Problem 94 - General Chemistry

Question

Calcium oxide (quicklime) reacts with water to produce calcium hydroxide (slaked lime). $$ \mathrm{CaO}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(s) ; \Delta H=-65.2 \mathrm{~kJ} $$ The heat released by this reaction is sufficient to ignite paper. How much heat is released when \(24.5 \mathrm{~g}\) of calcium oxide reacts?

Step-by-Step Solution

Answer

Approximately -28.5 kJ of heat is released.

Step 1: Convert grams to moles

First, we need to determine how many moles of calcium oxide (CaO) we have. The molar mass of CaO is the sum of the atomic masses of calcium \((40.08 \, \text{g/mol})\) and oxygen \((16.00 \, \text{g/mol})\), which gives a total of \((56.08 \, \text{g/mol})\). Therefore, we convert the given mass of 24.5 g of CaO to moles using the formula: \[ \text{moles of CaO} = \frac{24.5 \, \text{g}}{56.08 \, \text{g/mol}} \approx 0.437 \text{ mol} \]

Step 2: Calculate heat released per mole

From the balanced chemical equation, the reaction releases \(-65.2\) kJ of heat per 1 mole of CaO reacted. Therefore, we will use this information to find the total heat released.

Step 3: Calculate total heat released

Now, use the number of moles of CaO calculated in Step 1 to find the total heat released via the reaction:\[ \text{Heat released} = 0.437 \, \text{mol} \times (-65.2 \, \text{kJ/mol}) \approx -28.5 \, \text{kJ} \]This shows that approximately -28.5 kJ of heat is released when 24.5 g of CaO reacts with water.

Key Concepts

Enthalpy Change

When we talk about enthalpy change (\( \Delta H \)), we are referring to the heat change at constant pressure during a chemical reaction. In the reaction of calcium oxide (CaO) with water, the given \( \Delta H \) value of -65.2 \, \text{kJ/mol} indicates that this process is exothermic. Exothermic reactions release energy, in this case, heat is let off into the surroundings.

Reactants with higher energy transform into lower-energy products. The excess energy is released as heat, which can be enough to ignite paper, as mentioned in our exercise. Enthalpy changes are vital for understanding whether a reaction will be hot or cold.

• Exothermic reactions (\( \Delta H \)<0): Release heat; often feels hot.
• Endothermic reactions (\( \Delta H \)>0): Absorb heat; often feels cold.

In this case of calcium oxide and water, the heat release is -65.2 \text{kJ} for each mole of CaO reacting, which points to a spontaneous and energetically favorable reaction.

Moles Calculation

Calculating moles is a cornerstone in chemistry as it allows us to understand quantities in a chemical reaction. Moles denote the amount of substance, helping us to convert between masses and volume.

To find out how many moles of calcium oxide we have from our 24.5 \text{g} sample, we use the formula:\[ \text{moles of CaO} = \frac{\text{mass of CaO (g)}}{\text{molar mass of CaO (g/mol)}}\]Given that the molar mass of CaO is 56.08 \text{g/mol}, we calculate:\[ \frac{24.5 \, \text{g}}{56.08 \, \text{g/mol}} \approx 0.437 \, \text{mol}\]

Through this calculation, we deduced that 24.5 \text{g} of calcium oxide is equal to approximately 0.437 moles. This vital step allows for the further calculation of the heat released as a result of this chemical reaction.

Calcium Oxide Reaction

Calcium oxide, commonly known as quicklime, reacts quite significantly with water in a process that we write as:\[ \text{CaO}(s) + \text{H}_2\text{O}(l) \rightarrow \text{Ca(OH)}_2(s)\]This reaction forms calcium hydroxide (Ca(OH)_2), known as slaked lime. The reaction is not only notable for its chemical transformation but also the energy it releases.

The quicklime reacts with water, releasing 65.2 \text{kJ} of heat per mole of CaO. It is a classic example of an exothermic reaction capable of igniting flammable materials such as paper due to the intense heat release. The transformation is complete when given sufficient water, and it is widely used in various industrial processes.

• Purification in metallurgy.
• Neutralizing acidic soils.
• Producing mortars and plasters for building.

Understanding this reaction is crucial, especially given the heat release and its implications in both laboratory settings and industrial applications.