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Heat of Vaporization Formula - Definition, Equation, Solved Examples

Heat of Vaporization Formula: The heat of vaporization, denoted as ΔHvap, represents the energy required to transform a substance from liquid to gas at constant temperature and pressure.

Murtaza Mushtaq11 Oct, 2023

What is Heat of Vaporization?

Heat of Vaporization Formula : Heat of vaporization, often denoted as ΔHvap, is the amount of heat energy required to change a substance from its liquid phase to its gaseous phase at a constant temperature and pressure. It is a fundamental concept in thermodynamics and plays a significant role in various industrial processes, including distillation and refrigeration. Heat of vaporization, often denoted as ΔHvap, is the amount of heat energy required to change a substance from its liquid phase to its gaseous phase at a constant temperature and pressure. It is a fundamental concept in thermodynamics and plays a significant role in various industrial processes, including distillation and refrigeration.

The Formula for Heat of Vaporization

The formula to calculate the heat of vaporization is given by:

ΔHvap = (mass of substance) × (heat of vaporization per unit mass)

Where: - ΔHvap is the heat of vaporization (in joules or calories) - Mass of substance is the mass of the substance undergoing vaporization (in grams or kilograms) - Heat of vaporization per unit mass is the amount of heat energy required to vaporize one unit of mass (in joules per gram or calories per gram)

Also Check - Heat Input Formula

Solved Examples Of Heat of Vaporization Formula

Example 1:

Calculate the heat of vaporization for 50 grams of water. The heat of vaporization of water is 40.7 kJ/mol.

Solution:

First, we need to convert grams to moles using the molar mass of water (18.015 g/mol): Number of moles (n) = Mass (m) / Molar mass (M) n = 50 g / 18.015 g/mol ≈ 2.776 mol Now, we can calculate the heat of vaporization: ΔHvap = n × ΔHvap per mole ΔHvap = 2.776 mol × 40.7 kJ/mol ≈ 112.91 kJ So, the heat of vaporization for 50 grams of water is approximately 112.91 kJ.

Also Check - Critical Velocity Formula

Example 2:

Calculate the heat of vaporization for 100 grams of ethanol (C2H5OH). The heat of vaporization of ethanol is 38.56 kJ/mol.

Solution:

Calculate the molar mass of ethanol:

Molar mass (C2H5OH) = (2 × Atomic mass of C) + (6 × Atomic mass of H) + Atomic mass of O Molar mass (C2H5OH) = (2 × 12.01 g/mol) + (6 × 1.01 g/mol) + 16.00 g/mol ≈ 46.08 g/mol

Convert grams to moles:

Number of moles (n) = Mass (m) / Molar mass (M) n = 100 g / 46.08 g/mol ≈ 2.17 mol

Calculate the heat of vaporization:

ΔHvap = n × ΔHvap per mole ΔHvap = 2.17 mol × 38.56 kJ/mol ≈ 83.80 kJ So, the heat of vaporization for 100 grams of ethanol is approximately 83.80 kJ.

Also Check - Shear Modulus Formula

Example 3:

Find the heat of vaporization for 500 grams of ammonia (NH3). The heat of vaporization of ammonia is 23.35 kJ/mol.

Solution:

Calculate the molar mass of ammonia:

Molar mass (NH3) = (1 × Atomic mass of N) + (3 × Atomic mass of H) Molar mass (NH3) = 14.01 g/mol + (3 × 1.01 g/mol) ≈ 17.04 g/mol

Convert grams to moles:

Number of moles (n) = Mass (m) / Molar mass (M) n = 500 g / 17.04 g/mol ≈ 29.35 mol

Calculate the heat of vaporization:

ΔHvap = n × ΔHvap per mole ΔHvap = 29.35 mol × 23.35 kJ/mol ≈ 685.85 kJ The heat of vaporization for 500 grams of ammonia is approximately 685.85 kJ. These examples further illustrate how to calculate the heat of vaporization for different substances using the provided formula and their respective molar masses.

