Thermochemical Equations: Videos & Practice Problems

Thermochemical equations combine stoichiometry with the thermodynamics of chemical reactions, specifically focusing on the enthalpy change (${\mathrm{\Delta H}}_{\mathrm{rxn}}$). These equations include a balanced chemical equation alongside the ${\mathrm{\Delta H}}_{\mathrm{rxn}}$ of reaction, providing a quantitative measure of the heat absorbed or released during the reaction. To analyze these reactions, a thermochemical stoichiometric chart is employed, which allows for the conversion between different quantities—such as moles, grams, or molecules—and the associated enthalpy change. The key aspect of these equations is establishing a relationship between ${\mathrm{\Delta H}}_{\mathrm{rxn}}$ and the moles of a compound within the reaction. This enables the calculation of unknown quantities by using the coefficients from the balanced equation to perform mole-to-mole comparisons, ultimately allowing for the determination of the enthalpy change for an unknown component in the reaction. Understanding thermochemical equations is essential for predicting the energy changes that accompany chemical processes.

Thermochemical Equations

Stoichiometry is essential for understanding the numerical relationships between reactants and products in a balanced chemical equation. When we introduce thermochemical equations, we incorporate the concept of enthalpy change, denoted as ΔH_rxn, which represents the heat absorbed or released during a chemical reaction. This is crucial for analyzing how energy changes in conjunction with the reaction.

In thermochemical equations, a stoichiometric chart is utilized to relate the known quantity of one compound to the unknown quantity of another. This chart is paired with a balanced chemical equation, where the ΔH_rxn is indicated alongside the reaction. The primary goal is to establish a connection between the enthalpy change and various quantities such as moles, grams, or molecules of the substances involved.

Unlike traditional stoichiometry, which often focuses on mole-to-mole comparisons, thermochemical equations emphasize the relationship between ΔH and the number of moles. This distinction is vital for accurately calculating energy changes in reactions. Understanding this relationship allows for a deeper insight into the thermodynamics of chemical processes, enabling predictions about energy transfer and reaction feasibility.

Thermochemical Equations

Understanding thermochemical equations is essential in the study of stoichiometry, particularly when dealing with energy changes in chemical reactions. A thermochemical equation not only includes a balanced chemical equation but also specifies the change in enthalpy, denoted as ΔH. This value indicates the heat absorbed or released during the reaction.

To effectively utilize a stoichiometric chart in this context, one must start with the given ΔH of the reaction. The first step involves converting this ΔH into moles of the substance involved. This can be achieved through various conversions, such as from grams to moles or from ions, atoms, formula units, or molecules to moles. The relationship between these quantities is governed by the molar mass of the substances involved.

Once the moles of the given substance are established, the next critical step is to transition to the moles of the unknown substance. This transition, often referred to as "the jump," requires careful attention to the coefficients in the balanced chemical equation. These coefficients provide the necessary mole-to-mole ratios that facilitate this conversion.

After determining the moles of the unknown, you can convert this quantity into various forms, such as ions, atoms, formula units, or molecules, or even back to grams. Additionally, it is possible to calculate a new ΔH for the unknown substance based on the stoichiometric relationships established in the balanced equation.

In summary, mastering the connections between ΔH, moles, and the various forms of substances is crucial for solving problems in thermochemistry and stoichiometry. This knowledge allows for a comprehensive understanding of how energy changes relate to the quantities of reactants and products in chemical reactions.

Thermochemical Equations Example 1

In a thermochemical reaction, 2 moles of solid magnesium react with 1 mole of oxygen gas to produce 2 moles of solid magnesium oxide, releasing an enthalpy change of -1204 kilojoules. To determine how many grams of magnesium oxide are produced during an enthalpy change of -375 kilojoules, we first need to establish a relationship between the energy change and the amount of magnesium oxide produced.

Using the balanced equation, we can perform a mole-to-mole comparison. The enthalpy change indicates that for every 2 moles of magnesium oxide produced, -1204 kilojoules of energy is released. Therefore, we can set up a proportion to find the moles of magnesium oxide corresponding to -375 kilojoules:

Let \( x \) be the moles of magnesium oxide produced:

\[\frac{2 \text{ moles MgO}}{-1204 \text{ kJ}} = \frac{x \text{ moles MgO}}{-375 \text{ kJ}}\]

Cross-multiplying gives:

\[x = \frac{2 \times -375}{-1204} \approx 0.622 \text{ moles MgO}\]

Next, we convert moles of magnesium oxide to grams. The molar mass of magnesium oxide (MgO) is calculated as follows:

Magnesium (Mg) has a molar mass of 24.31 grams/mole, and oxygen (O) has a molar mass of 16 grams/mole. Thus, the molar mass of magnesium oxide is:

\[\text{Molar mass of MgO} = 24.31 \text{ g/mol} + 16 \text{ g/mol} = 40.31 \text{ g/mol}\]

Now, we can find the mass of magnesium oxide produced:

\[\text{Mass of MgO} = 0.622 \text{ moles} \times 40.31 \text{ g/mol} \approx 25.11 \text{ grams}\]

Thus, during an enthalpy change of -375 kilojoules, approximately 25.11 grams of magnesium oxide are produced. This calculation demonstrates the relationship between energy changes in a chemical reaction and the quantities of products formed.

Nitromethane (CH₃NO₂), sometimes used as a fuel for drag racing, burns according to the following reaction: 


4 CH₃NO₂ (l) + 7 O₂ (g) → 4 CO₂ (g) + 6 H₂O (g) + 4 NO₂ (g)      ∆Hº = – 2441.6 kJ


How much heat is released by burning 125.0 g of nitromethane (MW:61.044 g/mol)? 

