Problem 16 - Chemistry for Allied Health

Question

Calculate the quantity of heat that is absorbed or released during each process. a. \(655 \mathrm{~g}\) of water vapor condenses at \(100^{\circ} \mathrm{C}\) b. \(8.20 \mathrm{~kg}\) of water is frozen c. \(40.0 \mathrm{~mL}\) of ethanol is vaporized. The density of ethanol is \(0.789 \mathrm{~g} / \mathrm{mL}\). d. \(25.0 \mathrm{~mL}\) of ethanol condenses. The density of ethanol is \(0.789 \mathrm{~g} / \mathrm{mL}\).

Step-by-Step Solution

Answer

a) 1,480,300 J released, b) 2,738,800 J released, c) 26,826 J absorbed, d) 16,766 J released.

Step 1: Understand the Problem

To calculate the quantity of heat absorbed or released, we must identify the phase change under consideration: condensation, freezing, or vaporization. Using known values for latent heat, we can find the energy involved in these phase changes.

Step 2: Heat of Vaporization and Condensation for Water

The heat of vaporization (and condensation) of water is approximately 2260 J/g. When water vapor condenses, it releases heat. To find the heat released by 655 g of water vapor condensing at 100°C, use the formula: \[ Q = mL \] where \( m = 655 \text{ g} \) and \( L = 2260 \text{ J/g} \).

Step 3: Calculation for Water Vapor Condensation

Calculate the heat released: \[ Q = 655 \text{ g} \times 2260 \text{ J/g} = 1,480,300 \text{ J} \]So, 1,480,300 J of heat is released.

Step 4: Heat of Fusion for Freezing Water

The heat of fusion for water is 334 J/g. To determine the heat released when freezing 8.20 kg of water, first convert the mass from kg to g: \( 8.20 \text{ kg} = 8200 \text{ g} \). Use the formula: \[ Q = mL \]where \( m = 8200 \text{ g} \) and \( L = 334 \text{ J/g} \).

Step 5: Calculation for Freezing Water

Calculate the heat released: \[ Q = 8200 \text{ g} \times 334 \text{ J/g} = 2,738,800 \text{ J} \] So, 2,738,800 J of heat is released.

Step 6: Convert Volume of Ethanol to Mass

The density of ethanol is 0.789 g/mL. To calculate heat, first convert the volume of ethanol to mass: For vaporizing 40.0 mL: \[ \text{mass} = 40.0 \text{ mL} \times 0.789 \text{ g/mL} = 31.56 \text{ g} \]

Step 7: Heat of Vaporization for Ethanol

The heat of vaporization of ethanol is approximately 850 J/g. Use the formula \[ Q = mL \] where \( m = 31.56 \text{ g} \) and \( L = 850 \text{ J/g} \).

Step 8: Calculation for Vaporization of Ethanol

Calculate the heat absorbed: \[ Q = 31.56 \text{ g} \times 850 \text{ J/g} = 26,826 \text{ J} \] So, 26,826 J of heat is absorbed.

Step 9: Convert Volume of Ethanol to Mass for Condensation

For condensing 25.0 mL of ethanol, convert the volume to mass: \[ \text{mass} = 25.0 \text{ mL} \times 0.789 \text{ g/mL} = 19.725 \text{ g} \]

Step 10: Calculation for Condensation of Ethanol

Use the heat of vaporization of ethanol (850 J/g) for the reverse process (condensation): \[ Q = mL \] Calculate the heat released:\[ Q = 19.725 \text{ g} \times 850 \text{ J/g} = 16,766.25 \text{ J} \] So, 16,766 J of heat is released.

Key Concepts

Phase Change

Phase change refers to the transformation of a substance from one state of matter to another, such as solid to liquid, liquid to gas, or vice versa. This change occurs when the temperature reaches a point where the molecules have enough energy to change their state. For instance, water boils at 100°C, turning from liquid to vapor, and freezes at 0°C, transforming from liquid to solid.

It's crucial to understand that during a phase change, the temperature of the substance does not change until the entire phase transformation is complete. This is because the energy is used to change the state, not to increase the temperature. The process is isothermal, meaning the temperature remains constant.

• Melting and freezing are transitions between solid and liquid.
• Vaporization and condensation are between liquid and gas.

Recognizing these changes helps us calculate energy required or released during such processes.

Heat of Vaporization

The heat of vaporization is the amount of heat required to convert a liquid into a vapor without changing its temperature. It’s a significant concept because it helps in understanding how much energy is needed to turn a liquid into a gas. This concept is crucial for applications like distillation and even in weather phenomena.

For water, the heat of vaporization is approximately 2260 J/g. This means that to vaporize 1 gram of water, 2260 joules of energy are required. Conversely, the same amount of energy is released when water vapor condenses into water, which is why condensation is often an exothermic process.

Applications of the amount of heat needed for vaporization include

• Climate control systems that rely on evaporation cooling
• Industrial processes for insulation and heating

Understanding this energy requirement is critical for efficient use of energy resources.

Heat of Fusion

Heat of fusion is the energy needed to change a substance from solid to liquid at its melting point. For water, this is approximately 334 J/g. This means you need 334 joules to melt 1 gram of ice at 0°C. Unlike heat of vaporization, the heat of fusion deals with the solid-liquid transition.

For example, to freeze 8.20 kg of water, we consider its mass in grams and multiply by the heat of fusion. Since freezing is essentially reverse melting, the same amount of energy is released when liquid water turns into ice.

Understanding the heat of fusion is important because it affects:

• Food preservation techniques through freezing
• Climatology, where it impacts sea ice dynamics and glaciers

This concept is pivotal in designing energy-efficient methods for cooling and freezing.

Latent Heat

Latent heat is the energy absorbed or released by a substance during a phase change, without a change in temperature. It describes two main types:

• Latent heat of fusion, involved during melting and freezing.
• Latent heat of vaporization, involved during vaporization and condensation.

Understanding latent heat is crucial in numerous applications, ranging from metallurgy to meteorology. For example, it's why sweating cools the body; evaporation of sweat requires heat absorption, providing a cooling effect.

When you calculate latent heat, you're essentially covering the energy exchange accompanying phase changes, providing insight into how much energy is involved in these processes. It is distinct because the energy is utilized in changing the phase, not adjusting the temperature, making it key for energy calculations during phase changes.

Condensation and Vaporization Calculations

Condensation and vaporization calculations involve determining the heat exchanged during these processes. These calculations help understand the energy dynamics in phase changes between liquid and gas states.

In condensation, the process releases heat. For example, 655 g of water vapor condensing at 100°C releases significant energy into the surrounding. Using the formula \[ Q = mL \]where \( m \) is mass and \( L \) is latent heat, we can calculate this energy. Similarly, vaporizing a liquid, like ethanol, requires energy input, calculated using the same formula.

These calculations are vital for a variety of reasons, including:

• Designing energy-efficient HVAC systems
• Planning industrial processes involving steam or other vapors
• Estimating natural water cycles in environmental science

Proficiency in these calculations equips students to analyze and predict energy exchanges in both natural and engineered systems.