Question

Magnesium metal was added to a coffee-cup calorimeter containing 145.0 mL of 0.500 M hydrochloric acid. The temperature increased by 1.5 °C. What mass of metal was placed in the calorimeter? Mg(s) + 2HCl(aq) → MgCl2(aq) + H2(g), ΔHrxn = -44 kJ The heat capacity and density of solution in the calorimeter is the same as those for water: 4.184 J/(g·°C) and 1.00 g/mL. You can ignore change in the mass of solution caused by adding the magnesium and by escape of the hydrogen.

Answer 1

The temperature rise of the solution can be considered to be due to the

heat given from the reaction reaction of magnesium and the acid.

Mass of magnesium added, is approximately 502.63 mg

Reasons:

The given volume of the HCl = 145.0 mL

Increase in the temperature of the solution, ΔT = 1.5°C

Heat capacity of the solution, c = 4.184 J/(g·°C)

Density of the solution = 1.00 g/mL

Required:

Mass of the metal (magnesium) placed in the calorimeter

Solution:

Mass of the solution, m = 145.0 mL × 1.00 g/mL = 145.0 g

Heat gained by the solution, Δq = m·c·ΔT

∴ Δq = 145.0 g × 4.184 J/(g·°C) × 1.5°C = 910.02 J

Number of moles of HCl = 0.5 moles × 0.145 = 0.0725 moles

The given reaction is; Mg(s) + 2HCl(aq) → MgCl₂(aq) + H₂(g), ΔH$_{rxn}$ = -44 kJ

Therefore;

1 mole of Mg gives 44 kJ = 44,000 J of heat

910.02 J will be given by $\dfrac{910.02 \, J}{44,000 \, J/mol}$ ≈ 2.068 × 10⁻² moles of magnesium

Molar mass of magnesium = 24.305 g/mol

Mass of magnesium added, $m_{mg}$, is given as follows;

• $m_{mg}$ = 24.305 g/mol × 2.068 × 10^(-2) moles ≈  502.63 mg

Mass of magnesium added, $m_{mg}$ ≈ 502.63 mg.

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