Question

In a \(600 \mathrm{~mL}\) solution, \(0.50 \mathrm{~mol}\) of \(\mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{aq})\) and \(0.50 \mathrm{~mol}\) of \(\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq})\) are combined. The temperature of the solution increases by \(22.3^{\circ} \mathrm{C}\). What is the heat of the reaction, and what is the \(\Delta H\) of the reaction on a molar basis? Assume the solution has the same density and heat capacity of water.

Short answer

\(\Delta H = -111.876 \, \text{kJ/mol}\).

Step-by-step solution

Understand the Reaction

The reaction between calcium hydroxide and sulfuric acid is a neutralization reaction. The balanced chemical equation is:\[ \text{Ca(OH)}_2(aq) + \text{H}_2\text{SO}_4(aq) \rightarrow \text{CaSO}_4(s) + 2\text{H}_2\text{O}(l) \]

Determine the Heat of Reaction (q)

To calculate the heat of the reaction \(q\), use the formula: \[ q = m \cdot c \cdot \Delta T \]where \(m\) is the mass of the solution, \(c\) is the specific heat capacity of water (\(4.18 \, \text{J/g}^\circ\text{C}\)), and \( \Delta T \) is the change in temperature (\(22.3^\circ\text{C}\)).Assuming the density of water is \(1 \, \text{g/mL}\), the mass \(m\) is \(600 \, \text{g}\).Therefore: \[ q = 600 \, \text{g} \times 4.18 \, \text{J/g}^\circ\text{C} \times 22.3^\circ\text{C} \] \[ q = 55,938 \, \text{J} \] or \(55.938 \, \text{kJ}\).

Calculate \(\Delta H\) on a Molar Basis

The moles of limiting reactant for the reaction are both \(0.50 \, \text{mol}\). Since they are equal, they completely neutralize each other.The \(\Delta H\) per mole can be calculated by dividing the total heat by the moles of either reactant:\[ \Delta H = \frac{q}{\text{moles}} = \frac{55.938 \, \text{kJ}}{0.50 \, \text{mol}} = 111.876 \, \text{kJ/mol} \]

Report the Sign of \(\Delta H\)

Since the temperature of the solution increased, the reaction is exothermic. Therefore, \(\Delta H\) should be negative:\[ \Delta H = -111.876 \, \text{kJ/mol} \]

Key concepts

Neutralization Reaction

Neutralization reactions involve an acid and a base reacting to form a salt and water. In this case, calcium hydroxide \(\text{Ca(OH)}_2\), which is a base, reacts with sulfuric acid \(\text{H}_2\text{SO}_4\). When these two substances combine, they undergo a chemical change that results in the formation of calcium sulfate \(\text{CaSO}_4\) and water \(\text{H}_2\text{O}\).
\[ \text{Ca(OH)}_2(aq) + \text{H}_2\text{SO}_4(aq) \rightarrow \text{CaSO}_4(s) + 2\text{H}_2\text{O}(l) \]

These types of reactions are essential in many areas, including chemistry labs and industrial applications, where they help mitigate or neutralize acidic or basic wastes. The neutralization process usually results in the release or absorption of energy. In this example, the solution's temperature rise indicates the reaction is exothermic, releasing heat into the surroundings.

Heat of Reaction

The heat of reaction, often represented by \(q\), measures the change in thermal energy during a reaction. This is crucial in determining whether a reaction is exothermic (releases heat) or endothermic (absorbs heat). In the given scenario, the reaction between \(\text{Ca(OH)}_2\) and \(\text{H}_2\text{SO}_4\) resulted in a temperature increase of the solution, which signifies an exothermic process.

To calculate \(q\), use the formula:
\[ q = m \times c \times \Delta T \]
where:

\
• \(m\) is the mass of the solution
• \(c\) is the specific heat capacity of the solution (and water, in this case)
• \(\Delta T\) is the change in temperature\

The mass \(m\) here is assumed to be \(600 \text{ g}\) as the density of water is \(1 \text{ g/mL}\). The specific heat capacity \(c\) for water is approximately \(4.18 \text{ J/g}^\circ\text{C}\). Finally, \(\Delta T\) is \(22.3^\circ\text{C}\). Substituting these values, we get \(q = 55.938 \text{ kJ}\). This result shows how much energy is released as heat during the reaction.

Specific Heat Capacity

Specific heat capacity is a property that defines how much energy is required to change the temperature of a certain mass of a substance by one degree Celsius. It's a fundamental concept in calorimetry, where it allows the determination of heat transfer in a system. The specific heat capacity is unique to each material. For water, this value is relatively high at \(4.18 \text{ J/g}^\circ\text{C}\).

This means water can absorb or release a relatively large amount of heat with only a small temperature change. In calorimetry tasks, like calculating the heat of reaction, we often assume the solution has the same heat capacity as water for simplicity. Understanding the specific heat capacity helps predict how a substance behaves when subjected to thermal energy and is crucial for designing experiments and industrial processes efficiently.