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on November 22, 2024
How to Calculate Enthalpy Change of a Reaction: A Clear and Confident Guide
Enthalpy change is an essential concept in thermodynamics and is used to measure the heat absorbed or released during a chemical reaction. It is a crucial parameter for understanding the energy changes that occur during chemical reactions. Calculating enthalpy change is not only important for understanding the reaction but also for predicting its feasibility and efficiency. In this article, we will discuss how to calculate the enthalpy change of a reaction.
The enthalpy change of a reaction is the difference between the enthalpy of the products and the enthalpy of the reactants. Enthalpy is the sum of the internal energy of a system and the product of pressure and volume. It is denoted by the symbol ΔH and is measured in joules per mole (J/mol). The enthalpy change of a reaction can be either positive or negative, indicating whether the reaction is endothermic or exothermic, respectively.
There are several methods for calculating the enthalpy change of a reaction, including calorimetry, Hess's law, and bond enthalpy. Each method has its advantages and disadvantages, and the choice of method depends on the nature of the reaction and the available data. In the following sections, we will discuss each method in detail and provide step-by-step instructions for calculating enthalpy change.
Fundamentals of Enthalpy Definition of Enthalpy
Enthalpy is a thermodynamic property that describes the heat content of a system at a constant pressure. It is represented by the symbol "H" and is defined as the sum of the internal energy of the system and the product of the pressure and volume of the system. Enthalpy is a state function, which means that it only depends on the initial and final states of the system, not on the path taken to get there.
Thermodynamic Systems and Surroundings
A thermodynamic system is a region of space that is being studied, while the surroundings are everything outside of the system. The boundary between the system and surroundings can be either real or imaginary. In order to calculate the enthalpy change of a reaction, it is necessary to define the system and surroundings. The enthalpy change of the system is equal in magnitude but opposite in sign to the enthalpy change of the surroundings.
Enthalpy as a State Function
Enthalpy is a state function, which means that it only depends on the initial and final states of the system, not on the path taken to get there. This property makes it useful for studying chemical reactions, as it allows chemists to calculate the enthalpy change of a reaction without knowing the details of the reaction mechanism. Enthalpy can be calculated using the formula ΔH = Hfinal - Hinitial, where ΔH is the enthalpy change, Hfinal is the enthalpy of the final state, and Hinitial is the enthalpy of the initial state.
In summary, enthalpy is a thermodynamic property that describes the heat content of a system at a constant pressure. It is a state function, which means that it only depends on the initial and final states of the system, not on the path taken to get there. To calculate the enthalpy change of a reaction, it is necessary to define the system and surroundings and use the formula ΔH = Hfinal - Hinitial.
Understanding Chemical Reactions
Chemical reactions involve the transformation of one or more substances into new substances with different properties. The reactants are the substances that undergo the reaction, while the products are the new substances that are formed.
Reactants and Products
Chemical reactions involve the breaking of bonds between atoms in the reactants and the formation of new bonds in the products. The atoms in the reactants are rearranged to form the products. The law of conservation of mass states that the total mass of the reactants must be equal to the total mass of the products. This means that during a chemical reaction, no atoms are created or destroyed.
Chemical reactions can be represented using chemical equations, which show the reactants and products of the reaction. The reactants are written on the left-hand side of the equation, while the products are written on the right-hand side. The reactants and products are separated by an arrow, which indicates the direction of the reaction.
Exothermic and Endothermic Processes
Chemical reactions can be classified as exothermic or endothermic processes based on the change in enthalpy. Enthalpy is the heat content of a system, and it is a measure of the energy stored in the bonds between atoms.
In an exothermic process, the enthalpy of the products is lower than the enthalpy of the reactants. This means that energy is released during the reaction in the form of heat. Examples of exothermic processes include combustion reactions, where a fuel reacts with oxygen to produce heat and light.
In an endothermic process, the enthalpy of the products is higher than the enthalpy of the reactants. This means that energy is absorbed during the reaction. Examples of endothermic processes include the reaction between baking soda and vinegar, which absorbs heat from the surroundings and causes the mixture to become cold.
Understanding the nature of chemical reactions is important for calculating the enthalpy change of a reaction. By analyzing the bonds between atoms in the reactants and products, it is possible to determine whether a reaction is exothermic or endothermic, and to calculate the amount of heat that is released or absorbed during the reaction.
