Problem 28 - Chemistry Matter and Change

Question

Explain how you could calculate the heat released in freezing 0.250 mol water

Step-by-Step Solution

Answer

The heat released in freezing 0.250 mol of water can be calculated using the formula \(Q = n \times \Delta H_{fus}\), where \(Q\) is the heat released, \(n\) is the number of moles of water, and \(\Delta H_{fus}\) is the molal enthalpy of fusion of water. Given that \(n = 0.250\) mol and \(\Delta H_{fus} = 6.01\) kJ/mol, we can plug these values into the formula to find \(Q = 0.250 \times 6.01 = 1.5025\) kJ. Therefore, the heat released in freezing 0.250 mol of water is 1.5025 kJ.

Step 1: Identify given values and the formula needed

We are given the following information: - Number of moles (n) of water = 0.250 mol - Molal enthalpy of fusion of water (∆Hfus) = 6.01 kJ/mol We need to find the heat released (Q) during the freezing process. The formula to calculate the heat released is: Q = n × ∆Hfus

Step 2: Calculate the heat released during the freezing process

Plug the given values into the formula: Q = n × ∆Hfus Q = 0.250 mol × 6.01 kJ/mol

Step 3: Calculate the result

Multiply the values and calculate the heat released: Q = 1.5025 kJ Since the process is the freezing of water, the heat is being released, which means that the value we found (1.5025 kJ) is correct.

Step 4: Write the final answer

The heat released in freezing 0.250 mol of water is 1.5025 kJ.

Key Concepts

Calculate the heat of phase change

Understanding how to calculate the heat of phase change is vital knowledge in chemistry, specifically in thermodynamics. It's the energy absorbed or released during a transition from one phase of matter to another, for example, from a solid to a liquid or vice versa.

The general formula used in such a calculation is:
\[\begin{equation} Q = n \times \Delta H \ba\[\begin{equation} where \( Q \) represents the heat exchanged, \( n \) is the number of moles of the substance, and \( \Delta H \) is the enthalpy change for the phase transition, which can be specific to the substance and process, such as fusion or vaporization.

In the exercise provided, the phase change in question was freezing, which is the transition from liquid to solid. As the process is exothermic (releases heat), the calculated heat for the phase change will have a negative sign, indicating a release of energy.

To ensure full comprehension, remember that the enthalpy of fusion varies depending on the substance, so always confirm you have the right \( \Delta H \) for the material before plugging it into the formula.

Freezing process of water

When it comes to the freezing process of water, it's important to consider what happens on a molecular level. Water, known chemically as H2O, becomes less dense as it transitions from liquid to solid, forming a crystalline structure known as ice.

During this process, water releases energy into its surroundings, because energy is required to break the hydrogen bonds that keep water molecules in liquid form. As these bonds reform into a more stable solid state, energy is expelled. This is described thermodynamically as the enthalpy of fusion, with a fixed value for water at atmospheric pressure: \( \Delta H_{fus} = 6.01 kJ/mol \).

This particular enthalpy value plays a crucial role in calculations because it dictates the amount of heat a certain quantity of water, measured in moles, will release upon freezing. Knowing this, we can track energy transfers in various scientific and real-world applications, such as understanding weather patterns or designing refrigeration systems.

Molar heat calculations

Solving exercises involving molar heat calculations requires understanding moles and molar enthalpy. A mole is a unit that represents a very specific number of particles (be it atoms, molecules, or ions), referred to as Avogadro's number which is approximately \(6.022 \times 10^{23}\) entities per mole.

For accurate molar heat calculations, it is fundamental to know the compound's enthalpy change per mole during a phase change. In the given exercise, freezing of water, you'll use the molar enthalpy of fusion.

Here, the solution is made straightforward by multiplying the number of moles by the molar enthalpy of fusion. Students should note that this calculation gives the total heat involved in the process for the given amount of substance. The result provides insight into the energy changes involved in freezing or melting processes and can be applied in various scientific fields, from designing heating and cooling systems to understanding Earth’s climate.