Problem 34 - 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. \(\mathrm{CaO}(\mathrm{s})+3 \mathrm{C}(\mathrm{s}) \rightarrow \mathrm{CaC}_{2}(\mathrm{s})+\mathrm{CO}(\mathrm{g})\) $$ \Delta_{1} H^{\circ}=+464.8 \mathrm{kJ} / \mathrm{mol}-\mathrm{rxn} $$ 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, and the enthalpy change is approximately 82.8 kJ.

Step 1: Determine Reaction Type

The reaction is endothermic because the enthalpy change \( \Delta_1 H^{\circ} = +464.8 \, \text{kJ/mol-rxn} \) is positive, indicating that heat is absorbed during the reaction.

Step 2: Calculate Moles of CaO

First, determine the molar mass of \( \mathrm{CaO} \).\( \mathrm{Ca} \) has an atomic mass of 40.08 g/mol and \( \mathrm{O} \) has an atomic mass of 16.00 g/mol.\[ \text{Molar mass of } \mathrm{CaO} = 40.08 + 16.00 = 56.08 \, \text{g/mol} \]Next, calculate the moles of \( \mathrm{CaO} \) in 10.0 g.\[ \text{Moles of } \mathrm{CaO} = \frac{10.0 \, \text{g}}{56.08 \, \text{g/mol}} \approx 0.178 \mathrm{mol} \]

Step 3: Calculate Enthalpy Change for the Given Mass

Since the reaction enthalpy \( \Delta_1 H^{\circ} \) is given per mole of reaction, use the moles calculated to find the total enthalpy change.\[ \Delta H = 0.178 \, \text{mol} \times 464.8 \, \text{kJ/mol} \approx 82.8 \, \text{kJ} \]

Key Concepts

Endothermic Reactions in Chemistry

In chemistry, reactions can either absorb or release heat. This determines if they are endothermic or exothermic. An endothermic reaction requires an input of energy, usually in the form of heat. Thus, energy is absorbed from the surroundings. This is why the surroundings often feel cooler. An indicator of an endothermic reaction is a positive enthalpy change (\(\Delta H > 0\)). This means that the energy gained from breaking bonds in the reactants is less than the energy required to form bonds in the products.
If a reaction is said to be endothermic, like in our calcium carbide production process, it requires external heat to proceed.

• Positive enthalpy change = endothermic
• Energy absorbed = cooler surroundings

Understanding whether a reaction is endothermic is crucial for industrial processes. This determines how energy will be managed during manufacturing.

Calcium Carbide Production and Its Significance

Calcium carbide production is an important industrial process. It involves reacting calcium oxide (\(\mathrm{CaO}\)) with carbon (\(\mathrm{C}\)) to produce calcium carbide (\(\mathrm{CaC}_2\)). The chemical equation is:
\[\mathrm{CaO} + 3 \mathrm{C} \rightarrow \mathrm{CaC}_{2} + \mathrm{CO}\]
This reaction takes place at a high temperature. Calcium carbide is essential for making acetylene gas, used often as a fuel and in welding.
In the equation, the production of calcium carbide involves a significant absorption of heat, as indicated by its positive enthalpy change. These types of reactions often require a controlled environment due to their high energy demands.

• Reactants: \(\mathrm{CaO}\) and \(\mathrm{C}\)
• Products: \(\mathrm{CaC}_{2}\) and carbon monoxide (\(\mathrm{CO}\))
• Used to produce acetylene

Knowing about calcium carbide's production helps understand broader topics like energy management in chemical manufacturing.

Understanding Mole Calculations

To find out how much calcium carbide can be produced or how much heat is absorbed, we often need to calculate moles. A mole is a unit that measures the amount of a substance. It's based on Avogadro's number, which is approximately \(6.022 \times 10^{23}\) particles per mole.
When determining moles of a substance like \(\mathrm{CaO}\), two steps are key: finding the molar mass and using it to convert from grams. For \(\mathrm{CaO}\):

• Atomic mass of calcium (\(\mathrm{Ca}\)): 40.08 g/mol
• Atomic mass of oxygen (\(\mathrm{O}\)): 16.00 g/mol
• Molar mass of \(\mathrm{CaO}\): \(56.08 \text{ g/mol}\)

Calculating moles for a given mass uses the formula:
\[\text{Moles} = \frac{\text{mass in grams}}{\text{molar mass in g/mol}}\]
Grasping this concept is vital for translating mass measurements into amounts that chemists and engineers use for practical applications.

Calculating Enthalpy Change

The enthalpy change provides insights into the energy dynamics of a chemical reaction. To calculate the enthalpy change for a specific amount of reactant, in this case \(\mathrm{CaO}\), knowing the amount in moles is crucial.
The standard enthalpy change, given in kJ/mol, tells us the energy involved per mole of reaction. For our example, \(\Delta_1 H^{\circ} = +464.8 \, \text{kJ/mol-rxn}\).
To find the total enthalpy change for the reaction involving 10.0 g of \(\mathrm{CaO}\):

• Calculate moles of \(\mathrm{CaO}\): \(0.178 \text{ mol}\)
• Use \(\Delta H = \text{moles} \times \Delta_1 H^{\circ}\)
• \(\Delta H \approx 82.8 \, \text{kJ}\)

This shows that about 82.8 kJ of energy is absorbed due to the reaction, illustrating the energy requirements for transformation. Such calculations are critical for designing and scaling up industrial processes.