Measurement of Enthalpy Changes
Calorimetry
Calorimetry is a technique used to measure changes in enthalpy of chemical reactions. A calorimeter can be made up of a polystyrene drinking cup, a vacuum flask, or a metal can. A polystyrene cup can act as a calorimeter to find enthalpy changes in a chemical reaction. The energy needed to raise the temperature of 1 g of a substance by 1 K is known as specific heat. The specific heat of water is 4.18 J/g.K.
To measure the enthalpy change of a reaction, the reactants are placed in a calorimeter, and the temperature change is recorded. The heat absorbed or released by the reaction is equal to the heat absorbed or released by the calorimeter. By knowing the mass of the reactants and the specific heat of the calorimeter, the enthalpy change of the reaction can be calculated.
Hess's Law
Hess's Law states that the enthalpy change of a reaction is independent of the pathway between the reactants and the products. This means that if a reaction can be expressed as a sum of two or more reactions, the enthalpy change of the overall reaction is equal to the sum of the enthalpy changes of the individual reactions.
Hess's Law can be used to calculate the enthalpy change of a reaction that cannot be easily measured experimentally. For example, the enthalpy change of combustion of magnesium can be calculated by using the enthalpy changes of combustion of magnesium oxide and hydrogen.
In summary, calorimetry is a technique used to measure changes in enthalpy of chemical reactions, while Hess's Law can be used to calculate the enthalpy change of a reaction that cannot be easily measured experimentally.
Calculating Enthalpy Change
Calculating the enthalpy change of a reaction is an important aspect of thermodynamics. Enthalpy change is the amount of heat released or absorbed during a chemical reaction. It is typically measured in units of joules or kilojoules. There are different methods for calculating enthalpy change, including the standard enthalpy of formation, bond enthalpies, and using enthalpy change equations.
Standard Enthalpy of Formation
The standard enthalpy of formation is the enthalpy change that occurs when one mole of a compound is formed from its constituent elements in their standard states. The standard state of an element is its most stable form at a given temperature and pressure. The standard enthalpy of formation is denoted as ΔHf° and is typically measured at 298 K and 1 atm pressure.
The standard enthalpy of formation can be used to calculate the enthalpy change of a reaction using Hess's law. Hess's law states that the enthalpy change of a reaction is independent of the pathway taken to reach the final state. This means that the enthalpy change of a reaction can be calculated by summing the enthalpy changes of the reactions that lead to the final state.
Bond Enthalpies
Bond enthalpies are the energy required to break a chemical bond. The bond enthalpy is typically measured in units of kilojoules per mole (kJ/mol). Bond enthalpies can be used to calculate the enthalpy change of a reaction by subtracting the sum of the bond enthalpies of the reactants from the sum of the bond enthalpies of the products.
Bond enthalpies are not always accurate because the energy required to break a bond can vary depending on the environment. For example, the bond enthalpy of a C-H bond in methane is different from the bond enthalpy of a C-H bond in ethane.
Using Enthalpy Change Equations
Enthalpy change equations can be used to calculate the enthalpy change of a reaction using experimental data. The enthalpy change equation relates the enthalpy change of a reaction to the enthalpy changes of the reactions that lead to the final state. This equation can be derived using Hess's law.
To use an enthalpy change equation, the enthalpy changes of the reactions leading to the final state must be known. These enthalpy changes can be measured experimentally using calorimetry or estimated using bond enthalpies or the standard enthalpy of formation.
In conclusion, there are different methods for calculating the enthalpy change of a reaction. The standard enthalpy of formation, bond enthalpies, and enthalpy change equations are all useful tools for calculating enthalpy change. The choice of method depends on the available data and the accuracy required.
Practical Considerations
Temperature and Pressure Effects
Temperature and pressure can greatly affect the enthalpy change of a reaction. In order to obtain accurate results, it is important to control these variables as much as possible. The temperature should be measured and recorded before and after the reaction takes place. This can be done using a thermometer or a temperature probe. It is important to note that the reaction vessel may heat up or cool down during the reaction, so it is important to take multiple temperature readings throughout the experiment and calculate the average.
