Calculate The Energy Needed To Vaporize 75g Of Water.

Calculating the Energy Needed to Vaporize 75g of Water: A Comprehensive Guide

Understanding the energy required to change the phase of a substance, specifically from liquid to gas (vaporization), is crucial in various scientific fields, from engineering to meteorology. This comprehensive guide will walk you through the calculation of the energy needed to vaporize 75g of water, explaining the underlying principles and providing a step-by-step approach. We'll also explore the broader context of latent heat and its implications.

Understanding Latent Heat of Vaporization

Before diving into the calculation, let's clarify the core concept: latent heat of vaporization. This refers to the amount of energy (heat) required to change one unit of mass of a substance from a liquid to a gas at its boiling point without a change in temperature. For water at its normal boiling point (100°C or 212°F), the latent heat of vaporization (L_v) is approximately 2260 kJ/kg or 2260 J/g. This means that 2260 Joules of energy are needed to vaporize 1 gram of water at 100°C. This energy breaks the intermolecular hydrogen bonds holding the water molecules together in the liquid state, allowing them to escape as a gas (water vapor or steam).

Why is Latent Heat Important?

The concept of latent heat is vital for understanding a wide range of natural phenomena and technological processes. For instance:

• Weather patterns: Evaporation and condensation processes, driven by latent heat, play a significant role in weather formation, cloud development, and precipitation.
• Cooling systems: Refrigeration and air conditioning rely on the principle of latent heat absorption during vaporization to remove heat from a space.
• Power generation: Steam power plants utilize the latent heat of water vapor to drive turbines and generate electricity.
• Industrial processes: Many industrial processes involve phase changes, such as distillation and drying, where understanding latent heat is essential for efficient operation.

Calculating the Energy for Vaporizing 75g of Water

Now, let's address the main task: calculating the energy needed to vaporize 75g of water. We'll use the following formula:

Q = m * L_v

Where:

• Q represents the heat energy required (in Joules).
• m is the mass of the water (in grams).
• L_v is the latent heat of vaporization of water (in J/g).

Step-by-step calculation:

1. Identify the known values:

   • m = 75g (mass of water)
   • L_v = 2260 J/g (latent heat of vaporization of water at 100°C)

2. Substitute the values into the formula: Q = 75g * 2260 J/g

3. Perform the calculation: Q = 169500 J

Therefore, the energy needed to vaporize 75g of water at 100°C is 169,500 Joules or 169.5 kJ.

Factors Affecting Latent Heat of Vaporization

While we used a standard value for L_v, it's important to note that the latent heat of vaporization isn't always a constant. Several factors can influence it:

• Temperature: The latent heat of vaporization slightly decreases as the temperature increases. The value of 2260 J/g is accurate for water at 100°C. At lower temperatures, slightly more energy is required for vaporization. However, this change is relatively small within a reasonable temperature range and often negligible in many practical calculations.
• Pressure: Changes in atmospheric pressure affect the boiling point of water. A lower pressure results in a lower boiling point, and the latent heat of vaporization will change accordingly. At lower pressures, less energy is required for vaporization.
• Impurities: The presence of dissolved substances (salts, minerals, etc.) in water can slightly alter the latent heat of vaporization. Generally, the effect is small for low concentrations of impurities.

Beyond Vaporization: Considering Specific Heat Capacity

The calculation above assumes that the water is already at its boiling point (100°C). If the water is initially at a lower temperature, we need to account for the energy required to heat it up to 100°C before vaporization can occur. This requires considering the specific heat capacity of water.

Specific heat capacity (c) represents the amount of heat energy required to raise the temperature of one unit of mass of a substance by one degree Celsius (or one Kelvin). For water, the specific heat capacity is approximately 4.18 J/g°C.

To calculate the total energy required, we need to add the energy needed to heat the water to 100°C to the energy needed for vaporization. The formula becomes:

Q_total = m * c * ΔT + m * L_v

Where:

• Q_total is the total heat energy required.
• ΔT is the change in temperature (in °C).

Example: Let's say we have 75g of water at 25°C. We want to calculate the total energy required to vaporize it.

1. Calculate the energy to heat the water to 100°C: ΔT = 100°C - 25°C = 75°C Q_heating = 75g * 4.18 J/g°C * 75°C = 23512.5 J

2. Calculate the energy to vaporize the water at 100°C: Q_vaporization = 75g * 2260 J/g = 169500 J

3. Calculate the total energy: Q_total = Q_heating + Q_vaporization = 23512.5 J + 169500 J = 193012.5 J

Therefore, the total energy needed to heat 75g of water from 25°C to 100°C and then vaporize it is approximately 193,012.5 Joules or 193.0 kJ.

Practical Applications and Further Considerations

The calculations presented here provide a fundamental understanding of the energy requirements for water vaporization. However, real-world applications often involve more complex scenarios. Factors like heat losses to the surroundings, variations in atmospheric pressure, and the presence of impurities should be considered for precise calculations in engineering or scientific experiments.

Furthermore, the concept extends beyond water. Similar calculations can be performed for other substances by using their specific latent heat of vaporization and specific heat capacity values. This understanding is crucial in various fields, including:

• Chemical engineering: Designing distillation columns, evaporators, and other process equipment.
• Environmental science: Modeling atmospheric processes and understanding climate change.
• Materials science: Understanding the behavior of materials during phase transitions.

This comprehensive guide provides a solid foundation for calculating the energy needed to vaporize water. Remember to always account for all relevant factors, especially the initial temperature of the water, to obtain accurate and meaningful results. By grasping the fundamental principles of latent heat and specific heat capacity, you'll be well-equipped to tackle more complex thermodynamic problems.