# Enthalpy – Definition, Formula/Equation

What is Enthalpy?

Enthalpy is a thermodynamic property of a system.

It is the sum of the internal energy added to the product of the pressure and volume of the system.

It shows the capability to do non-mechanical work and the capability to release heat. It is represented by H. In general, enthalpy is equal to the internal energy, E plus the product of pressure and volume (PV).

Change in enthalpy is computed rather than enthalpy, in part because the total enthalpy of a system can not be measured because it is difficult to know the zero point.

However, it is possible to determine the difference in enthalpy between one state and another.

Enthalpy changes might be calculated under conditions of constant pressure.

##### Enthalpy Formula

Enthalpy is a state function. It is measured in joules. It is not possible, to determine the enthalpy of a system in a given state. However, change in enthalpy (ΔH) can be measured for a change in the state of the system. A change in enthalpy of a system can be written as:

ΔH = ΔE + Δ(PV)

or

ΔH = ΔE + VΔP + PΔV

Considering that, the gas is kept at a continuous pressure, = 0.

Thus

ΔH = ΔE + PΔV

In the case of liquids and solids, the changes in the state do not trigger significant volume change i.e. ΔV = 0. For such a process, ΔH and ΔE are around the same i.e. ΔH ≈ ΔE. According to the first law of thermodynamics:

ΔE = q + w

If w is pressure-volume work done by the system, then:

w = – PΔV

So,

ΔE = q – PΔV

Putting the value of ΔE in this equation we get:

ΔH = q – PΔV + PΔV

ΔH = q

Because the pressure is constant, for that reason,

ΔH = qp

This shows that change in enthalpy amounts to the heat of reaction at constant pressure. The reactions are carried out at continuous pressure more regularly than at constant volume. So, working with ΔH is easier rather than ΔE.

##### Enthalpy of a Reaction (ΔHo)

The standard enthalpy of a reaction ΔHo is the enthalpy change which takes place when the specific number of moles of reactants as indicated by the balanced chemical equation, react together entirely to give the products under basic conditions, i.e. 25 ° C (298K) and one atmospheric pressure.

In an exothermic reaction, the heat content or enthalpy of the product H2 is less than that of the reactants H1. Since the system has actually lost heat, we can state the enthalpy change for the reaction ΔH is negative.

In an endothermic reaction, the enthalpy of products H2, is greater than that of the reactants H1, and the enthalpy change, ΔH is positive.

All the reactants and products must be in their standard physical states. Its SI Units are kJ mol-1.

-285.8 kJmol-1 is the standard enthalpy of reaction.

##### Enthalpy of Formation (ΔHof)

The standard enthalpy of formation of a substance is the quantity of heat taken in or evolved when one mole of the substance is formed from its elements.

It is represented by ΔH ° f. All the substances involved are in their standard physical states and the reaction is performed under standard conditions i.e. at 25 ° C(298 K) and one atm. pressure. Its units are kJ mol-1. For instance, the enthalpy of formation, (ΔH ° f) for MgO (s) is- 692 kJmol-1.

Likewise, when carbon reacts with oxygen to form CO2, 393.7 kJ mol-1 of energy is released. It is ΔH ° f, of CO2(g).

##### Enthalpy of Atomization (ΔHo at)

The standard enthalpy of atomization of an element is defined as the quantity of heat absorbed when one mole of gaseous atoms is formed from the element under standard conditions.

It is denoted by Ho. For instance, the standard enthalpy of atomization of hydrogen is given below.

A vast array of speculative methods are available for figuring out enthalpies of the atomization of elements.

##### Enthalpy of Neutralization (ΔHo n)

The standard enthalpy of neutralization is the amount of heat evolved when one mole of hydrogen ions [H+] from an acid, react with one mole of hydroxide ions from a base to form one mole of water.

For instance, the enthalpy of neutralization of sodium hydroxide by hydrochloric (OH-) acid is -57.4 kJ mol-1. Note that a strong acid HCl and a strong base, NaOH, ionize entirely in dilute solutions as follows.

When these solutions are mixed together during the process of neutralization, the only change that actually occurs is the formation of water molecules leaving the salt ions and the chloride ions as free ions in solution. Therefore, the enthalpy of neutralization is simply the heat of formation of one mole of liquid water from its ionic elements,

Enthalpy of neutralization for any strong acid with a strong base is approximately the same i.e. -57.4 kJ mole-1.

##### Enthalpy of Combustion (ΔHo c)

The standard enthalpy of combustion of the compound is the amount of heat evolved when one mole of the substance is entirely burnt in excess of oxygen under standard conditions. It is signified by ΔHo c.