Pressure can also affect the enthalpy change of a reaction, particularly if gases are involved. The pressure should be measured and recorded before and after the reaction takes place. This can be done using a pressure gauge or a manometer. If the pressure changes significantly during the reaction, it may be necessary to repeat the experiment with a different pressure.
Catalysts and Reaction Rates
Catalysts can greatly affect the enthalpy change of a reaction by increasing the reaction rate. When a catalyst is used, the reaction may produce more heat than it would without the catalyst. It is important to take this into account when calculating the enthalpy change. The use of a catalyst should be noted in the experimental procedure, and the enthalpy change should be calculated both with and without the catalyst.
Reaction rates can also affect the enthalpy change of a reaction. If a reaction takes a long time to complete, the heat produced may dissipate into the surroundings, making it difficult to measure accurately. It is important to choose a reaction that has a reasonable rate, and to carry out the experiment in a timely manner. If necessary, the reaction can be sped up by using a catalyst or by increasing the temperature.
In summary, when calculating the enthalpy change of a reaction, it is important to control the variables of temperature and pressure as much as possible, and to take into account the effects of catalysts and reaction rates. By carefully controlling these factors, it is possible to obtain accurate and reliable results.
Applications of Enthalpy Change Industrial Processes
Enthalpy change plays an essential role in various industrial processes. For instance, in the production of ammonia, bankrate com calculator Haber's process involves the synthesis of nitrogen and hydrogen gas to form ammonia. The reaction is exothermic, and the enthalpy change of the reaction is -92.4 kJ/mol. The enthalpy change of the reaction is crucial in determining the optimum conditions for the reaction, such as temperature and pressure, to achieve maximum yield.
Another example is the production of iron from iron oxide in a blast furnace. The process involves the reduction of iron oxide using carbon monoxide gas to form iron and carbon dioxide. The reaction is exothermic, and the enthalpy change of the reaction is -12.6 kJ/mol. The enthalpy change of the reaction is vital in determining the amount of energy required to heat the reactants and the products.
Environmental Impact
Enthalpy change also plays a significant role in understanding the environmental impact of various chemical reactions. For instance, the combustion of fossil fuels such as coal, oil, and gas releases carbon dioxide into the atmosphere. The combustion of one mole of methane gas, which is the primary component of natural gas, releases 890.4 kJ of energy and 213.6 kJ of enthalpy change. The enthalpy change of the reaction is crucial in determining the amount of energy released and the environmental impact of the reaction.
Moreover, the enthalpy change of a reaction can be used to determine the amount of energy required to break the bonds in the reactants and the amount of energy released when the bonds in the products are formed. This information is essential in understanding the energy efficiency of various chemical reactions and their environmental impact.
In conclusion, the applications of enthalpy change are vast and significant in various fields, including industrial processes and environmental impact. Understanding the enthalpy change of a reaction is crucial in determining the optimum conditions for a reaction and the amount of energy required or released during the reaction.
Frequently Asked Questions What is the formula for calculating the enthalpy change of a reaction?
The formula for calculating the enthalpy change of a reaction is ΔH = H(products) - H(reactants). This formula represents the difference in enthalpy between the products and reactants of a chemical reaction.
How can bond energies be used to determine the enthalpy change?
Bond energies can be used to determine the enthalpy change by calculating the energy required to break the bonds in the reactants and the energy released when new bonds are formed in the products. The difference between these two values represents the enthalpy change of the reaction.
What is the process for calculating the enthalpy of formation?
The process for calculating the enthalpy of formation involves determining the enthalpy change that occurs when one mole of a compound is formed from its constituent elements in their standard states. This process involves using tabulated values of standard enthalpies of formation.
How does Hess's law relate to the calculation of reaction enthalpy change?
Hess's law states that the enthalpy change of a reaction is independent of the pathway taken to get from reactants to products. This means that the enthalpy change of a reaction can be calculated by summing the enthalpy changes of a series of reactions that add up to the overall reaction.
How can the enthalpy change of combustion be calculated?
The enthalpy change of combustion can be calculated by measuring the heat released when a substance is burned in excess oxygen. This value represents the enthalpy change of the reaction and can be used to determine the enthalpy change of other reactions involving the same substance.
What is the relationship between enthalpy change and temperature variation?
The relationship between enthalpy change and temperature variation is given by the equation Q = mcΔT, where Q is the heat absorbed or released, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature. This equation can be used to calculate the enthalpy change of a reaction from temperature data.
