Problem 40 - Chemistry: The Central Science in SI Units, Global Edition

Question

The decomposition of sodium bicarbonate (baking soda), \(\mathrm{NaHCO}_{3}(s)\), into \(\mathrm{Na}_{2} \mathrm{CO}_{3}(s), \mathrm{H}_{2} \mathrm{O}(l)\), and \(\mathrm{CO}_{2}(g)\) at constant pressure requires the addition of \(85 \mathrm{~kJ}\) of heat per two moles of \(\mathrm{NaHCO}_{3} .\) (a) Write a balanced thermochemical equation for the reaction. (b) Draw an enthalpy diagram for the reaction.

Step-by-Step Solution

Answer

(a) Balanced thermochemical equation: \[\mathrm{2NaHCO}_{3}(s) + 85 \,kJ \rightarrow \mathrm{Na}_{2}\mathrm{CO}_{3}(s) + \mathrm{H}_{2}\mathrm{O}(l) + \mathrm{CO}_{2}(g)\] (b) Enthalpy diagram: Reactants: 2NaHCO₃(s) -------->|↑ |↑ 85 kJ |↑ Products: Na₂CO₃(s) + H₂O(l) + CO₂(g)

Step 1: (a) Balanced Thermochemical Equation

: First, write down the balanced chemical equation for the decomposition of sodium bicarbonate: \[\mathrm{2NaHCO}_{3}(s) \rightarrow \mathrm{Na}_{2}\mathrm{CO}_{3}(s) + \mathrm{H}_{2}\mathrm{O}(l) + \mathrm{CO}_{2}(g)\] Now, incorporate the given heat value (85 kJ) for the required constant pressure process. Since heat is required for the reaction, it is an endothermic reaction, thus we'll add the heat term on the left side of the equation: \[\mathrm{2NaHCO}_{3}(s) + 85 \,kJ \rightarrow \mathrm{Na}_{2}\mathrm{CO}_{3}(s) + \mathrm{H}_{2}\mathrm{O}(l) + \mathrm{CO}_{2}(g)\] This is the balanced thermochemical equation for the given reaction.

Step 2: (b) Enthalpy Diagram for the Reaction

: An enthalpy diagram represents the changes in enthalpy during a reaction. Since this is an endothermic reaction, the products will have a higher enthalpy than the reactants. Follow these steps to draw the enthalpy diagram: 1. Label the y-axis as enthalpy (H), with an upward direction indicating an increase in enthalpy. 2. On the x-axis, write the reactant species on the left and the product species on the right. 3. Draw an arrow pointing upwards from the level of reactants to the level of products, indicating the change in enthalpy during the reaction. 4. Label the arrow with the amount of heat required for the reaction (85 kJ). The enthalpy diagram should look like this: Reactants: 2NaHCO₃(s) -------->|↑ |↑ 85 kJ |↑ Products: Na₂CO₃(s) + H₂O(l) + CO₂(g) This diagram showcases the endothermic nature of the reaction and the increase in enthalpy from reactants to products with the involvement of 85 kJ of heat.

Key Concepts

Enthalpy Diagram

An enthalpy diagram is a useful visual tool in chemistry that helps us understand the energy changes during a chemical reaction. It is particularly helpful for visualizing how energy flows into or out of a reaction system. In this case, with the decomposition of sodium bicarbonate, the enthalpy diagram highlights the energy needed for the reaction to occur.

• The vertical axis represents enthalpy (H), which is essentially the total heat content of the system.
• On the horizontal axis, we plot the reactants and products, with reactants on the left and products on the right.
• A key feature of the diagram is the arrow connecting the energy level of reactants to that of the products.

This arrow points upwards in this scenario because it is an endothermic reaction, indicating that the products have a higher enthalpy than the reactants. The label of 85 kJ along the arrow tells us that this amount of energy is absorbed from the surroundings to form the products from the reactants. It visually represents the demand for heat, which is crucial in endothermic reactions.

Endothermic Reaction

An endothermic reaction is a type of chemical reaction where energy is absorbed from the environment. This energy absorption causes the reaction's products to have higher energy than the reactants. For the decomposition of sodium bicarbonate, we see this endothermic nature reflected in both the balanced thermochemical equation and the enthalpy diagram. Key characteristics of endothermic reactions include:

• Heat is absorbed, resulting in a temperature drop in the surrounding environment.
• They usually require a continuous input of energy until the reaction completes.
• The energy absorption is necessary because the bonds formed in the products may be weaker or less stable than those in the reactants.

This kind of reaction is the opposite of exothermic reactions, where energy is released. In simple terms, for a reaction like sodium bicarbonate decomposition to occur, it needs an external source of heat.

Sodium Bicarbonate Decomposition

Sodium bicarbonate, often known as baking soda, decomposes into distinct products when heated under constant pressure. The chemical equation for its decomposition is:\[\mathrm{2NaHCO}_{3}(s) \rightarrow \mathrm{Na}_{2} \mathrm{CO}_{3}(s) + \mathrm{H}_{2} \mathrm{O}(l) + \mathrm{CO}_{2}(g)\]This process results in the formation of sodium carbonate, water, and carbon dioxide. Importantly, it requires an input of 85 kJ of heat to decompose two moles of sodium bicarbonate. Here are some essential points about this decomposition:

• The reaction occurs under constant pressure, typical for many laboratory and industrial processes.
• It is a practical example of an endothermic process as it needs an external heat source to proceed.
• Each compound formed plays a role in various applications, from culinary to industrial uses.

Understanding such decompositions can help explain everyday processes, like why baking soda is used in baking. Its ability to release carbon dioxide upon heating helps dough rise, making this knowledge both practically and scientifically insightful.