When 12.5 g of NH4NO3 is dissolved in 150.0 g of water of 25.0 °C in a coffee cup calorimeter, the final temperature of the solution of 19.7 °C. Assume that the specific heat of the solution is the same as that of water, 4.18 J/(g•°C). What is the ΔH per mol of NH4NO3? (LO 9.10) NH4NO3 (s) → NH4+ (aq) + NO3−(aq) ΔH = ? (a) +3.60 kJ (b) +23.0 kJ (c) +21.3 kJ (d) −3.60 kJ

Verified step by step guidance

1. Step 1: First, we need to calculate the heat absorbed or released by the solution using the formula q = mcΔT, where m is the mass of the solution, c is the specific heat capacity, and ΔT is the change in temperature. In this case, the mass of the solution is the mass of the water (150.0 g), the specific heat capacity is 4.18 J/(g•°C), and the change in temperature is the final temperature minus the initial temperature (19.7 °C - 25.0 °C).
2. Step 2: The heat absorbed or released by the solution is equal to the negative of the heat absorbed or released by the reaction, so q_reaction = -q_solution.
3. Step 3: To find the ΔH per mol of NH4NO3, we need to divide the heat of the reaction (q_reaction) by the number of moles of NH4NO3. The number of moles of NH4NO3 can be calculated by dividing the mass of NH4NO3 (12.5 g) by its molar mass (80.04 g/mol).
4. Step 4: The ΔH of the reaction is equal to q_reaction divided by the number of moles of NH4NO3. This will give us the ΔH per mol of NH4NO3.
5. Step 5: Finally, we need to determine the sign of ΔH. Since the temperature of the solution decreased, the reaction is exothermic and ΔH is negative. If the calculated ΔH per mol of NH4NO3 matches one of the given options, that is the correct answer.

Key Concepts

Enthalpy Change (ΔH)

Enthalpy change (ΔH) is the heat content change of a system at constant pressure. It indicates whether a reaction is exothermic (releases heat, ΔH < 0) or endothermic (absorbs heat, ΔH > 0). In this context, calculating ΔH for the dissolution of NH4NO3 involves determining the heat absorbed by the solution as the solid dissolves.

Calorimetry

Calorimetry is the science of measuring the heat of chemical reactions or physical changes. In this scenario, a coffee cup calorimeter is used to measure the temperature change of the solution when NH4NO3 dissolves. The heat absorbed by the solution can be calculated using the formula q = m × c × ΔT, where m is the mass of the solution, c is the specific heat capacity, and ΔT is the change in temperature.

Molar Mass and Stoichiometry

Molar mass is the mass of one mole of a substance, which is essential for converting grams of a substance to moles. For NH4NO3, the molar mass is approximately 80.04 g/mol. Understanding stoichiometry allows us to relate the amount of heat absorbed (calculated from calorimetry) to the number of moles of NH4NO3 dissolved, enabling the calculation of ΔH per mole.