For example, standard enthalpy of combustion of ethanol ΔHo cis -1368 kJ mol-1. The reaction is represented by the list below equation.

##### Enthalpy of Solution (ΔHo sol.)

The basic enthalpy of a solution is the quantity of heat absorbed or evolved when one mole of a substance is dissolved in a lot solvent that further dilution results in no detectable heat change.

For instance, enthalpy of solution (ΔHo sol.) of ammonium chloride is +16.2 kJmol-1 which of sodium carbonate is -25.0 kJmol-1. In the first case, heat absorbed from the surroundings is indicated by cooling of the solvent (water), an endothermic procedure. While in the 2nd case, the temperature of the solvent increases revealing that the process is exothermic.

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##### What Is the Significance of Enthalpy?
• Measuring the change in enthalpy allows us to determine whether a reaction was endothermic (absorbed heat, positive change in enthalpy) or exothermic (released heat, a negative change in enthalpy).
• It is utilized to compute the heat of the reaction of a chemical procedure.
• Change in enthalpy is utilized to measure heat flow in calorimetry.
• It is determined to assess a throttling procedure or Joule-Thomson expansion.
• Enthalpy is used to compute minimum power for a compressor.
• Enthalpy changes occur during a modification in the state of matter.
• There are lots of other applications of enthalpy in thermal engineering.
##### Measurement of Enthalpy of a Reaction

Exothermic and endothermic reactions can easily be detected by observing the temperature of the reaction vessel prior to and after the reaction, as long as the heat of reaction evolved or taken in is substantial. A more accurate value of ΔH can be figured out by using calorimeters as explained listed below.

###### (i) Glass Calorimeter

For the majority of functions, a normal glass calorimeter can be utilized to determine the value of ΔH. This typical kind of calorimeter is generally an insulated container with a thermometer and a stirrer.

Reactants in stoichiometric amounts are put in the calorimeter. When the reaction progress, the heat energy evolved or absorbed will either warm or cool the system. The temperature level of the system is taped before and after the reaction. Knowing the temperature change alters the mass of reactants present and the specific heat of water, we can calculate the quantity of heat q evolved or absorbed throughout the reaction. Thus:

q = m x s x ΔT

Where m = mass of reactants, s = specific heat of the reaction mixture and ΔT is the change in temperature level. The product of mass and specific heat of water is called the heat capacity of the entire system.

###### (ii) Bomb Calorimeter

A bomb calorimeter is normally utilized for the precise determination of the enthalpy of combustion for food, fuel, and other substances. It consists of a strong cylindrical steel vessel usually lined with enamel to prevent deterioration. A recognized mass (about one gram) of the test substance is placed in a platinum crucible inside the bomb.

The cover is screwed on firmly and oxygen is given in through a valve up until the pressure within is about 20 atm. After closing the screw valve, the bomb calorimeter is then immersed in a known mass of water in a well-insulated calorimeter.

Then, it is enabled to attain a stable temperature. The preliminary temperature is measured, by utilizing the thermometer present in the calorimeter. The test substance is then, ignited, electrically bypassing the current through the ignition coil. The temperature of the water, which is stirred continually, is taped at 30-sec intervals.

From the increase of temperature ΔT, heat capability (c) in kJK-1 of bomb calorimeter including bomb, water, etc., we can determine the enthalpy of combustion.

The heat capability ‘c’ of a body or a system is defined as the quantity of heat required to change its temperature by 1 kelvin.

q = c x ΔT

### MCQs with Answers on Enthalpy

1. What is Enthalpy?
• A) The ability to release light
• B) A thermodynamic property of a system
• C) The speed of a chemical reaction
• D) The number of moles in a system

2. What does Enthalpy represent?
• A) Internal energy minus pressure times volume
• B) The product of pressure and volume
• C) The speed of a chemical reaction
• D) The number of moles in a system

3. How is Change in Enthalpy (ΔH) calculated?
• A) ΔE + Δ(PV)
• B) VΔP + PΔV
• C) ΔE + VΔP + PΔV
• D) ΔE + PΔV

4. What is the significance of Enthalpy in chemical reactions?
• A) Measures the speed of a reaction
• B) Determines the color change in a reaction
• C) Indicates whether a reaction is endothermic or exothermic
• D) Measures the concentration of reactants

5. What is the standard unit for Enthalpy?
• A) Kelvin (K)
• B) Joules (J)
• C) Moles (mol)
• D) Pascal (Pa)

6. What does Enthalpy of Formation (ΔHof) represent?
• A) Heat evolved when a substance is dissolved
• B) Heat evolved during combustion
• C) Heat absorbed or evolved when one mole of a substance is formed
• D) Heat absorbed during atomization

