Problem 28 - Chemistry and Chemical Reactivity

Question

Calcium carbide, \(\mathrm{CaC}_{2}\), is manufactured by the reaction of CaO with carbon at a high temperature. (Calcium carbide is then used to make acetylene.) $$\mathrm{CaO}(\mathrm{s})+3 \mathrm{C}(\mathrm{s}) \longrightarrow \mathrm{CaC}_{2}(\mathrm{s})+\mathrm{CO}(\mathrm{g})$$ $$\Delta H_{\mathrm{rxn}}^{\circ}=+464.8 \mathrm{kJ}$$ Is this reaction endothermic or exothermic? If \(10.0 \mathrm{g}\) of CaO is allowed to react with an excess of carbon, what quantity of heat is absorbed or evolved by the reaction?

Step-by-Step Solution

Answer

The reaction is endothermic, and 82.80 kJ of heat is absorbed.

Step 1: Determine the Reaction Type

Endothermic reactions absorb heat from the surroundings, while exothermic reactions release heat. Given that \( \Delta H_{\mathrm{rxn}}^{\circ} = +464.8 \mathrm{kJ} \), the positive sign indicates that the reaction is endothermic.

Step 2: Calculate Moles of \( \mathrm{CaO} \)

Determine the moles of \( \mathrm{CaO} \) by using its molar mass. The molar mass of \( \mathrm{CaO} \) is approximately \( 56.08 \mathrm{\ g/mol} \). Calculate moles: \[ \text{Moles of } \mathrm{CaO} = \frac{10.0 \ \mathrm{g}}{56.08 \ \mathrm{g/mol}} \approx 0.178 \ \mathrm{mol} \]

Step 3: Relate Moles to Heat Absorbed

From the given balanced equation, \( 1 \ mol \) of \( \mathrm{CaO} \) requires \( +464.8 \ \mathrm{kJ} \) of heat. For \( 0.178 \ \mathrm{mol} \) of \( \mathrm{CaO} \), the heat absorbed is calculated as: \[ \text{Heat absorbed} = 0.178 \ \mathrm{mol} \times 464.8 \ \mathrm{kJ/mol} \]

Step 4: Calculate Total Heat Absorbed

Complete the calculation for the heat absorbed: \[ \text{Heat absorbed} = 0.178 \ \times 464.8 \approx 82.80 \ \mathrm{kJ} \] This means that 82.80 kJ of heat is absorbed when 10.0 g of \( \mathrm{CaO} \) reacts.

Key Concepts

Understanding Enthalpy Change

Enthalpy change is essential in identifying whether a reaction is endothermic or exothermic. It refers to the heat change occurring at constant pressure when a chemical reaction takes place. In the equation, this is represented as \( \Delta H \). For instance, a positive \( \Delta H \) indicates heat is absorbed from the surroundings, characterizing the reaction as endothermic. Conversely, a negative \( \Delta H \) signifies heat release, calling it exothermic. In our calcium oxide and carbon reaction, \( \Delta H_{\mathrm{rxn}}^{\circ} = +464.8 \mathrm{kJ} \), we deal with an endothermic process. Since the value is positive, it confirms that energy is absorbed. Recognizing this helps in predicting how the reaction will affect its surroundings, such as temperature changes.

Role of Calcium Oxide in Reactions

Calcium oxide, often called quicklime, is a widely used chemical compound. It plays a critical role in producing calcium carbide through the reaction with carbon. This interaction is vital in industries where acetylene gas production is required. Calcium oxide acts as a reactant that readily combines with carbon when heated, creating calcium carbide (\( \mathrm{CaC}_2 \)). This significance in industrial applications highlights its utility and value across various chemical processes.Additionally, calcium oxide's high reactivity with other substances means careful handling and measuring is mandatory. In our exercise, it serves as the starting reagent, needing a precise quantity to calculate endothermic heat absorption accurately.

Basics of Moles Calculation

Understanding how to calculate moles is fundamental in stoichiometry, a crucial part of chemistry that deals with the quantitative relationships of elements and compounds. The concept of moles allows you to convert mass into a number of particles, as atoms and molecules are incredibly small. To find moles, you need the substance's mass and its molar mass. The formula is:

• \( \text{Moles} = \frac{\text{mass}}{\text{molar mass}} \)

In the provided scenario, we have \( 10.0 \mathrm{g} \) of calcium oxide with a molar mass of approximately \( 56.08 \mathrm{g/mol} \). Thus, the calculation would be \( \frac{10.0}{56.08} \approx 0.178 \mathrm{mol} \). Understanding this conversion is essential for determining how much heat a specific amount of a reactant will absorb in a chemical reaction.

Introduction to Chemical Thermodynamics

Chemical thermodynamics is the branch of chemistry that explores the relationship between heat and other forms of energy in the context of chemical reactions or physical transformations. It provides insights into how reactions take place under various conditions of temperature and pressure. A fundamental concept in chemical thermodynamics is enthalpy. It helps in predicting whether a process is feasible or how much energy it will use or release. In our case, learning how to measure the enthalpy changes aids in predicting the amount of energy involved when calcium oxide reacts with carbon to form calcium carbide. Understanding chemical thermodynamics is essential for designing processes that are both efficient and environmentally conscious. It helps chemists control reaction pathways to obtain desirable products while minimizing unwanted energy expenditures.