To calculate the heat released or absorbed in a chemical reaction, determine how much the temperature of the surroundings changes, use the reaction’s enthalpy change, or calculate the energy difference between the chemical bonds broken and formed. The appropriate method depends on the information available, such as temperature measurements, the quantities of reactants and products, or standard enthalpy values.
Heat is the energy transferred between a chemical reaction and its surroundings because of a temperature difference. When a reaction releases heat, it is exothermic. When it absorbs heat, it is endothermic. Understanding this energy transfer makes it possible to calculate how much heat a reaction produces or requires, whether in a laboratory experiment, an industrial process, or a familiar chemical change such as combustion.
Understand how heat flows during a chemical reaction
Chemical reactions involve changes in the arrangement of atoms and the chemical bonds connecting them. Energy is required to break chemical bonds, while energy is released when new bonds form. The overall balance between these energy changes determines whether a reaction releases or absorbs heat under specified conditions.
In an exothermic reaction, forming new bonds releases more energy than breaking the original bonds requires. The excess energy transfers to the surroundings, often raising their temperature. Burning natural gas, reacting many acids with bases, and oxidizing many fuels are examples of exothermic processes.
In an endothermic reaction, breaking bonds and other energy-consuming processes require more energy than the formation of new bonds releases. The reaction absorbs energy from its surroundings, potentially lowering their temperature. Some chemical decompositions and reactions involving the dissolution of certain salts in water are examples of endothermic processes.
The amount of heat transferred depends on the reaction conditions and the quantities of substances involved. A reaction may release a large amount of heat per mole but transfer relatively little heat if only a small amount of reactant reacts.
Calculate heat using temperature change
One of the most common ways to calculate heat released or absorbed is to measure the temperature change of a substance surrounding the reaction. This method is widely used in calorimetry, the measurement of heat transferred during physical or chemical processes.
The basic equation is:
q = mcΔT
Where:
- q = heat transferred to or from the substance, measured in joules (J)
- m = mass of the substance, measured in grams (g)
- c = specific heat capacity, measured in joules per gram per degree Celsius (J/(g·°C))
- ΔT = temperature change, calculated as final temperature minus initial temperature, in degrees Celsius (°C)
Specific heat capacity describes how much energy is required to raise the temperature of one gram of a substance by one degree Celsius. Different substances have different specific heat capacities. For example, liquid water has a specific heat capacity of approximately 4.184 J/(g·°C) under ordinary conditions.
To use this equation, measure the mass of the substance, identify its specific heat capacity, and record its initial and final temperatures. Subtract the initial temperature from the final temperature to obtain the temperature change, then multiply the mass, specific heat capacity, and temperature change.
Example: Calculate heat absorbed by water
Suppose a reaction warms 200 g of water from 22°C to 30°C. Assume the water absorbs all the heat transferred from the reaction and that heat losses are negligible.
First, calculate the temperature change:
ΔT = 30°C − 22°C = 8°C
Next, use the heat equation with the specific heat capacity of water:
q = mcΔT
q = (200 g)(4.184 J/(g·°C))(8°C)
q = 6,694.4 J
The water absorbs approximately 6.69 kJ of heat.
If the reaction is the only source of this heat, the reaction releases the same amount of energy:
qᵣₑₐcₜᵢₒₙ = −6.69 kJ
The negative sign indicates that the reaction loses heat while the water gains it.
This example illustrates an important principle: the heat absorbed by the surroundings equals the heat released by the reaction, provided no energy is exchanged with anything else.
In an actual experiment, some energy may warm the container or escape into the room. Those effects must be considered when accurate results are needed.
Determine heat released or absorbed from enthalpy change
Another common approach uses enthalpy change, represented by ΔH. Enthalpy is a thermodynamic property that accounts for a system’s internal energy and pressure-volume contribution. Under constant pressure, the enthalpy change of a reacting system equals the heat transferred to or from that system, assuming only pressure-volume work occurs.
For a chemical reaction at constant pressure:
qₚ = ΔH
The enthalpy change is generally reported in joules or kilojoules. In chemistry, it is often expressed per mole of reaction as written in a balanced chemical equation, such as kJ/mol.
A negative enthalpy change indicates an exothermic reaction:
ΔH < 0
A positive enthalpy change indicates an endothermic reaction:
ΔH > 0
When a reaction’s molar enthalpy change is known, the heat transferred can be calculated by multiplying the enthalpy change per mole by the amount of reaction that occurs.
q = nΔHₘ
Where:
- q = heat transferred by the reaction
- n = amount of reaction that occurs, in moles
- ΔHₘ = enthalpy change per mole of reaction, in kJ/mol
Here, n refers to the extent of reaction in moles, consistent with the balanced chemical equation and the stated molar enthalpy change. In simpler cases, it can be determined from the moles of a limiting reactant, adjusted for its coefficient in the equation.
Example: Calculate heat released by combustion
Consider the combustion of methane:
CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l)
Suppose the enthalpy change for this reaction is approximately −890 kJ per mole of methane reacted under the conditions represented by the equation, including liquid water as a product.