Enthalpy change is an essential concept in thermodynamics and is used to measure the heat absorbed or released during a chemical reaction. It is a crucial parameter for understanding the energy changes that occur during chemical reactions. Calculating enthalpy change is not only important for understanding the reaction but also for predicting its feasibility and efficiency. In this article, we will discuss how to calculate the enthalpy change of a reaction.
The enthalpy change of a reaction is the difference between the enthalpy of the products and the enthalpy of the reactants. Enthalpy is the sum of the internal energy of a system and the product of pressure and volume. It is denoted by the symbol ΔH and is measured in joules per mole (J/mol). The enthalpy change of a reaction can be either positive or negative, indicating whether the reaction is endothermic or exothermic, respectively.
There are several methods for calculating the enthalpy change of a reaction, including calorimetry, Hess's law, and bond enthalpy. Each method has its advantages and disadvantages, and the choice of method depends on the nature of the reaction and the available data. In the following sections, we will discuss each method in detail and provide step-by-step instructions for calculating enthalpy change.
Fundamentals of Enthalpy Definition of Enthalpy
Enthalpy is a thermodynamic property that describes the heat content of a system at a constant pressure. It is represented by the symbol "H" and is defined as the sum of the internal energy of the system and the product of the pressure and volume of the system. Enthalpy is a state function, which means that it only depends on the initial and final states of the system, not on the path taken to get there.
Thermodynamic Systems and Surroundings
A thermodynamic system is a region of space that is being studied, while the surroundings are everything outside of the system. The boundary between the system and surroundings can be either real or imaginary. In order to calculate the enthalpy change of a reaction, it is necessary to define the system and surroundings. The enthalpy change of the system is equal in magnitude but opposite in sign to the enthalpy change of the surroundings.
Enthalpy as a State Function
Enthalpy is a state function, which means that it only depends on the initial and final states of the system, not on the path taken to get there. This property makes it useful for studying chemical reactions, as it allows chemists to calculate the enthalpy change of a reaction without knowing the details of the reaction mechanism. Enthalpy can be calculated using the formula ΔH = Hfinal - Hinitial, where ΔH is the enthalpy change, Hfinal is the enthalpy of the final state, and Hinitial is the enthalpy of the initial state.
In summary, enthalpy is a thermodynamic property that describes the heat content of a system at a constant pressure. It is a state function, which means that it only depends on the initial and final states of the system, not on the path taken to get there. To calculate the enthalpy change of a reaction, it is necessary to define the system and surroundings and use the formula ΔH = Hfinal - Hinitial.
Understanding Chemical Reactions
Chemical reactions involve the transformation of one or more substances into new substances with different properties. The reactants are the substances that undergo the reaction, while the products are the new substances that are formed.
Reactants and Products
Chemical reactions involve the breaking of bonds between atoms in the reactants and the formation of new bonds in the products. The atoms in the reactants are rearranged to form the products. The law of conservation of mass states that the total mass of the reactants must be equal to the total mass of the products. This means that during a chemical reaction, no atoms are created or destroyed.
Chemical reactions can be represented using chemical equations, which show the reactants and products of the reaction. The reactants are written on the left-hand side of the equation, while the products are written on the right-hand side. The reactants and products are separated by an arrow, which indicates the direction of the reaction.
Exothermic and Endothermic Processes
Chemical reactions can be classified as exothermic or endothermic processes based on the change in enthalpy. Enthalpy is the heat content of a system, and it is a measure of the energy stored in the bonds between atoms.
In an exothermic process, the enthalpy of the products is lower than the enthalpy of the reactants. This means that energy is released during the reaction in the form of heat. Examples of exothermic processes include combustion reactions, where a fuel reacts with oxygen to produce heat and light.
In an endothermic process, the enthalpy of the products is higher than the enthalpy of the reactants. This means that energy is absorbed during the reaction. Examples of endothermic processes include the reaction between baking soda and vinegar, which absorbs heat from the surroundings and causes the mixture to become cold.
Understanding the nature of chemical reactions is important for calculating the enthalpy change of a reaction. By analyzing the bonds between atoms in the reactants and products, it is possible to determine whether a reaction is exothermic or endothermic, and to calculate the amount of heat that is released or absorbed during the reaction.