7. How is Enthalpy of Atomization defined?
• A) Heat evolved during combustion
• B) Heat absorbed during solution
• C) Heat absorbed when one mole of gaseous atoms is formed
• D) Heat evolved during neutralization

8. What does Enthalpy of Combustion (ΔHo c) measure?
• A) Heat evolved during combustion
• B) Heat absorbed during solution
• C) Heat absorbed during neutralization
• D) Heat evolved when one mole of a substance is formed

9. What is the standard unit for Enthalpy of Solution (ΔHo sol.)?
• A) Kelvin (K)
• B) Joules per mole (J mol-1)
• C) Moles (mol)
• D) Pascal (Pa)

10. What is the Enthalpy of Neutralization?
• A) Heat evolved during combustion
• B) Heat absorbed during solution
• C) Heat evolved during neutralization
• D) Heat absorbed when one mole of gaseous atoms is formed

1. Which calorimeter is commonly used for precise determinations?
• A) Glass Calorimeter
• B) Bomb Calorimeter
• C) Plastic Calorimeter
• D) Metal Calorimeter

1. What is the primary purpose of a bomb calorimeter?
• A) To determine the color change in a reaction
• B) To measure the speed of a reaction
• C) To precisely determine the enthalpy of combustion
• D) To calculate the moles of reactants

1. What is the significance of measuring Change in Enthalpy?
• A) Determines the color change in a reaction
• B) Measures the concentration of reactants
• C) Indicates whether a reaction is endothermic or exothermic
• D) Measures the speed of a reaction

1. How is Enthalpy of a Reaction (ΔHo) defined?
• A) Heat absorbed during combustion
• B) Heat evolved during solution
• C) Heat evolved when specific moles of reactants react entirely
• D) Heat absorbed during neutralization

1. What is the standard unit for Enthalpy of Combustion (ΔHo c)?
• A) Kelvin (K)
• B) Joules per mole (J mol-1)
• C) Moles (mol)
• D) Pascal (Pa)
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1. How is Enthalpy of Solution (ΔHo sol.) defined?
• A) Heat evolved during combustion
• B) Heat absorbed or evolved when a substance is dissolved
• C) Heat evolved during neutralization
• D) Heat absorbed during atomization

1. What does the standard Enthalpy of Atomization (ΔHo at) measure?
• A) Heat absorbed during combustion
• B) Heat evolved during atomization of gaseous atoms
• C) Heat absorbed during solution
• D) Heat evolved during neutralization

1. What does Enthalpy of Formation (ΔHof) measure?
• A) Heat evolved during combustion
• B) Heat absorbed or evolved when one mole of a substance is formed
• C) Heat evolved during atomization
• D) Heat absorbed during solution

1. What is the formula for Change in Enthalpy (ΔH)?
• A) ΔE + Δ(PV)
• B) VΔP + PΔV
• C) ΔE + VΔP + PΔV
• D) ΔE + PΔV

### FAQs (Frequently Asked Questions) – Enthalpy Tutorial

1. What is Enthalpy?

• Enthalpy is a thermodynamic property of a system. It is the sum of the internal energy added to the product of the pressure and volume of the system. It shows the capability to do non-mechanical work and the capability to release heat.

2. Why is Change in Enthalpy (ΔH) used instead of total enthalpy?

• Total enthalpy of a system cannot be measured directly due to difficulty in determining the zero point. Change in enthalpy allows the measurement of the difference between two states, particularly under constant pressure.

3. How is Enthalpy calculated?

• Enthalpy (H) can be calculated using the formula: ΔH = ΔE + VΔP + PΔV. In the case of constant pressure, ΔH simplifies to ΔE + PΔV. For gases at constant pressure, ΔH is equal to the heat of reaction (qp).

4. What is the significance of Enthalpy in chemical reactions?

• Enthalpy is crucial in determining whether a reaction is endothermic (absorbs heat, positive ΔH) or exothermic (releases heat, negative ΔH). It is also used to calculate the heat of a reaction and measure heat flow in calorimetry.

5. How is Enthalpy of a Reaction (ΔHo) defined?

• The standard enthalpy of a reaction (ΔHo) is the enthalpy change when the specified moles of reactants, as indicated by the balanced chemical equation, react entirely to form products under standard conditions (25°C and 1 atm).

