Question

Instant hot packs and cold packs contain a solid salt in a capsule that is broken and dissolved in water to produce a temperature change. Which of the following salts would result in greatest decrease in temperature when dissolved in \(100.0 \mathrm{~mL}\) of water in a cold pack? Use the following thermochemical data to answer the question. \(\mathrm{LiF}(s) \longrightarrow \mathrm{Li}^{+}(a q)+\mathrm{F}(a q)\) \(\Delta H^{\circ}=+5.5 \mathrm{k} \mathrm{J}\) \(\mathrm{LiCl}(s) \longrightarrow \mathrm{Li}^{+}(a q)+\mathrm{Cl}^{-}(a q)\) \(\Delta H^{\circ}=-37.1 \mathrm{~kJ}\) \(\mathrm{BaSO}_{4}(s) \longrightarrow \mathrm{Ba}^{2+}(a q)+\mathrm{SO}_{4}^{2-}(a q) \quad \Delta H^{\circ}=+26.3 \mathrm{~kJ}\) \(\mathrm{CaCl}_{2}(s) \longrightarrow \mathrm{Ca}^{2+}(a q)+2 \mathrm{Cl}(a q) \quad \Delta H^{\circ}=-81.8 \mathrm{~kJ}\) (a) \(10.0 \mathrm{~g}\) of \(\mathrm{LiF}\) (b) \(10.0 \mathrm{~g}\) of \(\mathrm{BaSO}_{4}\) (c) \(10.0 \mathrm{~g}\) of \(\mathrm{LiCl}\) (d) \(10.0 \mathrm{~g}\) of \(\mathrm{CaCl}_{2}\)

Short answer

LiF absorbs the most heat, thus leading to the greatest temperature decrease.

Step-by-step solution

Determining Moles of Each Salt

First, determine the molar mass of each salt to calculate the number of moles in 10.0 g of the substance. - For \(\text{LiF}\), \(\text{Molar Mass} = 25.94\, \text{g/mol}\). - For \(\text{BaSO}_4\), \(\text{Molar Mass} = 233.39\, \text{g/mol}\). - For \(\text{LiCl}\), \(\text{Molar Mass} = 42.39\, \text{g/mol}\). - For \(\text{CaCl}_2\), \(\text{Molar Mass} = 110.98\, \text{g/mol}\). Calculate moles for each: - \(\text{LiF:} \frac{10.0\, \text{g}}{25.94\, \text{g/mol}} = 0.385\, \text{mol}\) - \(\text{BaSO}_4: \frac{10.0\, \text{g}}{233.39\, \text{g/mol}} = 0.043\, \text{mol}\) - \(\text{LiCl:} \frac{10.0\, \text{g}}{42.39\, \text{g/mol}} = 0.236\, \text{mol}\) - \(\text{CaCl}_2: \frac{10.0\, \text{g}}{110.98\, \text{g/mol}} = 0.090\, \text{mol}\)

Calculating Heat Absorbed or Released

Use enthalpy change (\(\Delta H^\circ\)) per mole to determine the total enthalpy change for dissolving each salt in water. - \(\text{LiF: } \Delta H = 0.385\, \text{mol} \times (+5.5\, \text{kJ/mol}) = +2.12\, \text{kJ}\) - \(\text{BaSO}_4: \Delta H = 0.043\, \text{mol} \times (+26.3\, \text{kJ/mol}) = +1.13\, \text{kJ}\) - \(\text{LiCl: } \Delta H = 0.236\, \text{mol} \times (-37.1\, \text{kJ/mol}) = -8.75\, \text{kJ}\) - \(\text{CaCl}_2: \Delta H = 0.090\, \text{mol} \times (-81.8\, \text{kJ/mol}) = -7.36\, \text{kJ}\)

Analyzing Heat Changes

A greater positive \(\Delta H\) indicates endothermic processes that absorb more heat and decrease the temperature more. Compare the values calculated. - Greater the positive value \(\Delta H\), the larger the decrease in temperature because more heat is absorbed. - From Step 2: LiF has a \(\Delta H = +2.12\, \text{kJ}\), BaSO4 has \(\Delta H = +1.13\, \text{kJ}\). Both are endothermic, but LiF absorbs more heat. - LiCl and CaCl2 are exothermic with negative \(\Delta H\), which means they release heat instead of absorbing it.

Conclusion

Since LiF has the highest positive enthalpy change among the salts that have endothermic reactions, it will result in the greatest decrease in temperature when dissolved in the water of a cold pack. Choose LiF for maximum cooling effect.

Key concepts

Thermochemistry

Thermochemistry is the branch of chemistry that studies the relationship between chemical reactions and heat changes. When chemicals react, energy is either absorbed or released, and thermochemistry involves understanding these processes in detail.
A key component is analyzing whether a reaction is endothermic or exothermic.

• Endothermic Reactions: These processes absorb heat from their surroundings, resulting in a cooling effect. When a salt is dissolved and the reaction is endothermic, it means more heat is taken from the surroundings, resulting in a decrease in temperature.
• Exothermic Reactions: In contrast, these release heat, warming the surroundings.

Understanding these concepts is essential for predicting temperature changes during chemical reactions. Thermochemistry helps us identify which substances will cause noticeable temperature shifts in practical applications like hot or cold packs. By studying the enthalpy changes of reactions, we can predict their thermal effects and choose appropriate materials for specific uses.

Enthalpy Change

Enthalpy change (denoted as \( \Delta H \)) is a measure of heat change at constant pressure. If a reaction absorbs heat, \( \Delta H \) is positive, indicating an endothermic process. When heat is released, \( \Delta H \) is negative, showing an exothermic process.
To understand enthalpy changes, consider the process of dissolving salts in water:

• Each salt has a specific enthalpy change value that describes how much heat is absorbed or released when it dissolves.
• When calculating enthalpy change, it's crucial to consider the number of moles involved. The enthalpy per mole allows you to calculate the total heat effect if you know the amount of substance reacting.
• Higher positive \( \Delta H \) values imply greater heat absorption, resulting in a greater cooling effect, as the reaction pulls more heat from its surroundings.

This concept is pivotal in choosing materials for cold packs, where the goal is to maximize temperature decrease by maximizing the heat absorbed.

Heat Absorption

Heat absorption refers to the process by which substances take in energy from their surroundings. In the context of chemical reactions, certain substances absorb heat, thus having a cooling effect on their environment.
Examining how different salts absorb heat when dissolved can help us understand their applications in cooling technologies:

• Endothermic reactions are specifically associated with heat absorption since they require energy from the surroundings to proceed. As heat is pulled from the environment, the temperature around them decreases.
• Calculation of heat absorbed involves multiplying the number of moles of the substance by the enthalpy change per mole. This gives the total energy change, indicating how much heat is absorbed.
• For practical applications such as cold packs, salts with high heat absorption capability are desirable due to their ability to cool their surroundings effectively.

Understanding the dynamics of heat absorption helps in the selection of materials that are efficient for cooling, highlighting the importance of detailed thermochemical data in designing chemical-based cooling solutions.