Problem 39 - General Chemistry: Principles and Modern Applications

Question

A 0.75 g sample of \(\mathrm{KCl}\) is added to \(35.0 \mathrm{g} \mathrm{H}_{2} \mathrm{O}\) in a Styrofoam cup and stirred until it dissolves. The temperature of the solution drops from 24.8 to \(23.6^{\circ} \mathrm{C}\) (a) Is the process endothermic or exothermic? (b) What is the heat of solution of KCl expressed in kilojoules per mole of KCl?

Step-by-Step Solution

Answer

(a) The process is endothermic. (b) The molar heat of solution of KCl is -17.32 kJ/mol.

Step 1: Identifying the type of process

The process is endothermic or exothermic based on whether the temperature drops or rises respectively. Given that the temperature drops from \(24.8^{\circ} \mathrm{C}\) to \(23.6^{\circ} \mathrm{C}\), it's clear that it's an endothermic reaction.

Step 2: Calculating change in temperature

\(\Delta T = T_f - T_i =(23.6^{\circ} \mathrm{C} - 24.8^{\circ} \mathrm{C}) = -1.2^{\circ} \mathrm{C} \). Where \(T_i\) and \(T_f\) are the initial and final temperatures respectively.

Step 3: Converting grams to moles

The number of moles of KCl = mass/molar mass = 0.75 g / 74.5513 g/mol = 0.01006 mol.

Step 4: Calculate the heat gained

Using the formula \(q=mc\Delta T\). The specific heat capacity of water (\(c\)) is usually given as 4.18 J/gC. The mass of water (\(m\)) is given as 35g and \(\Delta T\) as calculated in step 2 is -1.2C. Therefore, \(q = 35g * 4.18 J/gC * -1.2C = -174.36 J\).

Step 5: Convert J to kJ and then divide by moles of solute

This will give the heat of solution of KCl in kJ/mol. Since 1 Joule = 0.001 kJ, first convert J to kJ (-174.36 J = -0.17436 kJ) and then divide by number of moles. That is \(-0.17436kJ / 0.01006mol = -17.32 kJ/mol \)

Key Concepts

Heat of Solution

When a substance dissolves in a solvent, an energy exchange occurs—either absorbing or releasing heat. The heat of solution measures this energy change and indicates whether the process is endothermic or exothermic. In an endothermic reaction, like the one with KCl dissolving in water, the system absorbs heat from the surroundings, resulting in a temperature drop. By calculating the heat absorbed, you determine the heat of solution. It is expressed in kilojoules per mole (kJ/mol), which provides a standardized view of the energy change for each mole of solute. To find the heat of solution, measure the temperature change, calculate the heat absorbed using the specific heat of the solvent, and then scale it to a per-mole basis.

Molar Mass Conversion

Understanding how to convert between mass and moles is fundamental in chemistry. Molar mass serves as the bridge, as it tells you the mass of one mole of a substance typically expressed in grams per mole (g/mol). For KCl, the molar mass is approximately 74.5513 g/mol. In practical applications, like determining the heat of solution, you start by converting the sample mass into moles. This involves dividing the mass (in grams) by the molar mass, yielding the number of moles. This step is crucial as it allows you to relate mass measurements to chemical quantities, which are often given in moles when discussing chemical reactions and thermodynamic properties.

Specific Heat Capacity

Specific heat capacity is a property of a substance that tells us how much heat is required to change the temperature of one gram of the material by one degree Celsius (or Kelvin). Water, for example, has a relatively high specific heat capacity of 4.18 J/g°C, meaning it requires considerable heat to change its temperature. This property is particularly useful in determining the heat change in reactions involving aqueous solutions, like the dissolution of KCl. By multiplying the mass of the water, the specific heat capacity, and the change in temperature, you can calculate the total heat change (denoted as \( q \)) in the process. In our scenario, since the dissolution is endothermic, \( q \) is negative, indicating the water loses heat as KCl absorbs it.