When 1.80 g of magnesium metal reacts with 200 mL of 6.00 M aqueous HCl, the temperature rises from 25.0 °C to 42.1 °C. Calculate ΔH in kilojoules for the reaction, assuming the heat capacity of the calorimeter is 776 J/°C. What is the value of ΔH?

• A. -350 kJ
• B. -420 kJ
• C. -500 kJ
• D. -462 kJ

Answer: (D)

Verified step by step guidance

1. Determine the limiting reactant by calculating the moles of magnesium and hydrochloric acid. Use the molar mass of magnesium (24.31 g/mol) to find the moles of magnesium: \( \text{moles of Mg} = \frac{1.80 \text{ g}}{24.31 \text{ g/mol}} \). For HCl, use the concentration and volume: \( \text{moles of HCl} = 6.00 \text{ M} \times 0.200 \text{ L} \).
2. Identify the limiting reactant by comparing the stoichiometric ratio from the balanced chemical equation: \( \text{Mg} + 2\text{HCl} \rightarrow \text{MgCl}_2 + \text{H}_2 \). The reaction requires 2 moles of HCl for every mole of Mg.
3. Calculate the heat absorbed by the solution using the formula \( q = C_{cal} \times \Delta T \), where \( C_{cal} \) is the heat capacity of the calorimeter (776 J/°C) and \( \Delta T \) is the change in temperature (42.1 °C - 25.0 °C).
4. Convert the heat absorbed (q) from joules to kilojoules by dividing by 1000. This value represents the heat change for the reaction based on the limiting reactant.
5. Calculate \( \Delta H \) for the reaction per mole of limiting reactant. If magnesium is the limiting reactant, divide the heat change by the moles of magnesium. If HCl is the limiting reactant, divide by the moles of HCl used in the reaction. Adjust the sign of \( \Delta H \) to reflect the exothermic nature of the reaction (negative sign).