Problem 70 - Chemistry The Science in Context

Question

What is the \(\Delta H_{\text {rxn }}\) for the precipitation of AgCl if adding \(125 \mathrm{mL}\) of \(1.00 \mathrm{M} \mathrm{AgNO}_{3}\) to \(125 \mathrm{mL}\) of \(1.00 \mathrm{M} \mathrm{NaCl}\) at \(18.6^{\circ} \mathrm{C}\) causes the temperature to increase to \(26.4^{\circ} \mathrm{C} ?\) (Assume \(\left.c_{\mathrm{P}, \text { soln }}=c_{\text {P,water }}\right)\).

Step-by-Step Solution

Answer

Answer: The change in enthalpy for the precipitation reaction of AgCl is -65.4 kJ/mol.

Step 1: Write the balanced chemical equation for the precipitation reaction.

For the precipitation reaction of AgCl, we can write the balanced chemical equation as follows: AgNO3(aq) + NaCl(aq) -> AgCl(s) + NaNO3(aq)

Step 2: Calculate the moles of reactants

We will calculate the moles of AgNO3 and NaCl present in the solutions. moles of AgNO3 = volume × concentration = (125 mL)(1.00 M) = 125 mmol moles of NaCl = volume × concentration = (125 mL)(1.00 M) = 125 mmol

Step 3: Find the limiting reactant

In the balanced equation, the stoichiometric ratio between AgNO3 and NaCl is 1:1. Since we have the same amount of moles for both reactants, none of them is in excess, and the reaction will go to completion.

Step 4: Calculate the heat absorbed or released by the reaction

We'll use the temperature change and the heat capacity (specific heat) of water (which is assumed to be similar to the solution) to calculate the heat change. Also, given that the total volume of the solution is 250 mL, we can assume its mass to be 250 g (since the density of water is approximately 1 g/mL). \( q = mc\Delta T \) where \(q\) is the heat absorbed or released, \(m\) is the mass of the solution, \(c\) is the specific heat capacity of water (4.18 J/g·°C), and \(\Delta T\) is the temperature change. \(\Delta T = 26.4 - 18.6 = 7.8 °C\) Now, let's compute the heat absorbed or released by the reaction: \( q = (250\,\text{g})(4.18\,\text{J/g·°C})(7.8\,\text{°C}) = 8,175.6\,\text{J} \) Since the temperature has increased, the reaction should be exothermic, which means that the heat is released by the reaction. Therefore, the heat change, q, is negative: \( q = -8,175.6\,\text{J} \)

Step 5: Calculate the change in enthalpy of the reaction

Finally, we can determine the change in enthalpy for the precipitation reaction by dividing the heat change by the moles of AgCl produced: \(\Delta H_{rxn} = \frac{-8,175.6\,\text{J}}{125\,\text{mmol}} \times \frac{1\;\text{kJ}}{1000\;\text{J}} = -65.4\,\text{kJ/mol}\) So, the change in enthalpy for the precipitation of AgCl is \( -65.4\,\text{kJ/mol}\).

Key Concepts

Understanding Chemical Reactions

When chemicals interact to form new substances, we witness a chemical reaction. Every reaction involves rearrangements of atoms and is governed by the law of conservation of mass, meaning the mass of the reactants equals the mass of the resulting products. In the example problem provided, the combination of silver nitrate (AgNO3) with sodium chloride (NaCl) leads to the formation of silver chloride (AgCl), which precipitates out of the solution, and sodium nitrate (NaNO3). This demonstrates how reactions can result in the creation of new compounds with properties distinct from those of the original reactants.

It's essential to write down the balanced chemical equation because it provides insight into the stoichiometry of the reaction—the ratios in which reactants combine and products are formed. In our exercise, the equation is balanced with a one-to-one ratio of the reactants to form silver chloride and sodium nitrate. This balance is crucial for calculating the amount of product formed and is the foundation for further calculations involving the reaction's enthalpy change.

Stoichiometry in Action

Stoichiometry is like the recipe for a chemical reaction, dictating the proportions of each ingredient (or reactant) needed. It relies on the balanced chemical equation and allows us to predict the amounts of products and reactants involved in a chemical reaction. In our exercise, stoichiometry helped us identify that equal volumes and concentrations of AgNO3 and NaCl mean they react in equal molar amounts. Therefore, neither is a limiting reactant since they are present in stoichiometric amounts (one mole of AgNO3 reacts with one mole of NaCl).

In this reaction, stoichiometry guided us to determine the number of moles of AgCl that would be produced. Knowing the stoichiometric ratios and amounts of reactants allows us to then calculate other important properties of the reaction, such as the enthalpy change.

Enthalpy (ΔH) and Its Significance

Enthalpy, symbolized as ΔH, represents the heat content of a system at constant pressure and is a crucial concept in thermodynamics. It tells us how much heat is absorbed or released during a reaction. When we say a reaction has an enthalpy change of -65.4 kJ/mol, it means that 65.4 kilojoules of heat are released for every mole of product formed, under standard conditions.

In the exercise, we calculate enthalpy change by measuring the temperature change of the solution and applying the formula q = mcΔT, where q is the heat change, m is the mass, c is the specific heat capacity, and ΔT is the temperature change. By dividing the total heat released by the number of moles of precipitate formed, we have an accurate measurement of the enthalpy change per mole, allowing us to predict and measure the energy change associated with virtually any chemical process.

Exothermic Reactions and Temperature

When a reaction releases heat into its surroundings, we call it an exothermic reaction. The key hallmark of such reactions is the rise in temperature of the surroundings. Our example reaction, where silver chloride precipitates, is a perfect illustration of an exothermic process; the temperature of the solution increases as the reaction proceeds.

Understanding that the reaction is exothermic helps us deduce the sign of the enthalpy change. With an increase in temperature, the sign of the heat change, q, is negative because the system (the reaction) releases heat. This aligns with the general notion that negative enthalpy indicates an exothermic reaction whereas a positive value would indicate an endothermic reaction, where the system absorbs heat. Grasping the concept of exothermic reactions not only explains the temperature change but also builds a solid foundation for understanding energy transfer in chemical processes.