• A. 1.250 x 10³ kJ
• B. -1.250 x 10³ kJ
• C. 2.440 x 10³ kJ
• D. -2.440 x 10³ kJ

Answer: (B)

Consider the following reaction: 
2 C₆H₆ (l) + 15 O₂ (g) → 12 CO₂ (g) + 6 H₂­O (g)  ∆Hº = – 6278 kJ
What volume of benzene (C₆H₆, d = 0.880 g/mL, molar mass = 78.11 g/mol) is necessary to evolve 5.19 x 10⁹ kJ of heat? 

• A. 1.47 x 10⁸ mL
• B. 5.19 x 10⁹ mL
• C. 7.34 x 10⁷ mL
• D. 9.51 x 10⁹ mL

Answer: (A)

The creation of liquid methanol is accomplished by the hydrogenation of carbon monoxide: 
CO (g) + 2 H₂ (g) → CH₃OH (l)       ∆Hº = – 128.1 kJ
How much heat (in kJ) is released when 125.0 g CO reacts with 2.32 x 10² g H₂?

• A. 275 kJ
• B. -572 kJ
• C. -128 kJ
• D. 281 kJ

Answer: (B)

Here’s what students ask on this topic:

What are thermochemical equations?

Thermochemical equations are a form of chemical equations that not only show the balance between reactants and products but also include the change in enthalpy (ΔH) associated with the reaction. Enthalpy is a measure of the total energy of a thermodynamic system, and it includes both internal energy and the product of its volume and pressure.

In a thermochemical equation, the enthalpy change indicates whether the reaction is exothermic (releasing heat, $\Delta H$ is negative) or endothermic (absorbing heat, $\Delta H$ is positive). The coefficients in the equation represent the stoichiometry of the reaction and also the ratio in which the energy is absorbed or released. For example, if the equation includes a $\Delta H$ value with a negative sign, it tells us that the reaction releases that specific amount of energy as heat for the given stoichiometric amounts of reactants and products.

These equations are crucial for understanding the energy implications of chemical reactions, which is important in fields such as chemistry, materials science, and engineering. They help predict the energy changes that occur during chemical processes, which is essential for designing industrial chemical processes and understanding natural phenomena.

How do you calculate the enthalpy of reaction?

To calculate the enthalpy of reaction, also known as the heat of reaction, you typically use Hess's Law or the standard enthalpy of formation for the reactants and products involved in the reaction. Here's a step-by-step guide:

1. Write down the balanced chemical equation for the reaction.
2. Determine the standard enthalpy of formation (${\mathrm{\Delta H}}_f°$) values for each reactant and product from a data table. These values represent the enthalpy change when one mole of a substance is formed from its elements in their standard states.
3. Use the formula:
${\mathrm{\Delta H}}_{\mathrm{reaction}}°=\sum ({\mathrm{\Delta H}}_f°\text{of products})-\sum ({\mathrm{\Delta H}}_f°\text{of reactants})$
4. Multiply the standard enthalpy of formation for each substance by the number of moles in the balanced equation.
5. Subtract the total enthalpy of the reactants from the total enthalpy of the products to find the enthalpy of reaction.

Remember that the standard enthalpy of formation for an element in its standard state is zero. The enthalpy of reaction is typically expressed in kilojoules per mole (kJ/mol).

What does the enthalpy of reaction measure?

The enthalpy of reaction, often denoted as ${\mathrm{\Delta H}}_{\mathrm{rxn}}$, measures the total heat content change during a chemical reaction. It's the difference between the enthalpy of the products and the reactants. If ${\mathrm{\Delta H}}_{\mathrm{rxn}}$ is negative, the reaction is exothermic, meaning it releases heat to the surroundings. Conversely, if ${\mathrm{\Delta H}}_{\mathrm{rxn}}$ is positive, the reaction is endothermic, indicating that it absorbs heat from the surroundings. The enthalpy of reaction is a crucial concept in thermodynamics and is used to predict whether a reaction will occur spontaneously, as well as to understand the energy changes involved in chemical processes. It's typically measured in units of joules per mole (J/mol) or kilojoules per mole (kJ/mol).

What is the enthalpy of reaction?

The enthalpy of reaction, often denoted as ${\mathrm{\Delta H}}_{\mathrm{rxn}}$, is a thermodynamic quantity that measures the total heat content change during a chemical reaction. It is the difference between the enthalpy (heat content) of the products and the reactants. If ${\mathrm{\Delta H}}_{\mathrm{rxn}}$ is negative, the reaction is exothermic, meaning it releases heat into the surroundings. Conversely, if ${\mathrm{\Delta H}}_{\mathrm{rxn}}$ is positive, the reaction is endothermic, meaning it absorbs heat from the surroundings.

To calculate the enthalpy of reaction, you can use the enthalpies of formation of the reactants and products, which are the enthalpies required to form one mole of a substance from its elements in their standard states. The formula is:

${\mathrm{\Delta H}}_{\mathrm{rxn}}=\sum {\mathrm{\Delta H}}_f\left(\text{products}\right)-\sum {\mathrm{\Delta H}}_f\left(\text{reactants}\right)$

Where ∑ represents the sum over all reactants and products, and ΔHf is the standard enthalpy of formation for each substance. This value is crucial for understanding the energy changes involved in chemical processes and for the design of chemical reactors and processes.