Problem 4 - Chemistry: Introducing Inorganic, Organic and Physical Chemistry

Question

Calculate the onthalpy change when \(100 \mathrm{g}\) of water froezes at \(0^{\circ} \mathrm{C}\). (The standard enthalpy change of fusion of water is \(+6.01 \mathrm{kJmol}^{-1}\), ) (Section 13.2)

Step-by-Step Solution

Answer

The enthalpy change is approximately \(-33.3 \text{ kJ}\).

Step 1: Convert Mass to Moles

First, determine the number of moles of water. The molar mass of water is approximately 18.015 g/mol. Use the formula: number of moles = \( \frac{\text{mass}}{\text{molar mass}} \). With 100 g of water, the moles will be \( \frac{100}{18.015} \approx 5.55 \text{ moles} \).

Step 2: Consider Sign of Enthalpy Change

The problem involves freezing, and the given enthalpy change is for fusion (melting), which is an endothermic process. Freezing is the opposite and is exothermic, so the sign of the enthalpy change will be opposite of fusion: \(-6.01 \text{ kJ/mol} \).

Step 3: Calculate Total Enthalpy Change

Multiply the number of moles by the enthalpy change per mole. Total enthalpy change \( \Delta H = 5.55 \text{ moles} \times (-6.01 \text{ kJ/mol}) \approx -33.3 \text{ kJ} \).

Key Concepts

Water Freezing

Freezing is a fascinating phase change where water transitions from liquid to solid. In this process, water molecules slow down and arrange themselves into a rigid structure, forming ice. This change occurs at 0°C, which is the freezing point of water under normal atmospheric pressure. During freezing, energy is released into the surrounding environment. This is because the molecules in solid ice have lower energy compared to when they are in a liquid state. This release of energy is why you feel the cold when ice absorbs heat from your hand, melting back to water.

Enthalpy of Fusion

The enthalpy of fusion is an essential concept in thermal physics. It indicates the amount of energy required to transform a solid into a liquid at its melting point. For water, the standard enthalpy of fusion is +6.01 kJ/mol. This positive value tells us that melting ice into water is an endothermic process—energy is absorbed to overcome the forces holding the ice together.
In contrast, when freezing occurs, the process reverses. Energy is released as the water molecules form a solid crystalline lattice. Thus, the enthalpy change for freezing is simply negative of that for fusion. Remember, the absolute value remains the same, illustrating the conservation of energy.

Mole Calculation

Understanding how to calculate moles helps in determining how much substance is involved in a chemical process. A mole, in chemistry, refers to Avogadro's number (approximately 6.022 × 10²³) of molecules. Calculating moles from mass involves using the formula:

• Number of moles = \( \frac{\text{mass of substance}}{\text{molar mass}} \)

For water, where the molar mass is around 18.015 g/mol, converting 100 grams of water to moles provides a clear picture of the number of particles participating in the freezing process. This step is crucial in precise calculations for enthalpy changes or other chemical equations.

Exothermic Process

Exothermic processes are chemical reactions or physical changes that release energy to their surroundings. They often occur naturally and can be recognized by a temperature increase in the surrounding area. Examples include freezing, condensation, and many combustion reactions.
During freezing, as water transitions into ice, the process is exothermic. This can be understood as the system (water) losing energy, releasing it into the environment as heat. This release results in the surrounding area becoming warmer relative to the system. In practical terms, exothermic reactions are often sought for their efficiency, as they generally require less input energy once initiated, making them beneficial for various industrial applications.