Problem 61 - Chemistry The Science in Context

Question

If you were designing a chemical cold pack, which of the following salts would you choose to provide the greatest drop in temperature per gram: \(\mathrm{NH}_{4} \mathrm{Cl}\) \(\left(\Delta H_{\text {soln }}=14.6 \mathrm{kJ} / \mathrm{mol}\right), \mathrm{NH}_{4} \mathrm{NO}_{3}\left(\Delta H_{\text {soln }}=25.7 \mathrm{kJ} / \mathrm{mol}\right),\) or \(\mathrm{NaNO}_{3}\left(\Delta H_{\mathrm{soln}}=20.4 \mathrm{kJ} / \mathrm{mol}\right) ?\)

Step-by-Step Solution

Answer

Answer: NH4NO3

Step 1: Calculate the molar masses of the given salts

To compare the salts, we first need to find the molar mass of each salt. Use the periodic table to find the atomic masses of each element involved and add them together to calculate the molar mass of the salt: For NH4Cl: Molar mass = 14.01 (N) + 4 * 1.01 (H) + 35.45 (Cl) Molar mass = 53.49 g/mol For NH4NO3: Molar mass = 14.01 (N) + 4 * 1.01 (H) + 14.01 (N) + 3 * 16.00 (O) Molar mass = 80.05 g/mol For NaNO3: Molar mass = 22.99 (Na) + 14.01 (N) + 3 * 16.00 (O) Molar mass = 85.00 g/mol

Step 2: Calculate the drop in temperature per gram for each salt

To find the temperature change per gram for each salt, divide the enthalpy of solution (ΔH_soln) by the molar mass: For NH4Cl: Drop in temperature per gram = (14.6 kJ/mol) / (53.49 g/mol) = 0.273 kJ/g For NH4NO3: Drop in temperature per gram = (25.7 kJ/mol) / (80.05 g/mol) = 0.320 kJ/g For NaNO3: Drop in temperature per gram = (20.4 kJ/mol) / (85.00 g/mol) = 0.240 kJ/g

Step 3: Compare the values obtained and determine the best salt for the cold pack

Now that we have the drop in temperature per gram for each salt, we can compare these values to determine which salt would provide the greatest drop in temperature per gram: NH4Cl: 0.273 kJ/g NH4NO3: 0.320 kJ/g NaNO3: 0.240 kJ/g Since NH4NO3 has the highest value (0.320 kJ/g), it will produce the greatest drop in temperature per gram. So, NH4NO3 would be the best choice for designing a chemical cold pack.

Key Concepts

Thermochemistry

Thermochemistry is the branch of chemistry that deals with the relationships between chemical reactions and energy changes involving heat. Specifically, in the context of the exercise, the focus is on the enthalpy of solution, which is the heat change associated with the dissolving of a compound in a solvent. This process can be either exothermic (releasing heat) or endothermic (absorbing heat).

Understanding the enthalpy of solution is critical when designing products such as chemical cold packs, which are used to treat injuries or reduce inflammation. If a salt's enthalpy of solution is endothermic, the salt will absorb heat as it dissolves, resulting in a cooling effect. The greater the ratio of heat absorbed to the amount of salt used, the more efficient the cold pack will be.

Chemical Cold Pack

A chemical cold pack takes advantage of an endothermic chemical reaction to absorb heat from its surroundings and provide localized cold therapy. When the substances inside a cold pack—a typically water and a salt—are mixed, the salt dissolves and the process absorbs heat, leading to a temperature drop.

The choice of the salt is crucial, as different salts will have different enthalpies of solution. The ideal salt for a cold pack is one that has a high enthalpy of solution and is safe, cost-effective, and non-toxic. In the textbook exercise, students are asked to assess which salt would be the most suitable for this purpose based on enthalpy values and molar masses, providing a practical example of thermochemical considerations in product design.

Molar Mass Calculation

Molar mass calculation is an essential skill in chemistry, as it allows us to convert between the mass of a substance and the amount of substance (in moles). This conversion is fundamental to stoichiometry, which is the calculation of reactants and products in chemical reactions.

In the provided exercise, students calculate the molar mass of several salts by adding together the atomic masses of the constituent elements. The calculated molar mass then helps determine how much heat is absorbed per gram of each salt when dissolved in water. Calculating molar mass is vital for many laboratory and industrial processes, including the design of chemical cold packs, as it aids in determining the optimal amount of material needed for the desired thermal effect.