we will balance the equation by adjusting the coefficients to ensure that the number of atoms of each element on the reactant side equals the number on the product side.

Step 4: (b) Balanced Chemical Equation for Sucrose Formation

After balancing the equation, we obtain: \(12 C(graphite) + 11 H_{2}(g) + 11 O_{2}(g) \rightarrow C_{12}H_{22}O_{11}(s)\) This balanced chemical equation represents the standard enthalpy of formation of sucrose, \(\Delta H_{f}^{\circ}\left[\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(s)\right]\).

Key Concepts

Enthalpy Change

Enthalpy change is a crucial concept in thermodynamics, often symbolized by \( \Delta H \). It represents the heat change at constant pressure, which can occur during a chemical reaction. When a reaction takes place, products form from reactants, and energy either gets absorbed or released. If a system absorbs heat, it's an endothermic reaction, and when it releases heat, it's exothermic.
\( \Delta H \) helps us understand this heat exchange. It's determined by the difference between the enthalpy of the products and the enthalpy of the reactants.

• To calculate, use: \( \Delta H = H_{products} - H_{reactants} \)
• A negative \( \Delta H \) indicates an exothermic process.
• A positive \( \Delta H \) indicates an endothermic process.

By studying enthalpy change, we gain insights into the energetic behavior of substances during reactions, making it a foundational aspect of chemistry.

Standard State

In chemistry, the standard state of a substance is its typical phase and form at a standard set of conditions. These conditions include a pressure of 1 bar (or 1 atm, approximately), and the temperature is usually considered to be 298.15 K (25°C), unless stated otherwise.
This uniform set of conditions allows chemists to compare different properties like enthalpy or entropy across different substances.

• For gases, the standard state is pure gas at 1 bar.
• For liquids and solids, it's the pure substance in its most stable form at 1 bar and 25°C.
• For solutions, the standard state is the solute dissolved at 1 molar concentration.

Understanding the standard state is crucial because it provides a reference point for measuring and reporting various thermodynamic properties, such as the standard enthalpy of formation.

Chemical Equation

A chemical equation represents a chemical reaction where reactants transform into products. It uses chemical formulas to show the substances involved. Each chemical symbol identifies specific elements, and stoichiometric coefficients help balance the equation to ensure mass conservation.
Balancing a chemical equation involves making sure that there are equal numbers of each type of atom on both sides of the equation, which complies with the law of conservation of mass.

• Start by writing the unbalanced equation.
• Identify the number of atoms of each element involved.
• Add coefficients to balance the number of atoms on both sides.

For example, in the formation of sucrose, the balanced chemical equation is:\[12 \ C(graphite) + 11 \ H_{2}(g) + 11 \ O_{2}(g) \rightarrow C_{12}H_{22}O_{11}(s)\]This equation indicates that 12 carbon atoms, 22 hydrogen atoms, and 11 oxygen molecules produce one molecule of sucrose.

Formation of Sucrose

The formation of sucrose involves combining its constituent elements: carbon, hydrogen, and oxygen. Each of these elements exists in a specific standard state. For carbon, this state is as solid graphite. Hydrogen and oxygen are both diatomic gases, represented as \(H_2\) and \(O_2\), respectively.
To form one mole of sucrose \(C_{12}H_{22}O_{11}\), these elements react under standard conditions as described in the balanced chemical equation:
\[\ 12 \ C (graphite) + 11 \ H_{2} (g) + 11 \ O_{2} (g) \rightarrow C_{12} H_{22} O_{11}(s)\]

• It's essential to start with these elements in their standard states.
• This equation reflects the change in enthalpy known as the standard enthalpy of formation for sucrose.
• Understanding formation reactions helps in studying how substances are built from their most fundamental components, providing insight into chemical relationships and energy changes involved.

In essence, knowing how sucrose forms marries concepts like stoichiometry, standard state, and enthalpy change into a coherent understanding of its production process.