Question

The value of \(\Delta H_{\text {sol }}\) of anhydrous \(\begin{array}{lllll}\text { copper (II) sulphate } & \text { is } & -66.11 & \mathrm{~kJ}\end{array}\) Dissolution of 1 mole of blue vitriol, [Copper (II) sulphate pentahydrate] is followed by absorption of \(11.5 \mathrm{~kJ}\) of heat. The enthalpy of dehydration of blue vitriol is (a) \(-77.61 \mathrm{~kJ}\) (b) \(+77.61 \mathrm{~kJ}\) (c) \(-54.61 \mathrm{~kJ}\) (d) \(+54.61 \mathrm{~kJ}\)

Short answer

+77.61 kJ

Step-by-step solution

Understand Enthalpies Involved

Recognize that the enthalpy change for the dissolution of anhydrous copper(II) sulfate is \(\Delta H_{\text{sol, anhydrous}} = -66.11 \text{ kJ}\). The process of the dissolution of blue vitriol (copper(II) sulfate pentahydrate) absorbs \(11.5 \text{ kJ}\) of heat, indicating this is an endothermic process with positive enthalpy change \(\Delta H_{\text{sol, hydrated}} = +11.5 \text{ kJ}\). The enthalpy of dehydration is the difference between these two enthalpy changes.

Calculate the Enthalpy of Dehydration

The enthalpy of dehydration can be expressed as follows: \[\Delta H_{\text{dehydration}} = \Delta H_{\text{sol, hydrated}} - \Delta H_{\text{sol, anhydrous}}\]Since \(\Delta H_{\text{sol, hydrated}}\) is the heat absorbed by the dissolution of blue vitriol and \(\Delta H_{\text{sol, anhydrous}}\) is the heat released by the dissolution of anhydrous copper(II) sulfate, their difference will give us the enthalpy change for the dehydration of blue vitriol.

Perform the Calculation

Now, substitute the values into the equation from the previous step: \[\Delta H_{\text{dehydration}} = +11.5 \text{ kJ} - (-66.11 \text{ kJ})\]\[\Delta H_{\text{dehydration}} = +11.5 \text{ kJ} + 66.11 \text{ kJ}\]\[\Delta H_{\text{dehydration}} = +77.61 \text{ kJ}\]The positive sign indicates that the dehydration of blue vitriol is an endothermic process.

Key concepts

Chemical Thermodynamics

Chemical thermodynamics combines the principles of chemistry and physics to investigate the relationships between heat, work, temperature, and energy in chemical processes. It's a crucial area of study as it allows us to predict the direction of chemical reactions and understand the energy changes associated with them.

At the heart of chemical thermodynamics is the first law of thermodynamics, which states that energy cannot be created or destroyed, only transformed. This is particularly important in chemical reactions, where energy is often converted from one form to another, typically as heat or work. In the exercise, we see the application of thermodynamic principles in determining the enthalpy of dehydration of blue vitriol. The energy change due to the absorption or release of heat during the transition of blue vitriol from its hydrated to anhydrous form demonstrates the direct application of thermodynamics in chemistry.

Enthalpy Change Calculations

Enthalpy change, denoted by \( \Delta H \), is the measurement of heat change under constant pressure during a chemical reaction. It's a central concept in understanding energy differences between the reactants and products.

In calculations, a negative \( \Delta H \) denotes an exothermic process - the system releases heat to the surroundings. Conversely, a positive \( \Delta H \) signifies an endothermic process - the system absorbs heat from the surroundings. This allows chemists to quantify the energy involved in breaking and forming bonds during chemical reactions.

The exercise we're discussing showcases how enthalpy change calculations are essential in determining the energy profile of a reaction. By subtracting the heat released during the dissolution of anhydrous copper(II) sulfate from the heat absorbed during the dissolution of hydrated blue vitriol, we find the enthalpy change for the dehydration process. These calculations underpin many applications, from industrial processes to environmental science, highlighting the versatility and importance of understanding enthalpy change.

Endothermic Reactions

Endothermic reactions are chemical reactions that require an input of energy, typically in the form of heat, from their surroundings to proceed. In an endothermic process, the energy needed to break the chemical bonds of the reactants is greater than the energy released when new bonds form in the products.

Visual cues such as temperature drops, the absorption of heat, or even the need for continuous heating are common indicators of endothermic reactions. These reactions are common in various situations, including photosynthesis in plants and the evaporation of water.

The dehydration of blue vitriol, as elucidated in the exercise, is a prime example of an endothermic reaction. Heat is absorbed from the surroundings to convert the hydrated blue vitriol into its anhydrous form, signified by a positive enthalpy change. Understanding endothermic reactions is vital for energy management in chemical industries and can also have broader ecological and environmental implications.