Final answer:
The enthalpy change for the dissolution of NH₄NO₃ in a coffee-cup calorimeter is calculated by determining the heat change of the water, adjusting that value for the amount of NH₄NO₃ in moles, and expressing this as kilojoules per mole.
Step-by-step explanation:
The student is asking about calculating the enthalpy change (ΔH) for the dissolution of ammonium nitrate (NH₄NO₃) in a coffee-cup calorimeter. To find the enthalpy change per mole, we need to calculate the amount of heat (q) absorbed or released during the dissolution, and then adjust for the number of moles. The steps include calculating the heat change using the specific heat capacity of water, the mass of the water, and the change in temperature (ΔT).
First, we find the heat absorbed by the water using the formula q = m⋅Cs⋅ΔT, where 'm' is the mass of the water (77.0g), 'Cs' is the specific heat capacity (4.18 J/g°C), and ΔT is the change in temperature (23.95°C - 25.00°C = -1.05°C). Since ΔT is negative, the water has lost heat and the solution has absorbed it. Next, we convert q from joules to kilojoules and then calculate the number of moles of NH₄NO₃ that were dissolved. The molar mass of NH₄NO₃ is 80.04 g/mol, so 1.40 g corresponds to 0.01749 moles. Finally, we calculate ΔH by taking q (in kilojoules) and dividing by the number of moles. Since this scenario resulted in heat absorption by the solution, ΔH will be positive, indicating an endothermic process.
To conclude, the enthalpy change for dissolution in kilojoules per mole can be calculated by adjusting the heat change for the specific amount of substance that has dissolved. Specific heat capacity, temperature changes, and molar mass are crucial elements to solve these types of thermochemical problems.