Zinc metal reacts with hydrochloric acid according to the balanced equation: Zn(s) + 2 HCl(aq) → ZnCl₂(aq) + H₂(g) When 0.103 g of Zn(s) is combined with enough HCl to make 50.0 mL of solution in a coffee-cup calorimeter, all of the zinc reacts, raising the temperature of the solution from 22.5 °C to 23.7 °C. Find ΔH_rxn for this reaction as written. (Use 1.0 g/mL for the density of the solution and 4.18 J/g•°C as the specific heat capacity.)

Verified step by step guidance

1. <Step 1: Calculate the mass of the solution.> Since the density of the solution is given as 1.0 g/mL and the volume is 50.0 mL, the mass of the solution can be calculated using the formula: \( \text{mass} = \text{density} \times \text{volume} \).
2. <Step 2: Calculate the change in temperature (\( \Delta T \)).> The change in temperature is the final temperature minus the initial temperature: \( \Delta T = 23.7 \, ^\circ\text{C} - 22.5 \, ^\circ\text{C} \).
3. <Step 3: Calculate the heat absorbed by the solution (q).> Use the formula \( q = m \cdot c \cdot \Delta T \), where \( m \) is the mass of the solution, \( c \) is the specific heat capacity (4.18 J/g°C), and \( \Delta T \) is the change in temperature.
4. <Step 4: Calculate the moles of Zn reacted.> Use the molar mass of Zn (65.38 g/mol) to convert the mass of Zn (0.103 g) to moles using the formula: \( \text{moles of Zn} = \frac{\text{mass of Zn}}{\text{molar mass of Zn}} \).
5. <Step 5: Calculate \( \Delta H_{\text{rxn}} \) per mole of Zn.> Use the formula \( \Delta H_{\text{rxn}} = \frac{q}{\text{moles of Zn}} \) to find the enthalpy change for the reaction as written, ensuring the sign reflects the exothermic or endothermic nature of the reaction.>

Key Concepts

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on balanced equations. It allows us to determine the amount of substance consumed or produced in a reaction. In this case, knowing the mass of zinc and the balanced equation helps us find the moles of zinc reacting, which is essential for calculating the enthalpy change.

Enthalpy Change (ΔH)

Enthalpy change (ΔH) is the heat content change of a system at constant pressure during a chemical 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. In this scenario, we need to calculate the heat absorbed by the solution to find ΔH for the reaction.

Calorimetry

Calorimetry is the science of measuring the heat of chemical reactions or physical changes. In this experiment, a coffee-cup calorimeter is used to measure the temperature change of the solution, which is directly related to the heat released by the reaction. The specific heat capacity and the mass of the solution are used to calculate the total heat change, which is crucial for determining ΔHrxn.