Citric acid has three dissociable hydrogens. When 5.00 mL of 0.64 M citric acid and 45.00 mL of 0.77 M NaOH are mixed at an initial temperature of 26.0 °C, the temperature rises to 27.9 °C as the citric acid is neutralized. The combined mixture ahs a mass of 51.6 g and a specific heat of 4.0 J/(g·°C). Assuming that no heat is transferred to the surroundings, cal- culate the enthalpy change for the reaction of 1.00 mol of cit-ric acid in kJ. Is the reaction exothermic or endothermic?

Verified step by step guidance

1. Calculate the total moles of citric acid used by multiplying the volume of the citric acid solution by its concentration: Moles of citric acid = Volume (L) imes Concentration (M).
2. Calculate the total moles of NaOH used by multiplying the volume of the NaOH solution by its concentration: Moles of NaOH = Volume (L) imes Concentration (M).
3. Determine the limiting reactant by comparing the mole ratio of citric acid to NaOH required for complete neutralization. Citric acid can donate three protons, so the stoichiometric ratio with NaOH (which accepts one proton per molecule) is 1:3.
4. Calculate the heat released or absorbed during the reaction using the formula: Q = mass imes specific heat imes ext{change in temperature} ( ext{final temperature} - ext{initial temperature}).
5. Determine the enthalpy change per mole of citric acid by dividing the total heat by the moles of citric acid reacted, and convert this value to kJ. To determine if the reaction is exothermic or endothermic, observe the sign of the enthalpy change (negative for exothermic, positive for endothermic).

Key Concepts

Dissociation of Acids

Citric acid is a triprotic acid, meaning it can donate three protons (H⁺ ions) in solution. Understanding the dissociation process is crucial for calculating the amount of acid that reacts with a base, such as NaOH, in a neutralization reaction. Each dissociation step can affect the pH and the overall reaction dynamics.

Enthalpy Change (ΔH)

Enthalpy change is a measure of the heat absorbed or released during a chemical reaction at constant pressure. In this scenario, the temperature change of the solution indicates that heat is released, allowing us to calculate the enthalpy change per mole of citric acid. This is essential for determining whether the reaction is exothermic (releases heat) or endothermic (absorbs heat).

Calorimetry

Calorimetry is the science of measuring the heat of chemical reactions or physical changes. In this problem, the specific heat capacity, mass of the solution, and temperature change are used to calculate the total heat released during the neutralization. This data is then used to find the enthalpy change per mole of citric acid, which is key to understanding the thermal properties of the reaction.