A piece of magnesium ribbon is reacted with aqueous hydrochloric acid inside a constant-pressure coffee-cup calorimeter. The data collected are:
• Mass of magnesium ribbon: 0.100 g (molar mass 24.3 g mol⁻¹)
• Volume of HCl(aq): 100.0 mL; density 1.00 g mL⁻¹
• Initial temperature: 22.4 °C
• Final temperature: 28.9 °C
• Specific heat capacity of the solution: 4.18 J g⁻¹ °C⁻¹ (assume equal to that of water)
The measured reaction is
Mg(s) + 2 HCl(aq) → MgCl₂(aq) + H₂(g) ΔH₁ = ?
A literature value for the following reaction is available:
H₂(g) + Cl₂(g) → 2 HCl(aq) ΔH₂ = –184 kJ (per 2 mol HCl produced)
Using these reactions, the student wishes to determine the enthalpy change for
Mg(s) + Cl₂(g) → MgCl₂(aq) ΔH_target = ?
(a) Calculate the heat (q, in kJ) absorbed or released by the calorimeter solution during the magnesium–acid reaction.
(b) Determine ΔH₁, the molar enthalpy change (in kJ mol⁻¹ of Mg) for the magnesium–acid reaction. Make sure to include the correct sign.
(c) Using ΔH₁ and the given ΔH₂, obtain ΔH_target for the formation of aqueous MgCl₂ from its elements. Show the algebraic combination of the two chemical equations before reporting the numerical value.