Measurement of Enthalpy Changes
Calorimetry
Calorimetry is a technique used to measure changes in enthalpy of chemical reactions. A calorimeter can be made up of a polystyrene drinking cup, a vacuum flask, or a metal can. A polystyrene cup can act as a calorimeter to find enthalpy changes in a chemical reaction. The energy needed to raise the temperature of 1 g of a substance by 1 K is known as specific heat. The specific heat of water is 4.18 J/g.K.
To measure the enthalpy change of a reaction, the reactants are placed in a calorimeter, and the temperature change is recorded. The heat absorbed or released by the reaction is equal to the heat absorbed or released by the calorimeter. By knowing the mass of the reactants and the specific heat of the calorimeter, the enthalpy change of the reaction can be calculated.
Hess's Law
Hess's Law states that the enthalpy change of a reaction is independent of the pathway between the reactants and the products. This means that if a reaction can be expressed as a sum of two or more reactions, the enthalpy change of the overall reaction is equal to the sum of the enthalpy changes of the individual reactions.
Hess's Law can be used to calculate the enthalpy change of a reaction that cannot be easily measured experimentally. For example, the enthalpy change of combustion of magnesium can be calculated by using the enthalpy changes of combustion of magnesium oxide and hydrogen.
In summary, calorimetry is a technique used to measure changes in enthalpy of chemical reactions, while Hess's Law can be used to calculate the enthalpy change of a reaction that cannot be easily measured experimentally.
Calculating Enthalpy Change
Calculating the enthalpy change of a reaction is an important aspect of thermodynamics. Enthalpy change is the amount of heat released or absorbed during a chemical reaction. It is typically measured in units of joules or kilojoules. There are different methods for calculating enthalpy change, including the standard enthalpy of formation, bond enthalpies, and using enthalpy change equations.
Standard Enthalpy of Formation
The standard enthalpy of formation is the enthalpy change that occurs when one mole of a compound is formed from its constituent elements in their standard states. The standard state of an element is its most stable form at a given temperature and pressure. The standard enthalpy of formation is denoted as ΔHf° and is typically measured at 298 K and 1 atm pressure.
The standard enthalpy of formation can be used to calculate the enthalpy change of a reaction using Hess's law. Hess's law states that the enthalpy change of a reaction is independent of the pathway taken to reach the final state. This means that the enthalpy change of a reaction can be calculated by summing the enthalpy changes of the reactions that lead to the final state.
Bond Enthalpies
Bond enthalpies are the energy required to break a chemical bond. The bond enthalpy is typically measured in units of kilojoules per mole (kJ/mol). Bond enthalpies can be used to calculate the enthalpy change of a reaction by subtracting the sum of the bond enthalpies of the reactants from the sum of the bond enthalpies of the products.
Bond enthalpies are not always accurate because the energy required to break a bond can vary depending on the environment. For example, the bond enthalpy of a C-H bond in methane is different from the bond enthalpy of a C-H bond in ethane.
Using Enthalpy Change Equations
Enthalpy change equations can be used to calculate the enthalpy change of a reaction using experimental data. The enthalpy change equation relates the enthalpy change of a reaction to the enthalpy changes of the reactions that lead to the final state. This equation can be derived using Hess's law.
To use an enthalpy change equation, the enthalpy changes of the reactions leading to the final state must be known. These enthalpy changes can be measured experimentally using calorimetry or estimated using bond enthalpies or the standard enthalpy of formation.
In conclusion, there are different methods for calculating the enthalpy change of a reaction. The standard enthalpy of formation, bond enthalpies, and enthalpy change equations are all useful tools for calculating enthalpy change. The choice of method depends on the available data and the accuracy required.
Practical Considerations
Temperature and Pressure Effects
Temperature and pressure can greatly affect the enthalpy change of a reaction. In order to obtain accurate results, it is important to control these variables as much as possible. The temperature should be measured and recorded before and after the reaction takes place. This can be done using a thermometer or a temperature probe. It is important to note that the reaction vessel may heat up or cool down during the reaction, so it is important to take multiple temperature readings throughout the experiment and calculate the average.
Pressure can also affect the enthalpy change of a reaction, particularly if gases are involved. The pressure should be measured and recorded before and after the reaction takes place. This can be done using a pressure gauge or a manometer. If the pressure changes significantly during the reaction, it may be necessary to repeat the experiment with a different pressure.
