Instant cold packs used to treat athletic injuries contain solid NH4NO3 and a pouch of water. When the pack is squeezed, the pouch breaks and the solid dissolves, lowering the tem-perature because of the endothermic reaction NH4NO31s2 ¡ NH4NO31aq2 ∆H = +25.7 kJ What is the final temperature in a squeezed cold pack that contains 50.0 g of NH4NO3 dissolved in 125 mL of water? Assume a specific heat of 4.18 J/(g C) for the solution, an initial temperature of 25.0 °C, and no heat transfer between the cold pack and the environment.

Verified step by step guidance

1. Calculate the moles of NH4NO3 used by using its molar mass. The molar mass of NH4NO3 is approximately 80 g/mol.
2. Determine the total heat absorbed by the solution using the enthalpy change of the reaction (∆H). Multiply the moles of NH4NO3 by the ∆H value given (+25.7 kJ/mol).
3. Convert the heat absorbed from kJ to Joules to match the units of specific heat (1 kJ = 1000 J).
4. Calculate the change in temperature using the formula: ∆T = q / (m * c), where q is the heat absorbed in Joules, m is the mass of the solution (mass of water plus mass of NH4NO3), and c is the specific heat of the solution (4.18 J/(g°C)).
5. Subtract the change in temperature (∆T) from the initial temperature of the solution to find the final temperature of the cold pack.

Key Concepts

Endothermic Reactions

Endothermic reactions absorb heat from their surroundings, resulting in a decrease in temperature. In the case of the cold pack, the dissolution of NH4NO3 is an endothermic process, which means it requires energy to break the ionic bonds in the solid, leading to a cooling effect. This concept is crucial for understanding why the temperature drops when the pack is activated.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. For the solution in the cold pack, the specific heat is given as 4.18 J/(g°C). This property is essential for calculating how much the temperature of the solution will change when a certain amount of heat is absorbed during the dissolution of NH4NO3.

Heat Transfer and Conservation of Energy

The principle of conservation of energy states that energy cannot be created or destroyed, only transformed. In the context of the cold pack, the heat absorbed by the dissolution of NH4NO3 must equal the heat lost by the water in the pack. This relationship allows us to set up an equation to find the final temperature of the solution after the cold pack is activated.