When 1.50 g of magnesium metal is allowed to react with 200 mL of 6.00 M aqueous HCl, the temperature rises from 25.0 °C to 42.9 °C. Calculate ΔH in kilojoules for the reaction, assumign that the heat capacity of the calorimeter is 776 J/°C, that the specific heat of the final soltuion is the same as that of water [4.18 J(g·°C)] and that the density of the solution is 1.00 g/mL

Verified step by step guidance

1. Step 1: Calculate the total heat absorbed by the calorimeter using the formula: \( q_{calorimeter} = C_{cal} \times \Delta T \), where \( C_{cal} \) is the heat capacity of the calorimeter and \( \Delta T \) is the change in temperature.
2. Step 2: Calculate the mass of the solution. Since the density of the solution is given as 1.00 g/mL, multiply the volume of the solution (200 mL) by the density to find the mass in grams.
3. Step 3: Calculate the heat absorbed by the solution using the formula: \( q_{solution} = m_{solution} \times c_{solution} \times \Delta T \), where \( m_{solution} \) is the mass of the solution, \( c_{solution} \) is the specific heat capacity of the solution, and \( \Delta T \) is the change in temperature.
4. Step 4: Calculate the total heat change for the reaction by adding the heat absorbed by the calorimeter and the heat absorbed by the solution: \( q_{total} = q_{calorimeter} + q_{solution} \).
5. Step 5: Convert the total heat change from joules to kilojoules by dividing by 1000, and then determine the enthalpy change (\( \Delta H \)) for the reaction. Since the reaction is exothermic, \( \Delta H \) will be negative.

Key Concepts

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions. It involves using balanced chemical equations to determine the relationships between the amounts of substances consumed and produced. In this question, stoichiometry is essential to relate the mass of magnesium reacting to the moles of HCl and the heat produced during the reaction.

Calorimetry

Calorimetry is the science of measuring the heat of chemical reactions or physical changes. In this scenario, the temperature change of the solution is measured to calculate the heat absorbed or released during the reaction. The heat capacity of the calorimeter and the specific heat of the solution are crucial for determining the total heat change, which is necessary for calculating ΔH.

Enthalpy Change (ΔH)

Enthalpy change (ΔH) represents the heat content change of a system at constant pressure during a reaction. It can be calculated using the formula ΔH = q/n, where q is the heat absorbed or released and n is the number of moles of the limiting reactant. Understanding ΔH is vital for evaluating the energy changes associated with the reaction between magnesium and hydrochloric acid.