Problem 68 - General Chemistry

Question

When \(23.6 \mathrm{~g}\) of calcium chloride, \(\mathrm{CaCl}_{2}\), was dissolved in water in a calorimeter, the temperature rose from \(25.0^{\circ} \mathrm{C}\) to \(38.7^{\circ} \mathrm{C}\). If the heat capacity of the solution and the calorimeter is \(1258 \mathrm{~J} /{ }^{\circ} \mathrm{C}\), what is the enthalpy change when \(1.20 \mathrm{~mol}\) of calcium chloride dissolves in water? The solution process is $$ \mathrm{CaCl}_{2}(s) \longrightarrow \mathrm{Ca}^{2+}(a q)+2 \mathrm{Cl}^{-}(a q) $$

Step-by-Step Solution

Answer

The enthalpy change for 1.20 mol of dissolving \( \mathrm{CaCl}_2 \) is approximately 97.2 kJ.

Step 1: Identify Known Values

We know the mass of calcium chloride, \( m = 23.6 \, \mathrm{g} \), initial temperature, \( T_i = 25.0^{\circ} \, \mathrm{C} \), and final temperature, \( T_f = 38.7^{\circ} \, \mathrm{C} \). The heat capacity of the solution and calorimeter, \( C = 1258 \, \mathrm{J}/{\circ} \mathrm{C} \).

Step 2: Calculate Temperature Change

Calculate the temperature change using the formula: \( \Delta T = T_f - T_i \). \[ \Delta T = 38.7^{\circ} \mathrm{C} - 25.0^{\circ} \mathrm{C} = 13.7^{\circ} \mathrm{C} \]

Step 3: Calculate Heat Absorbed

The heat absorbed, \( q \), is calculated using the formula: \( q = C \cdot \Delta T \). \[ q = 1258 \, \mathrm{J}/{\circ} \mathrm{C} \times 13.7^{\circ} \mathrm{C} = 17224.6 \, \mathrm{J} \]

Step 4: Convert Heat Absorbed to Enthalpy Change Per Mole

Since we need the enthalpy change for \( 1.20 \, \mathrm{mol} \) of \( \mathrm{CaCl}_2 \), convert \( q \) to kilojoules and then calculate the enthalpy change per mole. \[ \Delta H = \frac{17224.6 \, \mathrm{J}}{1000} = 17.2246 \, \mathrm{kJ} \]

Step 5: Calculate Moles of Initial Calcium Chloride

First, calculate the moles of calcium chloride used in the experiment with its molar mass being approximately \( 40.08 + 2 \times 35.45 = 110.98 \, \mathrm{g/mol} \). \[ \text{Moles of } \mathrm{CaCl}_2 = \frac{23.6 \, \mathrm{g}}{110.98 \, \mathrm{g/mol}} = 0.2125 \, \mathrm{mol} \]

Step 6: Determine Enthalpy Change for 1.20 mol

Now, scale the enthalpy change to find it for \( 1.20 \, \mathrm{mol} \) using the ratio of moles: \[ \Delta H_{1.20 \, \mathrm{mol}} = \frac{17.2246 \, \mathrm{kJ}}{0.2125 \, \mathrm{mol}} \times 1.20 \, \mathrm{mol} \approx 97.2 \, \mathrm{kJ} \]

Key Concepts

Calorimetry

Calorimetry is a fascinating technique used to measure the amount of heat involved in chemical reactions or physical changes. This method is essential for understanding how substances interact with each other energetically.

When you think about calorimetry, picture a special container known as a calorimeter. This device helps capture heat changes in a carefully controlled environment.

For instance, if you dissolve a substance like calcium chloride in water, a calorimeter can help you see how much the temperature changes.

• The change in temperature tells us how much heat was absorbed or released by the substance.
• In our case, the calorimeter absorbs the heat given off by the dissolution process, noting the start and end temperatures.

This provides crucial data to calculate the overall enthalpy change for the process.

Heat Capacity

Heat capacity is a key concept related to the ability of a substance to absorb heat without significantly changing temperature. It's a property that tells us how much heat energy a substance can hold.

The specific heat capacity depends on the material, while the calorimeter and solution have a total measured heat capacity.

This means when we hear that the heat capacity is 1258 J/°C, we know:

• It takes 1258 joules of energy to raise the temperature of the entire setup by 1°C.
• This value integrates both the calorimeter and the solution's abilities to absorb heat.

Using this information, we can determine and quantify the heat absorbed during the process, which in turn helps calculate the enthalpy change.

Chemical Reactions

All chemical reactions involve changes in energy. These energy changes are crucial as they can tell us a lot about the stability or reactivity of substances.

In the case of calcium chloride dissolving in water, the reaction must be monitored closely because it includes energy exchange between reactants and products.
Let's break down the process:

• Calcium chloride ( CaCl_2 ) is a solid that dissociates into ions when dissolved.
• The process is represented by the reaction: ( CaCl_2 ightarrow Ca^{2+} + 2Cl^{-} )

By using calorimetry, these energetic changes become apparent.

Knowing how heat is exchanged during reactions helps chemists tailor processes, enhancing efficiency and safety, especially in industrial applications.

Calcium Chloride Dissolution

Dissolution is a process where a solute, such as calcium chloride, breaks down into its constituent ions in a solvent, like water. This event is common in many chemistry applications.

During the dissolution of calcium chloride, you observe an increase in temperature, indicating it's an exothermic process.

• The term "exothermic" means that the process releases heat into the surrounding environment.
• This release of heat is the energy required to break the ionic bonds in the solid and allows calcium chloride to separate into ( Ca^{2+} ) and ( 2Cl^{-} ) ions.

Once dissolved, these ions interact with water molecules, stabilizing them in solution. Understanding such processes helps predict the behavior of ions in solutions, critical for calculating the enthalpy change, which offers insights into the energetics of the reaction.