Question

A coffee-cup calorimeter initially contains 125 \(\mathrm{g}\) water at \(24.2^{\circ} \mathrm{C} .\) Potassium bromide \((10.5 \mathrm{g}),\) also at \(24.2^{\circ} \mathrm{C},\) is added to the water, and after the KBr dissolves, the final temperature is \(21.1^{\circ} \mathrm{C}\) . Calculate the enthalpy change for dissolving the salt in \(\mathrm{J} / \mathrm{g}\) and \(\mathrm{kJ} / \mathrm{mol}\) . Assume that the specific heat capacity of the solution is 4.18 \(\mathrm{J} / \mathrm{C} \cdot \mathrm{g}\) and that no heat is transferred to the surroundings or to the calorimeter.

Short answer

The enthalpy change for dissolving potassium bromide in water is approximately -167.97 J/g or -19.99415 kJ/mol.

Step-by-step solution

Calculate the temperature change of the solution

The initial and final temperatures of the solution are given. Determine the temperature change (ΔT) by subtracting the final temperature from the initial temperature: ΔT = T_final - T_initial ΔT = \(21.1^{\circ} \mathrm{C} - 24.2^{\circ} \mathrm{C}\) ΔT = --3.1°C

Calculate the heat transfer (q) in the solution

Use the formula for heat transfer (q = mcΔT) to find the amount of heat absorbed or released by the solution, where m is the mass of the solution, c is the heat capacity, and ΔT is the temperature change. The mass of the solution is the combined masses of the water and potassium bromide: m = 125 g (water) + 10.5 g (KBr) = 135.5 g Using the heat capacity (c) of 4.18 J/g°C and the previously calculated temperature change (ΔT = -3.1°C), calculate q: q = mcΔT q = (135.5 g)(4.18 J/g°C)(-3.1°C) q = -1763.67 J

Calculate the enthalpy change per gram

Divide the heat transfer (q) by the mass of potassium bromide to find the enthalpy change per gram: Enthalpy change per gram = q / mass of KBr = -1763.67J / 10.5g Enthalpy change per gram = -167.97 J/g

Calculate the enthalpy change per mole

To find the enthalpy change per mole, first find the molar mass of potassium bromide (KBr). The molar mass of K is 39.1 g/mol, and the molar mass of Br is 79.9 g/mol. Thus, the molar mass of KBr is: Molar mass of KBr = 39.1 g/mol + 79.9 g/mol = 119 g/mol Next, divide the heat transfer (q) by the number of moles of potassium bromide: Number of moles of KBr = mass of KBr / molar mass of KBr = 10.5g / 119 g/mol = 0.0882 mol Enthalpy change per mole = q / number of moles of KBr = -1763.67J / 0.0882 mol Enthalpy change per mole = -19994.15 J/mol Convert this value to kJ/mol: Enthalpy change per mole = -19.99415 kJ/mol Finally, the enthalpy change for dissolving potassium bromide in water is approximately -167.97 J/g or -19.99415 kJ/mol.

Key concepts

Coffee-Cup Calorimeter

A coffee-cup calorimeter is a simple, easy-to-use device commonly utilized in chemistry labs to measure heat changes during chemical reactions. The name "coffee-cup" comes from its basic structure, which often resembles an insulated coffee cup. It is typically made from two nested Styrofoam cups.
This calorimeter is often used in educational settings to study reactions that occur in solution at atmospheric pressure. It provides an insulated environment where the heat exchange between the solution and surrounding air is minimized.
Key advantages of the coffee-cup calorimeter include its affordability, simplicity, and suitability for small-scale reactions that don't involve gases or high temperatures.

• It's best for measuring enthalpy changes in aqueous solutions.
• It's assumed no heat is lost to the surroundings for accurate calculations.

Heat Transfer

Heat transfer in the context of calorimetry refers to the energy exchange between the system and its surroundings. When we talk about a calorimetric experiment, like dissolving potassium bromide in water, we track how much heat is absorbed or released.
The amount of heat transferred is calculated using the formula: \[q = mc\Delta T\]Where:

• \(q\) is the heat transfer in joules.
• \(m\) is the mass of the substance in grams.
• \(c\) is the specific heat capacity, often in \( \text{J/g°C} \).
• \( \Delta T \) is the change in temperature.

In the given problem, the temperature decrease indicates an endothermic process, meaning the solution absorbs heat as the potassium bromide dissolves.

Dissolution of Potassium Bromide

The dissolution of potassium bromide (KBr) in water is an important chemical process, involving the breaking apart of the ionic lattice and hydration of ions. In this reaction, potassium (\(K^+\)) and bromide (\(Br^-\)) ions separate and interact with water molecules.
When KBr dissolves, it absorbs heat, indicated by a drop in temperature of the solution from the initial to the final state. This absorption is an endothermic reaction which is typical when ionic compounds dissolve in water.

• The initial temperature decrease in the calorimetry experiment signifies this heat absorption.
• This process is crucial for determining the enthalpy changes in the reaction.

Understanding the dissolution process at a molecular level helps explain why specific salts have positive or negative enthalpy changes when dissolving.

Specific Heat Capacity

Specific heat capacity is a property that indicates how much heat a substance can absorb before its temperature changes by one degree Celsius. It is expressed in units of \( \text{J/g°C} \).
In this exercise, we consider the specific heat capacity of the entire solution, which is assumed to be similar to water since the solution is mostly water. The specific heat capacity of water is approximately 4.18 \( \text{J/g°C} \), which means it requires 4.18 joules of energy to raise the temperature of one gram of water by one degree Celsius.

• The specific heat capacity is used to calculate the heat transfer (q), indicating how much energy has been absorbed or released.
• In our calculations, it helps determine how much heat is involved during the temperature change as the potassium bromide dissolves.

A material's specific heat capacity can indicate how it will react to heating, which in the case of calorimetry, is essential for estimating the energy changes in reactions.