Question

Citric acid has three dissociable hydrogens. When \(5.00 \mathrm{~mL}\) of 0.64 M citric acid and \(45.00 \mathrm{~mL}\) of \(0.77 \mathrm{M} \mathrm{NaOH}\) are mixed at an initial temperature of \(26.0^{\circ} \mathrm{C}\), the temperature rises to \(27.9^{\circ} \mathrm{C}\) as the citric acid is neutralized. The combined mixture has a mass of \(51.6 \mathrm{~g}\) and a specific heat of \(4.0 \mathrm{~J} /\left(\mathrm{g} \cdot{ }^{\circ} \mathrm{C}\right)\). Assuming that no heat is transferred to the surroundings, calculate the enthalpy change for the reaction of \(1.00 \mathrm{~mol}\) of citric acid in \(\mathrm{kJ}\). Is the reaction exothermic or endothermic?

Short answer

The enthalpy change is \(-122.4 \text{ kJ/mol}\); the reaction is exothermic.

Step-by-step solution

Calculate the moles of citric acid and NaOH

First, determine the moles of citric acid using its molarity and volume. The molarity (M) of citric acid is 0.64 M, and the volume is 5.00 mL (or 0.005 L). Use the formula: \[ \text{moles of citric acid} = 0.64 \times 0.005 = 0.0032 \text{ moles} \].For NaOH, the volume is 45.00 mL (or 0.045 L), and the molarity is 0.77 M:\[ \text{moles of NaOH} = 0.77 \times 0.045 = 0.03465 \text{ moles} \].

Determine the limiting reactant

Citric acid has three dissociable hydrogens, meaning 1 mole of citric acid reacts with 3 moles of NaOH.Moles of NaOH needed for 0.0032 moles of citric acid = \[ 0.0032 \times 3 = 0.0096 \text{ moles} \].Since there are 0.03465 moles of NaOH available, NaOH is in excess. Therefore, citric acid is the limiting reactant.

Calculate the heat absorbed by the solution

Use the formula for heat absorbed or released: \[ q = m \cdot c \cdot \Delta T \], where \( m \) is the mass of the solution, \( c \) is the specific heat capacity, and \( \Delta T \) is the change in temperature.\( m = 51.6 \text{ g} \), \( c = 4.0 \text{ J/g} \cdot{ }^{\circ} \text{C} \), and \( \Delta T = 27.9^{\circ} \text{C} - 26.0^{\circ} \text{C} = 1.9^{\circ} \text{C} \).Thus, \[ q = 51.6 \times 4.0 \times 1.9 = 391.68 \text{ J (or 0.39168 kJ)} \].

Calculate the enthalpy change per mole of citric acid

The enthalpy change \( \Delta H \) for the reaction is calculated using:\[ \Delta H = \frac{q}{\text{moles of citric acid}} \].We have previously determined \( q = 0.39168 \text{ kJ} \) and moles of citric acid = 0.0032 moles.\[ \Delta H = \frac{0.39168}{0.0032} \approx -122.4 \text{ kJ/mol} \].The negative sign indicates that the reaction is exothermic.

Key concepts

Citric Acid Dissociation

When we talk about citric acid dissociation, we are referring to the process by which citric acid releases its hydrogen ions in a solution. Citric acid is a triprotic acid, which means it has three hydrogen atoms that can dissociate. In the context of the exercise, this means one mole of citric acid is capable of reacting with three moles of a base like NaOH. This is crucial for calculating reactions involving citric acid as it determines how the acid behaves during reactions with bases. The hydrogen ions will each dissociate separately, which is an important factor when considering chemical reactions and stoichiometry.

Limiting Reactant

The limiting reactant is the substance that is entirely consumed first in a chemical reaction, thereby limiting the extent of the reaction. In this exercise, we have two reactants: citric acid and NaOH. By calculating the moles of each, we can determine which reactant will run out first. For 0.0032 moles of citric acid, and knowing it requires three times its amount in NaOH to fully react, we need 0.0096 moles of NaOH. Since there are actually 0.03465 moles available, NaOH is in excess. Therefore, citric acid is the limiting reactant. Identifying the limiting reactant is key to determining how much product will be formed and how much energy will be involved.

Exothermic Reaction

An exothermic reaction is one that releases heat to its surroundings. This is typically observed as a rise in temperature of the substance or environment. In the given exercise, when citric acid reacts with NaOH, the temperature of the solution rises from 26.0°C to 27.9°C. This increase indicates that the reaction is exothermic, as heat is being released during the neutralization process. Not only does this temperature change signify the release of energy, but it also plays a role in calculating the enthalpy change, as seen through the specific formulas provided in the solution.

Neutralization Reaction

Neutralization reactions are specific types of chemical reactions where an acid and a base react to form water and a salt. The neutralization in our exercise involves citric acid reacting with NaOH, a strong base. This interaction leads to the formation of water molecules and sodium citrate, which is the salt. The significance of the neutralization process is crucial because it often entails energy changes; in this case, it is the exothermic release of energy which results in an observable temperature increase. Understanding this reaction helps in appreciating the conversion of reactants to products and is key to calculating enthalpy changes and the overall reaction dynamics.