Instant cold packs used to ice athletic injuries on the field contain ammonium nitrate and water separated by a thin plastic divider. When the divider is broken, the ammonium nitrate dissolves according to the endothermic reaction: NH₄NO₃(s) → NH₄⁺(aq) + NO₃^– (aq) In order to measure the enthalpy change for this reaction, 1.25 g of NH₄NO₃ is dissolved in enough water to make 25.0 mL of solution. The initial temperature is 25.8 °C and the final temperature (after the solid dissolves) is 21.9 °C. Calculate the change in enthalpy for the reaction in kJ. (Use 1.0 g/mL as the density of the solution and 4.18 J/g•°C as the specific heat capacity.)

Verified step by step guidance

1. Calculate the mass of the solution using the density and volume: \( \text{mass} = \text{density} \times \text{volume} \).
2. Determine the temperature change (\( \Delta T \)) by subtracting the final temperature from the initial temperature: \( \Delta T = T_{\text{final}} - T_{\text{initial}} \).
3. Calculate the heat absorbed by the solution using the formula: \( q = m \cdot c \cdot \Delta T \), where \( m \) is the mass of the solution, \( c \) is the specific heat capacity, and \( \Delta T \) is the temperature change.
4. Convert the heat absorbed (\( q \)) from joules to kilojoules by dividing by 1000.
5. Calculate the enthalpy change per mole of \( \text{NH}_4\text{NO}_3 \) by dividing the heat absorbed (in kJ) by the number of moles of \( \text{NH}_4\text{NO}_3 \) dissolved.

Key Concepts

Endothermic Reactions

Endothermic reactions are chemical processes that absorb heat from their surroundings, resulting in a decrease in temperature. In the context of the cold pack, the dissolution of ammonium nitrate is endothermic, meaning it requires energy, which is taken from the water and the surrounding environment, leading to a drop in temperature.

Enthalpy Change (ΔH)

Enthalpy change (ΔH) is a measure of the heat content of a system at constant pressure. It quantifies the energy absorbed or released during a chemical reaction. In this case, calculating ΔH for the dissolution of ammonium nitrate involves determining the heat absorbed by the solution as the temperature decreases.

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 this problem, the specific heat capacity of water (4.18 J/g·°C) is used to calculate the heat absorbed by the solution when the temperature changes, which is essential for determining the enthalpy change.