Problem 96 - Chemical Principles: The Quest for Insight

Question

The heat capacity of a certain empty calorimeter is \(488.1 \mathrm{~J} \cdot\left({ }^{\circ} \mathrm{C}\right)^{-1}\). When \(25.0 \mathrm{~mL}\) of \(0.700 \mathrm{M}\) \(\mathrm{NaOH}(\mathrm{aq})\) was mixed in that calorimeter with \(25.0 \mathrm{~mL}\) of \(0.700 \mathrm{M} \mathrm{HCl}\) (aq), both initially at \(20.00^{\circ} \mathrm{C}\), the temperature increased to \(21.34^{\circ} \mathrm{C}\). Calculate the enthalpy of neutralization in kilojoules per mole of HCI.

Step-by-Step Solution

Answer

The enthalpy of neutralization for HCl is -37.37 kJ/mol.

Step 1: Identify the Reaction

The reaction taking place is the neutralization between hydrochloric acid (HCl) and sodium hydroxide (NaOH). The balanced chemical equation for the neutralization is:\[\mathrm{NaOH(aq) + HCl(aq) \rightarrow NaCl(aq) + H_2O(l)}\]In this reaction, one mole of NaOH reacts with one mole of HCl to produce one mole of NaCl and one mole of water.

Step 2: Calculate the Number of Moles of HCl

To find the number of moles of HCl, use the concentration and volume of the HCl solution. The number of moles is calculated by the product of concentration (M) and volume (L):\[\text{mol HCl} = 0.700 \, \frac{\text{mol}}{\text{L}} \times 0.0250 \, \text{L} = 0.0175 \, \text{mol}\]

Step 3: Calculate the Energy Change of the System

The energy change (q) can be found by using the formula:\[q = C_{cal} \times \Delta T\]where \( C_{cal} \) is the heat capacity of the calorimeter and \( \Delta T \) is the change in temperature. Thus:\[q = 488.1 \, \text{J/}^{\circ}\text{C} \times (21.34^{\circ}\text{C} - 20.00^{\circ}\text{C}) = 488.1 \, \text{J/}^{\circ}\text{C} \times 1.34^{\circ}\text{C} = 654.054 \, \text{J}\]

Step 4: Calculate the Enthalpy of Neutralization Per Mole of HCl

The enthalpy of neutralization (\(\Delta H_{neut}\)) is the energy change per mole of reactant. Since the reaction involves one mole of HCl reacting, calculate the enthalpy change per mole of HCl as follows:\[\Delta H_{neut} = \frac{q}{\text{mol HCl}} = \frac{654.054 \, \text{J}}{0.0175 \, \text{mol}} = 37374.514 \, \text{J/mol}\]Convert this value to kilojoules per mole (kJ/mol) by dividing by 1000:\[\Delta H_{neut} = \frac{37374.514 \, \text{J/mol}}{1000} = 37.37 \, \text{kJ/mol}\]

Key Concepts

Chemical Thermodynamics

Chemical thermodynamics is the branch of chemistry that deals with the relationship between chemical reactions and energy changes. Specifically, it studies the transfer of energy, in various forms, during chemical processes.

Central to this field is the understanding of the first law of thermodynamics, which states that energy cannot be created or destroyed, only transformed from one form to another. The concept of enthalpy, denoted as 'H', is key to chemical thermodynamics. Enthalpy is the measure of the total heat content of a system at constant pressure and is closely connected to the heat of reactions.

Enthalpy of Neutralization

Referring to the exercise above, the enthalpy of neutralization is the change in enthalpy when an acid and base react to form water and a salt. This is an exothermic reaction, meaning it releases heat, resulting in an increase in the temperature of the solution within the calorimeter.

Calorimetry

Calorimetry is a technique for measuring the amount of heat involved in a chemical reaction, physical change, or heat capacity. This is achieved by using an instrument called a calorimeter. There are two types of calorimeters: constant-pressure and constant-volume calorimeters.

The calorimetry experiment typically involves measuring the temperature change of a solution or substance when a reaction occurs. By knowing the heat capacity of the calorimeter and the temperature change (as seen in the exercise), the amount of heat absorbed or released can be calculated. The heat capacity of a calorimeter, which is known prior to the experiment, is crucial for determining the energy change of the reaction.

Stoichiometry

Stoichiometry is the section of chemistry that involves using balanced chemical equations to calculate the relative quantities of reactants and products involved in a chemical reaction.

In the context of the exercise, stoichiometry allows us to determine the exact amount of reactants – in this case, the moles of hydrochloric acid and sodium hydroxide – that will react. Using the molarity (concentration in moles per liter) and the volume of the reactants, stoichiometry is used to convert these values into moles, which are required for further calculations like determining the enthalpy of neutralization.

Acid-Base Reactions

Acid-base reactions are a type of chemical reaction that typically occur in an aqueous solution, where an acid and a base react to form a salt and water. This reaction is also referred to as a neutralization reaction.

In an acid-base reaction, the acid donates a proton (H+) to the base. In the provided exercise, hydrochloric acid (HCl) acts as the acid and sodium hydroxide (NaOH) as the base. The balanced equation for the reaction is key for understanding how molecules interact and, as shown, indicates that an equal number of moles of each reactant are required for the reaction to proceed to completion.