Catalysts and Reaction Rates
Catalysts can greatly affect the enthalpy change of a reaction by increasing the reaction rate. When a catalyst is used, the reaction may produce more heat than it would without the catalyst. It is important to take this into account when calculating the enthalpy change. The use of a catalyst should be noted in the experimental procedure, and the enthalpy change should be calculated both with and without the catalyst.
Reaction rates can also affect the enthalpy change of a reaction. If a reaction takes a long time to complete, the heat produced may dissipate into the surroundings, making it difficult to measure accurately. It is important to choose a reaction that has a reasonable rate, and to carry out the experiment in a timely manner. If necessary, the reaction can be sped up by using a catalyst or by increasing the temperature.
In summary, when calculating the enthalpy change of a reaction, it is important to control the variables of temperature and pressure as much as possible, and to take into account the effects of catalysts and reaction rates. By carefully controlling these factors, it is possible to obtain accurate and reliable results.
Applications of Enthalpy Change Industrial Processes
Enthalpy change plays an essential role in various industrial processes. For instance, in the production of ammonia, bankrate com calculator Haber's process involves the synthesis of nitrogen and hydrogen gas to form ammonia. The reaction is exothermic, and the enthalpy change of the reaction is -92.4 kJ/mol. The enthalpy change of the reaction is crucial in determining the optimum conditions for the reaction, such as temperature and pressure, to achieve maximum yield.
Another example is the production of iron from iron oxide in a blast furnace. The process involves the reduction of iron oxide using carbon monoxide gas to form iron and carbon dioxide. The reaction is exothermic, and the enthalpy change of the reaction is -12.6 kJ/mol. The enthalpy change of the reaction is vital in determining the amount of energy required to heat the reactants and the products.
Environmental Impact
Enthalpy change also plays a significant role in understanding the environmental impact of various chemical reactions. For instance, the combustion of fossil fuels such as coal, oil, and gas releases carbon dioxide into the atmosphere. The combustion of one mole of methane gas, which is the primary component of natural gas, releases 890.4 kJ of energy and 213.6 kJ of enthalpy change. The enthalpy change of the reaction is crucial in determining the amount of energy released and the environmental impact of the reaction.
Moreover, the enthalpy change of a reaction can be used to determine the amount of energy required to break the bonds in the reactants and the amount of energy released when the bonds in the products are formed. This information is essential in understanding the energy efficiency of various chemical reactions and their environmental impact.
In conclusion, the applications of enthalpy change are vast and significant in various fields, including industrial processes and environmental impact. Understanding the enthalpy change of a reaction is crucial in determining the optimum conditions for a reaction and the amount of energy required or released during the reaction.
Frequently Asked Questions What is the formula for calculating the enthalpy change of a reaction?
The formula for calculating the enthalpy change of a reaction is ΔH = H(products) - H(reactants). This formula represents the difference in enthalpy between the products and reactants of a chemical reaction.
How can bond energies be used to determine the enthalpy change?
Bond energies can be used to determine the enthalpy change by calculating the energy required to break the bonds in the reactants and the energy released when new bonds are formed in the products. The difference between these two values represents the enthalpy change of the reaction.
What is the process for calculating the enthalpy of formation?
The process for calculating the enthalpy of formation involves determining the enthalpy change that occurs when one mole of a compound is formed from its constituent elements in their standard states. This process involves using tabulated values of standard enthalpies of formation.
How does Hess's law relate to the calculation of reaction enthalpy change?
Hess's law states that the enthalpy change of a reaction is independent of the pathway taken to get from reactants to products. This means that the enthalpy change of a reaction can be calculated by summing the enthalpy changes of a series of reactions that add up to the overall reaction.
How can the enthalpy change of combustion be calculated?
The enthalpy change of combustion can be calculated by measuring the heat released when a substance is burned in excess oxygen. This value represents the enthalpy change of the reaction and can be used to determine the enthalpy change of other reactions involving the same substance.
What is the relationship between enthalpy change and temperature variation?
The relationship between enthalpy change and temperature variation is given by the equation Q = mcΔT, where Q is the heat absorbed or released, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature. This equation can be used to calculate the enthalpy change of a reaction from temperature data.