If 2 moles of methane burn completely, the heat transferred by the reaction is:
q = nΔHₘ
q = (2 mol)(−890 kJ/mol)
q = −1,780 kJ
The reaction releases approximately 1,780 kJ of heat.
The negative value describes the reaction’s energy change. If the question asks how much heat is released as a positive magnitude, the answer is 1,780 kJ released.
The physical state of each substance matters when using enthalpy values. Producing liquid water releases a different amount of energy than producing water vapor because condensation also releases energy. Therefore, enthalpy values must match the chemical equation and the states of the substances involved.
Calculate heat using standard enthalpies of formation
Sometimes the heat of a reaction is not given directly. Instead, the enthalpies of formation of the reactants and products are available.
The standard enthalpy of formation, ΔH°f, is the enthalpy change when one mole of a substance forms from its constituent elements in their standard states under specified standard conditions. These values can be used to calculate the standard enthalpy change of a reaction.
The equation is:
ΔH°ᵣₓₙ = ΣnΔH°f(products) − ΣnΔH°f(reactants)
In this equation, each formation enthalpy is multiplied by its stoichiometric coefficient in the balanced chemical equation. The symbol Σ means to add the contributions from all products or all reactants.
The calculation follows a straightforward process. First, balance the chemical equation. Next, obtain the standard enthalpy of formation for each substance, ensuring that the physical states match those in the equation. Multiply each value by its coefficient, add the product contributions, and subtract the total reactant contribution from the total product contribution.
The resulting value is the standard enthalpy change for the reaction as written.
Example: Calculate the enthalpy change for forming water
Consider the reaction:
2H₂(g) + O₂(g) → 2H₂O(l)
The standard enthalpy of formation of hydrogen gas and oxygen gas in their standard states is zero. The standard enthalpy of formation of liquid water is approximately −285.8 kJ/mol.
Using the equation:
ΔH°ᵣₓₙ = ΣnΔH°f(products) − ΣnΔH°f(reactants)
ΔH°ᵣₓₙ = [2 × (−285.8 kJ/mol)] − [2 × 0 + 1 × 0]
ΔH°ᵣₓₙ = −571.6 kJ
The reaction releases approximately 571.6 kJ of heat per reaction as written, which consumes 2 moles of hydrogen and 1 mole of oxygen to form 2 moles of liquid water.
The negative sign indicates that the reaction is exothermic. If the quantities of reactants change, the total heat transfer changes proportionally, provided the reaction proceeds under the same conditions and follows the stated stoichiometry.
Estimate heat using chemical bond energies
Heat released or absorbed can also be estimated from the average energies required to break chemical bonds and the energies released when new bonds form.
Breaking a chemical bond requires energy. Forming a chemical bond releases energy. The overall reaction energy therefore depends on the balance between the energy needed to break bonds in the reactants and the energy released by forming bonds in the products.
The approximate relationship is:
ΔH ≈ ΣE(bonds broken) − ΣE(bonds formed)
Bond energies are commonly expressed in kJ/mol. To use this equation, identify the bonds in the reactants that must be broken and the bonds formed in the products. Multiply the energy associated with each bond type by the number of such bonds, then subtract the total energy released during bond formation from the total energy required for bond breaking.
If the result is negative, the reaction is estimated to be exothermic. If it is positive, the reaction is estimated to be endothermic.
For example, in the reaction between hydrogen and oxygen to form water, energy must be supplied to break H–H and O=O bonds. Energy is released when O–H bonds form in water. Because the formation of the product bonds releases more energy than is required to break the reactant bonds, the overall reaction releases energy.
Bond-energy calculations are useful when formation enthalpies are unavailable, but they generally provide estimates rather than exact values. Tabulated bond energies are usually averages across different molecular environments. More precise reaction enthalpies are typically obtained from thermochemical data specific to the substances and their physical states.
Use calorimetry to measure heat experimentally
Calorimetry provides a practical way to determine how much heat a chemical reaction releases or absorbs. The central idea is to measure the temperature change of a material that exchanges heat with the reacting system.
A simple coffee-cup calorimeter consists of an insulated cup, a lid, a thermometer, and the reacting solutions. It is often used for reactions that occur in aqueous solutions at approximately constant atmospheric pressure.
For a reaction carried out in a solution, the heat absorbed by the solution can be estimated using:
qₛₒₗᵤₜᵢₒₙ = mₛₒₗᵤₜᵢₒₙcₛₒₗᵤₜᵢₒₙΔT
If the solution gains heat, its temperature rises and the calculated heat is positive. Assuming negligible heat exchange with the environment and negligible energy absorbed by the calorimeter itself, the reaction heat is:
qᵣₑₐcₜᵢₒₙ = −qₛₒₗᵤₜᵢₒₙ
In a more accurate experiment, the calorimeter’s heat capacity must also be considered. If the calorimeter absorbs heat, the energy balance becomes:
qᵣₑₐcₜᵢₒₙ = −(qₛₒₗᵤₜᵢₒₙ + q꜀ₐₗₒᵣᵢₘₑₜₑᵣ)
The calorimeter’s heat absorption can be calculated from its heat capacity and temperature change:
q꜀ₐₗₒᵣᵢₘₑₜₑᵣ = C꜀ₐₗₒᵣᵢₘₑₜₑᵣΔT
Here, the calorimeter heat capacity, C, is measured in J/°C.
