Consider two solutions, the first being 50.0 mL of 1.00 M CuSO4 and the second 50.0 mL of 2.00 M KOH. When the two solutions are mixed in a constant-pressure calorimeter, a precipitate forms and the temperature of the mixture rises from 21.5 to 27.7 °C (d) From the calorimetric data, calculate ΔH for the reaction that occurs on mixing. Assume that the calorimeter absorbs only a negligible quantity of heat, that the total volume of the solution is 100.0 mL, and that the specific heat and density of the solution after mixing are the same as those of pure water.
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Identify the chemical reaction that occurs when CuSO4 and KOH are mixed. The reaction is: \( \text{CuSO}_4 (aq) + 2 \text{KOH} (aq) \rightarrow \text{Cu(OH)}_2 (s) + \text{K}_2\text{SO}_4 (aq) \).
Calculate the moles of each reactant. For CuSO4: \( \text{moles of CuSO}_4 = \text{Volume (L)} \times \text{Molarity} = 0.050 \times 1.00 \). For KOH: \( \text{moles of KOH} = \text{Volume (L)} \times \text{Molarity} = 0.050 \times 2.00 \).
Determine the limiting reactant by comparing the stoichiometric ratios. Since the reaction requires 2 moles of KOH for every mole of CuSO4, calculate the moles of KOH needed for the moles of CuSO4 present.
Calculate the heat absorbed or released using the formula \( q = m \cdot c \cdot \Delta T \), where \( m \) is the mass of the solution (assuming density of water, \( 1 \text{ g/mL} \), so \( m = 100 \text{ g} \)), \( c \) is the specific heat capacity of water (\( 4.18 \text{ J/g°C} \)), and \( \Delta T \) is the change in temperature (\( 27.7 - 21.5 \text{ °C} \)).
Calculate \( \Delta H \) for the reaction. Since \( q \) is the heat change for the reaction and the reaction occurs at constant pressure, \( \Delta H = q \). Divide \( q \) by the moles of the limiting reactant to find \( \Delta H \) per mole of reaction.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Calorimetry
Calorimetry is the science of measuring the heat of chemical reactions or physical changes. In this context, it involves using a calorimeter to determine the heat exchange during the reaction between CuSO4 and KOH. The temperature change observed in the calorimeter allows us to calculate the heat absorbed or released, which is essential for determining the enthalpy change (ΔH) of the reaction.
Enthalpy change (ΔH) represents the heat content change of a system at constant pressure. 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 reactants. In this scenario, the temperature increase indicates an exothermic reaction, and calculating ΔH will provide insight into the energy dynamics of the reaction between the two solutions.
Stoichiometry involves the calculation of reactants and products in chemical reactions based on balanced chemical equations. In this case, understanding the stoichiometry of the reaction between CuSO4 and KOH is crucial for determining the limiting reactant and the amount of heat produced. This information is necessary to accurately calculate the enthalpy change (ΔH) for the reaction based on the moles of reactants used.
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