Question

How much energy is evolved as heat when \(1.0 \mathrm{L}\) of water at \(0^{\circ} \mathrm{C}\) solidifies to ice? (The heat of fusion of water is \(333 \mathrm{J} / \mathrm{g} .\) )

Short answer

333,000 J of heat is evolved.

Step-by-step solution

Determine the Mass of Water

First, we need to find the mass of 1.0 L of water since volume is given. We use the fact that the density of water is approximately 1 g/mL (or 1000 g/L). Thus, 1.0 L of water has a mass of 1000 g.

Use the Heat of Fusion Formula

The heat of fusion formula is given as the amount of energy required to change a certain mass from solid to liquid or vice versa. The formula is: \( q = m \times \Delta H_f \), where \( q \) is the heat energy, \( m \) is the mass, and \( \Delta H_f \) is the heat of fusion. For water, \( \Delta H_f = 333 \text{ J/g} \).

Calculate the Energy as Heat

Using the formula from Step 2: \( q = 1000 \text{ g} \times 333 \text{ J/g} = 333,000 \text{ J} \). This is the thermal energy evolved when the water freezes.

Key concepts

Heat of Fusion

Understanding the heat of fusion is essential when studying how substances change state. It refers to the amount of energy needed to change a substance from solid to liquid at its melting point, without changing its temperature. In the context of our exercise, it’s about transitioning water between its solid and liquid phases without any change in temperature during this process.

When you have 1.0 L of water at 0°C and want to solidify it into ice, you're looking at how much energy is involved in changing each gram of water into ice. Given that the heat of fusion for water is 333 J/g, this tells us that it takes 333 Joules of energy to freeze each gram of water.

This concept helps in understanding how energy is involved in phase transitions, highlighting that even without a temperature change, significant energy can still be exchanged.

Phase Transition

Phase transition is a process where a substance changes from one state of matter to another. These states include solid, liquid, and gas. For our exercise example, we are focusing on the change from liquid water to solid ice. This specific phase transition is called freezing.

A phase transition occurs because the kinetic energy of the particles changes, causing an alteration in the forces between them. During freezing, the energy within the water molecules decreases, thus reducing their movement and allowing them to form a structured solid — ice. This happens at a constant temperature, and the energy change involved in this process is governed by its heat of fusion.

• For water, freezing occurs at 0°C.
• During this change, energy is released as heat when water molecules form a solid structure.

Thermal Energy

Thermal energy is a form of energy that flows from a warmer object to a cooler one. It is often associated with changes in temperature and can be absorbed or released during physical or chemical processes. In our calorimetry exercise, the focus is on how thermal energy is related to phase changes, such as the transition from liquid water to solid ice.

When 1.0 L of water at 0°C is turned into ice, thermal energy is released. This energy transfer is calculated using the heat of fusion formula. The concept also illustrates how, despite the temperature remaining constant during the phase change, there is a significant energy shift.

• An example: 1.0 L of water solidifying releases 333,000 J of thermal energy.
• This energy is a product of mass and the heat of fusion, calculated as: \[ q = m \times \Delta H_f \]