6. What is the Enthalpy of Formation (ΔHof)?

• The standard enthalpy of formation (ΔHof) is the heat absorbed or evolved when one mole of a substance is formed from its elements under standard conditions (25°C and 1 atm).

7. How is Enthalpy of Atomization (ΔHo at) defined?

• The standard enthalpy of atomization (ΔHo at) measures the heat absorbed when one mole of gaseous atoms is formed from an element under standard conditions.

8. What is Enthalpy of Neutralization (ΔHo n)?

• The standard enthalpy of neutralization (ΔHo n) is the heat evolved when one mole of hydrogen ions from an acid reacts with one mole of hydroxide ions from a base to form one mole of water.

9. How is Enthalpy of Combustion (ΔHo c) measured?

• The standard enthalpy of combustion (ΔHo c) measures the heat evolved when one mole of a substance is entirely burnt in excess oxygen under standard conditions.

10. What is Enthalpy of Solution (ΔHo sol.)?

• The enthalpy of solution (ΔHo sol.) is the heat absorbed or evolved when one mole of a substance is dissolved in a solvent, resulting in no detectable heat change upon further dilution.

11. How is the Enthalpy Change measured in reactions?

• The change in enthalpy (ΔH) can be measured using calorimeters. Common types include the glass calorimeter for most purposes and the bomb calorimeter for precise determination of the enthalpy of combustion.

12. What is the significance of measuring Enthalpy in thermal engineering?

• Measuring enthalpy is crucial in assessing processes such as throttling, Joule-Thomson expansion, and computing minimum power for a compressor. It is also applied during state changes of matter.

13. What is the heat capacity of a system in a bomb calorimeter?

• The heat capacity (c) of a bomb calorimeter system, including the bomb, water, etc., is crucial in determining the enthalpy of combustion. It is defined as the quantity of heat required to change the system’s temperature by 1 kelvin.

### 10 Enthalpy Problem/Solutions

Problem 1: Calculate Change in Enthalpy

Problem: Given a reaction A + B → C with ΔH = -150 kJ. Calculate the change in enthalpy if the reaction produces 3 moles of C.

Solution: ΔH = -150 kJ. Since the reaction produces 3 moles of C, the change in enthalpy (q) is given by ΔH * moles of product. Therefore, q = -150 kJ * 3 moles = -450 kJ.

Problem 2: Enthalpy of Combustion Calculation

Problem: Determine the enthalpy of combustion for ethanol (C₂H₅OH) given the balanced equation C₂H₅OH + 3O₂ → 2CO₂ + 3H₂O. The standard enthalpy change is -1368 kJ/mol.

Solution: The enthalpy of combustion (ΔHc) is the heat evolved when one mole of a substance is burnt in excess oxygen. Therefore, ΔHc = -1368 kJ/mol.

Problem 3: Enthalpy of Formation Calculation

Problem: Find the standard enthalpy of formation for water (H₂O) from its elements, given the balanced equation H₂ + 1/2O₂ → H₂O with ΔHf = -285.8 kJ/mol for H₂O.

Solution: The standard enthalpy of formation (ΔHf) is the heat absorbed or evolved when one mole of a substance is formed from its elements. Therefore, ΔHf for water is -285.8 kJ/mol.

Problem 4: Enthalpy of Atomization Calculation

Problem: Calculate the standard enthalpy of atomization for chlorine (Cl₂) using the balanced equation Cl₂(g) → 2Cl(g) with ΔHo at = +121 kJ/mol.

Solution: The standard enthalpy of atomization (ΔHo at) measures the heat absorbed when one mole of gaseous atoms is formed from the element under standard conditions. Therefore, ΔHo at for chlorine is +121 kJ/mol.

Problem 5: Enthalpy of Neutralization Calculation

Problem: Determine the standard enthalpy of neutralization for the reaction between hydrochloric acid (HCl) and sodium hydroxide (NaOH), given the balanced equation HCl + NaOH → NaCl + H₂O with ΔHon = -57.4 kJ/mol.

Solution: The standard enthalpy of neutralization (ΔHon) is the heat evolved when one mole of hydrogen ions from an acid reacts with one mole of hydroxide ions from a base. Therefore, ΔHon = -57.4 kJ/mol.

Problem 6: Enthalpy of Solution Calculation

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Problem: Calculate the enthalpy of solution for ammonium chloride (NH₄Cl), given the balanced equation NH₄Cl + H₂O → NH₄⁺ + Cl⁻ with ΔHsol = +16.2 kJ/mol.