Consider a reaction in which 100 g of solution warms by 5°C. If the solution’s specific heat capacity is approximated as 4.18 J/(g·°C), its heat gain is:
qₛₒₗᵤₜᵢₒₙ = (100 g)(4.18 J/(g·°C))(5°C)
qₛₒₗᵤₜᵢₒₙ = 2,090 J
If heat exchange with the surroundings and the calorimeter’s contribution are negligible, the reaction released approximately 2.09 kJ of heat.
This method requires careful temperature measurements and reasonable assumptions about the solution. For dilute aqueous solutions, treating the solution’s density and specific heat capacity as similar to those of water is often a useful approximation. For concentrated solutions or other liquids, their actual properties may differ significantly.
A bomb calorimeter is used for reactions such as combustion. It contains the sample in a sealed, rigid vessel surrounded by a known amount of water or another heat-absorbing system. Because the vessel’s volume remains essentially constant, the experiment directly measures the energy change associated with the reaction at constant volume. Converting that result to an enthalpy change may require an additional thermodynamic calculation.
Convert heat into heat released per mole
Chemists often want to compare reactions independently of the amounts used. Reporting heat per mole makes that comparison possible.
The molar heat of reaction is obtained by dividing the heat transferred by the amount of reaction, provided both quantities use a consistent basis:
ΔHₘ = qᵣₑₐcₜᵢₒₙ ÷ n
For example, suppose a reaction releases 12 kJ when 0.50 mol of the limiting reactant is consumed, and the balanced equation assigns that reactant a coefficient of 1. The molar enthalpy change is:
ΔHₘ = −12 kJ ÷ 0.50 mol
ΔHₘ = −24 kJ/mol
The reaction releases 24 kJ per mole of reaction as defined by the balanced equation.
If the limiting reactant has a coefficient other than 1, the amount of reaction must be calculated by dividing the moles consumed by that coefficient. This ensures that the molar enthalpy change is reported on the same basis as the balanced chemical equation.
The limiting reactant is the reactant that is consumed first and therefore determines the maximum extent of reaction. Calculating the available moles of each reactant and accounting for their stoichiometric coefficients helps establish how much reaction can occur.
Understand what affects the calculated heat
The amount of heat released or absorbed depends on more than the chemical identity of the reaction. Several factors influence the result or the accuracy of its measurement.
The amount of reactant consumed determines the total heat transfer when the reaction proceeds under fixed conditions. If a reaction releases 100 kJ per mole and twice as many moles react completely, the total heat released doubles.
The physical states of the substances also matter. A product formed as a liquid may have a different enthalpy from the same substance in the gaseous state. Changes involving melting, freezing, vaporization, or condensation can contribute to the overall heat transfer.
Temperature and pressure can affect enthalpy. Standard enthalpy values refer to specified reference conditions, so they may not precisely represent a reaction carried out at substantially different temperatures or pressures. Corrections may be needed when high accuracy is required.
Heat loss to the environment can distort experimental results. If a reaction releases heat but some of it escapes before the temperature is measured, a simple temperature-based calculation may underestimate the amount released. Conversely, heat entering the apparatus from the surroundings can affect the observed temperature change.
Incomplete reactions and competing processes can also change the result. If a reactant does not react completely, or if side reactions occur, the measured heat may differ from the value predicted for the intended reaction.
Finally, reaction rate and total heat release are different quantities. A reaction that releases a given amount of energy rapidly may produce a larger temperature increase over a short period than one that releases the same energy slowly. The total heat depends on the amount and pathway of reaction under the specified conditions, while the rate describes how quickly the energy is transferred.
Choose the right method for the calculation
The most appropriate calculation method depends on the information available.
Use q = mcΔT when the mass, specific heat capacity, and temperature change of the heat-absorbing or heat-releasing material are known. This is especially useful for interpreting calorimetry experiments.
Use q = nΔHₘ when the molar enthalpy change and amount of reaction are known. This is usually the most direct way to calculate the heat released or absorbed by a specified quantity of reactants.
Use standard enthalpies of formation when thermochemical data are available for the reactants and products but the reaction enthalpy is not given directly.
Use bond energies when an approximate estimate is sufficient and suitable bond-energy data are available.
Whichever method you choose, keep track of the sign convention. Heat absorbed by the chemical system is positive, while heat released by the system is negative. The surroundings have the opposite heat change when the system and surroundings exchange energy with each other without significant losses.
The key to calculating heat released or absorbed in a chemical reaction is to identify the energy transfer being measured, select the appropriate equation, and use consistent units and chemical quantities. With those steps in place, temperature measurements and thermochemical data can reveal how much energy a reaction transfers and whether the process warms or cools its surroundings.
