Problem 22 - General Chemistry: Principles and Modern Applications

Question

The heat of solution of \(\mathrm{KI}(\mathrm{s})\) in water is \(+20.3 \mathrm{kJ} / \mathrm{mol}\) KI. If a quantity of KI is added to sufficient water at \(23.5^{\circ} \mathrm{C}\) in a Styrofoam cup to produce \(150.0 \mathrm{mL}\) of 2.50 M KI, what will be the final temperature? (Assume a density of \(1.30 \mathrm{g} / \mathrm{mL}\) and a specific heat of \(2.7 \mathrm{Jg}^{-1}\) \(\left.^{\circ} \mathrm{C}^{-1} \text {for } 2.50 \mathrm{M} \mathrm{KI} .\right)\)

Step-by-Step Solution

Answer

The final temperature of the solution will be 37.8 °C.

Step 1: Calculate the moles of \(\mathrm{KI}\)

Firstly, we need to determine the amount of \(\mathrm{KI}\) in moles. To do so, multiply the volume of the solution by its molarity: \(n = V \cdot M\) where \(V = 150 \, mL = 0.150 \, L\) and \(M = 2.5 \, M\). Thus, \(n = 0.150 \, L \cdot 2.5 \, mol/L = 0.375 \, mol\).

Step 2: Calculate the heat of solution Q

The heat of solution of \(\mathrm{KI}\) is given as \(+20.3 \, kJ/mol\). Therefore, the total heat produced when \(\mathrm{KI}\) dissolves can be calculated by multiplying the heat of solution per mole by the number of moles dissolved: \(Q = +20.3 \, kJ/mol \cdot 0.375 \, mol = +7.613 \, kJ\). The positive sign indicates this is an endothermic process, so the solution absorbs heat from its surroundings.

Step 3: Convert Q to J

The value of Q obtained in the previous step should be converted from kJ to J because the specific heat is given in J/g°C. \(Q = +7.613 \, kJ = +7613 \, J\).

Step 4: Calculate the mass of the solution

The mass (m) of the solution can be calculated by multiplying the volume of the solution by its density: \(m = V \cdot d = 150 \, mL \cdot 1.30 \, g/mL = 195 \, g\).

Step 5: Determine \(\Delta T\) (change in temperature)

Use the formula \(q=mc\Delta T\) to find \( \Delta T\', which is \( \Delta T=q/(mc)\). The total heat Q=7613 J, the mass m of the solution is 195 g, and the specific heat c is 2.7 J/g°C. So, \( \Delta T = 7613 J / (195 g \cdot 2.7 J/g°C) = \Delta T = 14.3 °C ).

Step 6: Calculate the final temperature

The final temperature is calculated by summing the initial temperature with the change in temperature: \(T_{final} = T_{initial} + \Delta T = 23.5 °C + 14.3 °C = 37.8 °C\).

Key Concepts

Enthalpy Change

Enthalpy change is a measure of the total energy absorbed or released during a chemical reaction at constant pressure. In the context of the heat of solution, it signifies the energy change when a solute dissolves in a solvent. For the exercise we described, the quantity is given as a positive value of +20.3 kJ/mol for KI. This indicates that energy is absorbed from the surroundings.

When dealing with such processes, it is essential to consider whether the enthalpy change is positive or negative. A positive enthalpy change means the process is endothermic, requiring an input of energy. Conversely, a negative change signifies exothermic reactions, where energy is released.

• The enthalpy change helps predict how temperature varies in chemical solutions.
• Note that enthalpy is often measured in kilojoules per mole (kJ/mol).

Understanding enthalpy change is crucial in determining whether the surrounding environment will heat up or cool down during the solution process. Thus, it plays a fundamental role in forecasting the behavior of the reaction.

Endothermic Process

An endothermic process is one in which the system absorbs energy from its surroundings. This absorption usually manifests as a temperature decrease in the surroundings because the system is taking in heat. For our KI solution, the positive enthalpy change implies it's an endothermic process. As KI dissolves in water, energy is drawn from the environment, making the surroundings cooler initially.

It's important to recognize when a process is endothermic:

• Endothermic reactions require energy to proceed, often sourced from the environment.
• Typical signs of such processes include a temperature drop in the surrounding area.

In this exercise, as KI dissolves, the system absorbs 7613 J of energy. This justifies why the process feels cool to the touch initially. Eventually, however, since a protective Styrofoam cup isolate the system, the equilibrium restores, resulting in the observed final temperature increase to 37.8°C.

Specific Heat Capacity

Specific heat capacity is a fundamental concept in understanding how different substances react to heat energy. It is defined as the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius. In the given problem, the specific heat capacity of the KI solution is 2.7 J/g°C. This relatively low specific heat implies that only a small amount of energy is needed to cause a relatively large temperature change.

To apply this in calculations, you must understand that:

• Specific heat capacity is unique to each material.
• A low specific heat means the substance heats up and cools down rapidly.
• Specific heat is typically measured in joules per gram per degree Celsius (J/g°C).

In the exercise, the small specific heat capacity of 2.7 J/g°C allows for significant temperature changes with relatively little heat exchange. This is why the absorbed 7613 J of energy results in a noticeable final temperature increase from 23.5°C to 37.8°C. By understanding this value, you predict how much energy will affect temperature changes.