Solution: The enthalpy of solution (ΔHsol) is the heat absorbed or evolved when one mole of a substance is dissolved in a solvent. Therefore, ΔHsol for ammonium chloride is +16.2 kJ/mol.

Problem 7: Enthalpy Calculation in a Reaction

Problem: Given the reaction A + B → C with the enthalpy change ΔH = +250 kJ, calculate the enthalpy change if the reaction produces 5 moles of C.

Solution: ΔH = +250 kJ. Since the reaction produces 5 moles of C, the enthalpy change (q) is given by ΔH * moles of product. Therefore, q = +250 kJ * 5 moles = +1250 kJ.

Problem 8: Enthalpy Measurement using Calorimeter

Problem: Use a bomb calorimeter to measure the enthalpy of combustion for a sample of butane (C₄H₁₀). Given the increase in temperature ΔT is 30°C and the heat capacity of the calorimeter is 1500 J/°C.

Solution: The enthalpy of combustion (ΔHc) can be calculated using the formula q = c * ΔT, where q is the heat absorbed by the calorimeter. Therefore, ΔHc = q = 1500 J/°C * 30°C = 45,000 J.

Problem 9: Enthalpy Change in Endothermic Reaction

Problem: Determine the enthalpy change for an endothermic reaction with ΔH = +180 kJ. If the reaction produces 2 moles of product, calculate the heat absorbed.

Solution: ΔH = +180 kJ. Since the reaction is endothermic, the enthalpy change (q) is positive. Therefore, q = +180 kJ * 2 moles = +360 kJ.

Problem 10: Enthalpy of Formation for a Compound

Problem: Find the standard enthalpy of formation for carbon dioxide (CO₂) given the balanced equation C + O₂ → CO₂ with ΔHf = -393.7 kJ/mol for CO₂.

Solution: The standard enthalpy of formation (ΔHf) is the heat absorbed or evolved when one mole of a substance is formed from its elements. Therefore, ΔHf for carbon dioxide is -393.7 kJ/mol.

### Summary: Enthalpy Tutorial

Enthalpy is a crucial thermodynamic property representing the sum of a system’s internal energy, pressure, and volume. It is denoted by H and plays a vital role in understanding the energy changes in chemical processes. Here’s a brief summary of key points covered in the tutorial:

1. Enthalpy Definition:
• Enthalpy (H) is the total energy of a system, including internal energy, pressure, and volume contributions.
• It signifies the system’s ability to perform non-mechanical work and release heat.
2. Enthalpy Formula:
• Enthalpy is a state function, measured in joules (J).
• Change in enthalpy (ΔH) can be expressed as ΔH = ΔE + PΔV under constant pressure conditions.
3. Enthalpy of Reaction (ΔHo):
• ΔHo represents the standard enthalpy change in a reaction under basic conditions (25°C, 1 atm).
• Exothermic reactions have negative ΔHo, indicating heat release; endothermic reactions have positive ΔHo, indicating heat absorption.
4. Enthalpy of Formation (ΔHof):
• ΔHof is the standard enthalpy change when one mole of a substance forms from its elements under standard conditions.
• It is represented by ΔH ° f and measured in kJ/mol.
5. Enthalpy of Atomization (ΔHo at):
• ΔHo at is the heat absorbed when one mole of gaseous atoms forms from an element under standard conditions.
• It is denoted by Ho and can be experimentally determined.
6. Enthalpy of Neutralization (ΔHo n):
• ΔHo n is the heat evolved when one mole of hydrogen ions from an acid reacts with one mole of hydroxide ions from a base to form one mole of water.
• The value is approximately -57.4 kJ/mol for strong acid-base neutralizations.
7. Enthalpy of Combustion (ΔHo c):
• ΔHo c is the heat evolved when one mole of a substance is completely burned in excess oxygen under standard conditions.
• It is signified by ΔHo c and measured in kJ/mol.
8. Enthalpy of Solution (ΔHo sol.):
• ΔHo sol. is the heat absorbed or evolved when one mole of a substance is dissolved in a solvent.
• It is used to understand endothermic and exothermic dissolution processes.
9. Significance of Enthalpy:
• ΔH helps identify endothermic and exothermic reactions.
• It is crucial in calculating the heat of a chemical reaction, measuring heat flow in calorimetry, and assessing various thermodynamic processes.
10. Measurement of Enthalpy:
• Calorimeters, such as glass and bomb calorimeters, are used to measure heat changes accurately.
• These devices help determine ΔH through temperature changes, mass, and specific heat considerations.

In conclusion, understanding enthalpy is fundamental in studying energy changes during chemical reactions and has diverse applications in thermal engineering and scientific research.