Final answer:
The enthalpy change (ΔHrxn) for the reaction of zinc metal with hydrochloric acid can be calculated by determining the heat absorbed using the mass, specific heat capacity, and temperature change, then dividing by the moles of zinc reacted. The result is an exothermic ΔHrxn of approximately -345 kJ/mol.
Step-by-step explanation:
When zinc metal reacts with hydrochloric acid, the observed reaction produces an aqueous solution of zinc chloride and releases hydrogen gas. This is a single replacement reaction and also a redox reaction, where zinc is oxidized and hydrochloric acid is reduced. The heat evolved in this reaction can be quantified to find the enthalpy change (ΔHrxn) using the specific heat capacity formula: q = m × c × ΔT, where 'q' is the heat absorbed or released, 'm' is the mass of the solution, 'c' is the specific heat capacity, and ΔT is the change in temperature.
To calculate ΔHrxn, we first determine the amount of heat absorbed by the solution: mass of the solution is assumed to be the same as the volume (50.7 ml) since the density is 1.0 g/ml, therefore, m = 50.7 g. The specific heat capacity (c) is 4.18 J/g°C, and the temperature change (ΔT) is 24.4°C - 21.5°C = 2.9°C. Now we can compute the heat (q): q = 50.7 g × 4.18 J/g°C × 2.9°C = 617.2986 J.
Next, we find the molar amount of zinc used: the molar mass of zinc is approximately 65.38 g/mol, and 0.117 g of zinc were reacted, which gives us moles of Zn = 0.117 g / 65.38 g/mol = 0.001789 moles. To find ΔHrxn per mole of reaction, we divide the heat by the moles of Zn: ΔHrxn = 617.2986 J / 0.001789 moles ≈ 345,000 J/mol. Since this heat is absorbed by the solution, the reaction is exothermic and ΔHrxn = -345 kJ/mol.