Also Check - Soil Erosion Formula

Applications Of Heat of Vaporization Formula

Distillation: Heat of vaporization is vital in distillation processes, separating liquids based on their differing boiling points, such as in the production of alcoholic beverages and petroleum refining.
Refrigeration: Refrigeration and air conditioning systems use the heat of vaporization to cool substances by evaporating refrigerants inside coils, absorbing heat from the surroundings.
Food Industry: In cooking and food preservation, understanding the heat of vaporization is crucial for maintaining food texture and taste during processes like boiling, steaming, and baking.
Chemical Reactions : Heat of vaporization plays a role in various chemical reactions involving phase changes, such as in the synthesis of pharmaceuticals and chemical manufacturing.
Power Plants: Steam turbines in power generation plants utilize the heat of vaporization to produce mechanical energy by expanding high-pressure steam.
Environmental Science: In meteorology, the heat of vaporization is essential for understanding weather phenomena like evaporation, condensation, and cloud formation, which impact climate and precipitation patterns.

Heat of Vaporization Formula FAQs

What is the significance of heat of vaporization in everyday life?

Heat of vaporization is crucial for understanding processes like cooking, where water evaporates, and in industries like distillation and refrigeration.

Can the heat of vaporization change with temperature and pressure?

Yes, it can vary with temperature and pressure. However, it's typically measured at standard conditions.

What units are used to express heat of vaporization?

Heat of vaporization is often expressed in joules per gram (J/g) or calories per gram (cal/g).

Can heat of vaporization be negative?

No, it is always positive because it represents energy input to change a substance from liquid to gas.

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What is Heat of Vaporization?

The Formula for Heat of Vaporization

The formula to calculate the heat of vaporization is given by:

ΔHvap = (mass of substance) × (heat of vaporization per unit mass)

Also Check - Heat Input Formula

Solved Examples Of Heat of Vaporization Formula

Example 1:

Calculate the heat of vaporization for 50 grams of water. The heat of vaporization of water is 40.7 kJ/mol.

Solution:

Also Check - Critical Velocity Formula

Example 2:

Calculate the heat of vaporization for 100 grams of ethanol (C2H5OH). The heat of vaporization of ethanol is 38.56 kJ/mol.

Solution:

Calculate the molar mass of ethanol:

Molar mass (C2H5OH) = (2 × Atomic mass of C) + (6 × Atomic mass of H) + Atomic mass of O Molar mass (C2H5OH) = (2 × 12.01 g/mol) + (6 × 1.01 g/mol) + 16.00 g/mol ≈ 46.08 g/mol

Convert grams to moles:

Number of moles (n) = Mass (m) / Molar mass (M) n = 100 g / 46.08 g/mol ≈ 2.17 mol

Calculate the heat of vaporization:

ΔHvap = n × ΔHvap per mole ΔHvap = 2.17 mol × 38.56 kJ/mol ≈ 83.80 kJ So, the heat of vaporization for 100 grams of ethanol is approximately 83.80 kJ.

Also Check - Shear Modulus Formula

Example 3:

Find the heat of vaporization for 500 grams of ammonia (NH3). The heat of vaporization of ammonia is 23.35 kJ/mol.

Solution:

Calculate the molar mass of ammonia:

Molar mass (NH3) = (1 × Atomic mass of N) + (3 × Atomic mass of H) Molar mass (NH3) = 14.01 g/mol + (3 × 1.01 g/mol) ≈ 17.04 g/mol

Convert grams to moles:

Number of moles (n) = Mass (m) / Molar mass (M) n = 500 g / 17.04 g/mol ≈ 29.35 mol

Calculate the heat of vaporization:

Also Check - Soil Erosion Formula

Applications Of Heat of Vaporization Formula

Distillation: Heat of vaporization is vital in distillation processes, separating liquids based on their differing boiling points, such as in the production of alcoholic beverages and petroleum refining.
Refrigeration: Refrigeration and air conditioning systems use the heat of vaporization to cool substances by evaporating refrigerants inside coils, absorbing heat from the surroundings.
Food Industry: In cooking and food preservation, understanding the heat of vaporization is crucial for maintaining food texture and taste during processes like boiling, steaming, and baking.
Chemical Reactions : Heat of vaporization plays a role in various chemical reactions involving phase changes, such as in the synthesis of pharmaceuticals and chemical manufacturing.
Power Plants: Steam turbines in power generation plants utilize the heat of vaporization to produce mechanical energy by expanding high-pressure steam.
Environmental Science: In meteorology, the heat of vaporization is essential for understanding weather phenomena like evaporation, condensation, and cloud formation, which impact climate and precipitation patterns.