Problem 26 - Chemistry and Chemical Reactivity

Question

Calcium carbide, \(\mathrm{CaC}_{2}\), is manufactured by the reaction of CaO with carbon at a high temperature. (Calcium carbidCalcium 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.)e is then used to make acetylene.) \(\begin{aligned} \mathrm{CaO}(\mathrm{s})+3 \mathrm{C}(\mathrm{s}) \rightarrow \mathrm{CaC}_{2}(\mathrm{s}) &+\mathrm{CO}(\mathrm{g}) \\ & \Delta_{\mathrm{r}} H^{\circ}=+464.8 \mathrm{kJ} / \mathrm{mol}-\mathrm{rxn} \end{aligned}\) Is this reaction endothermic or exothermic? What is the enthalpy change if \(10.0 \mathrm{g}\) of \(\mathrm{CaO}\) is allowed to react with an excess of carbon?

Step-by-Step Solution

Answer

The reaction is endothermic with an enthalpy change of about 82.94 kJ.

Step 1: Understanding Reaction and Enthalpy Change

The reaction is given as \( \mathrm{CaO}(\mathrm{s}) + 3 \mathrm{C}(\mathrm{s}) \rightarrow \mathrm{CaC}_{2}(\mathrm{s}) + \mathrm{CO}(\mathrm{g}) \). The \( \Delta_{r} H^{\circ} \) is \(+464.8 \mathrm{kJ/mol-rxn} \). Since the enthalpy change (\( \Delta H \)) is positive, the reaction is endothermic, meaning it absorbs heat.

Step 2: Determine Molar Mass of Calcium Oxide

To find the enthalpy change for 10.0 g of \( \mathrm{CaO} \), first calculate its molar mass. The molar mass of \( \mathrm{CaO} \) is the sum of the molar mass of \( \mathrm{Ca} \) (40.08 g/mol) and \( \mathrm{O} \) (16.00 g/mol), giving a total of 56.08 g/mol.

Step 3: Calculate Moles of Calcium Oxide

Now, calculate the number of moles of \( \mathrm{CaO} \) in 10.0 grams: \[ \text{{moles of }} \mathrm{CaO} = \frac{10.0 \text{{ g}}}{56.08 \text{{ g/mol}}} \approx 0.1784 \text{{ moles}} \].

Step 4: Calculate Enthalpy Change for Given Mass

The enthalpy change \( \Delta H \) for the reaction per mole of \( \mathrm{CaO} \) is \(+464.8 \mathrm{kJ/mol} \). Calculate \( \Delta H \) for 0.1784 moles by multiplying the moles by the enthalpy change per mole: \[ \Delta H = 0.1784 \text{{ moles}} \times 464.8 \frac{{\mathrm{kJ}}}{\text{{mol}}} \approx 82.94 \text{{ kJ}} \].

Key Concepts

Enthalpy Change

In chemical reactions, energy can be either absorbed or released, which we refer to as the enthalpy change. The enthalpy change is denoted by the symbol \( \Delta H \). A positive \( \Delta H \) value indicates an endothermic reaction, meaning the reaction absorbs heat from its surroundings. In the case of the reaction between calcium oxide (CaO) and carbon to produce calcium carbide (CaC\(_2\)) and carbon monoxide (CO), the enthalpy change is given as \(+464.8 \text{kJ/mol-rxn} \). This positive value confirms the reaction is endothermic.

• An endothermic reaction requires energy input to proceed, often resulting in a temperature drop in the reaction surroundings.
• Understanding whether a reaction is endothermic or exothermic helps predict the energy requirements for industrial processes like the production of acetylene from calcium carbide.
• Knowledge of \( \Delta H \) also aids in calculating the amount of energy absorbed for a given quantity of reactant.

Molar Mass Calculation

To determine the enthalpy change for a specific amount of a substance, it’s necessary to first calculate its molar mass. Molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol). For calcium oxide (CaO), the molar mass is calculated by adding the molar masses of calcium (Ca) and oxygen (O).
- The molar mass of calcium (Ca) is \(40.08 \text{ g/mol}\).
- The molar mass of oxygen (O) is \(16.00 \text{ g/mol}\).
Putting these together, the molar mass of calcium oxide is \(56.08 \text{ g/mol}\).
Calculating the molar mass enables us to find how many moles are present in a given mass of the compound. This calculation is crucial when we need to relate the mass of a reactant to its enthalpy change. For instance, with 10.0 grams of \( \text{CaO} \), you can find the moles by dividing the mass by the molar mass: \[ \text{moles of CaO} = \frac{10.0 \text{ g}}{56.08 \text{ g/mol}} \approx 0.1784 \text{ moles} \].
This helps in determining the corresponding enthalpy change for this quantity of CaO.

Calcium Oxide

Calcium oxide, commonly known as quicklime or burnt lime, is a white, caustic alkaline earth oxide. It is produced by heating limestone or other calcium-containing materials to high temperatures in a process called calcination. When calcium oxide is reacted with carbon under high temperatures, it is converted into calcium carbide (CaC\(_2\)) and carbon monoxide (CO).

• This chemical process is highly significant in industrial applications, particularly in the production of acetylene gas.
• Calcium oxide is also used in various chemical processes, waste treatment, and as a desiccant due to its ability to react readily with water.
• Its chemical reactivity makes understanding its potential energy changes during reactions valuable both in practical and theoretical chemistry contexts.

Appreciating the behavior of calcium oxide in reactions helps chemists develop efficient processes, predict reaction conditions, and improve outcomes in its numerous applications. The endothermic nature of its reaction with carbon also hints at potential uses for controlling temperature and energy within industrial settings.