Problem 72 - General Chemistry

Question

Hydrogen peroxide, \(\mathrm{H}_{2} \mathrm{O}_{2}\), is a colorless liquid whose solutions are used as a bleach and an antiseptic. \(\mathrm{H}_{2} \mathrm{O}_{2}\) can be prepared in a process whose overall change is $$ \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}_{2}(l) $$ Calculate the enthalpy change using the following data: $$ \begin{gathered} 2 \mathrm{H}_{2} \mathrm{O}_{2}(l) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(g) ; \Delta H=-196.0 \mathrm{~kJ} \\ \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l) ; \Delta H=-285.8 \mathrm{~kJ} \end{gathered} $$

Step-by-Step Solution

Answer

The enthalpy change is \(-187.8 \mathrm{~kJ}\).

Step 1: Write the Target Reaction

The target reaction for which we need to calculate the enthalpy change is \( \mathrm{H}_{2}(g) + \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}_{2}(l) \).

Step 2: Write the Given Reactions

We are given two reactions with their enthalpy changes:1) \( 2 \mathrm{H}_{2} \mathrm{O}_{2}(l) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l) + \mathrm{O}_{2}(g) \); \( \Delta H = -196.0 \mathrm{~kJ} \)2) \( \mathrm{H}_{2}(g) + \frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l) \); \( \Delta H = -285.8 \mathrm{~kJ} \).

Step 3: Manipulate Given Reactions to Match the Target

Reverse the first reaction to match the required formation of \( \mathrm{H}_{2} \mathrm{O}_{2}(l) \) and half it:\[ \mathrm{H}_{2} \mathrm{O}(l) + \frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}_{2}(l) \]; \( \Delta H = 98.0 \mathrm{~kJ} \) (half of the reverse, so change the sign and divide by 2).Use the second given reaction as is.

Step 4: Add Up the Reactions

Combine the adjusted reactions:\( \mathrm{H}_{2}(g) + \frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l) \); \( \Delta H = -285.8 \mathrm{~kJ} \)\( \mathrm{H}_{2} \mathrm{O}(l) + \frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}_{2}(l) \); \( \Delta H = 98.0 \mathrm{~kJ} \).

Step 5: Summation of Enthalpy Changes

Add the enthalpy changes from Step 4:\[ \Delta H = (-285.8 \mathrm{~kJ}) + (98.0 \mathrm{~kJ}) = -187.8 \mathrm{~kJ} \].

Step 6: Finalize the Result

The calculated enthalpy change for the formation of hydrogen peroxide from hydrogen and oxygen is \( \Delta H = -187.8 \mathrm{~kJ} \).

Key Concepts

Enthalpy Change

Enthalpy change is a fundamental concept in thermodynamics that helps us understand the energy involved in a chemical reaction. It represents the heat absorbed or released during a reaction at constant pressure. Enthalpy, denoted as \( \Delta H \), can be either positive or negative.
- A positive \( \Delta H \) indicates that the reaction absorbs heat (endothermic),- A negative \( \Delta H \) indicates the reaction releases heat (exothermic).
When applying Hess's Law, enthalpy changes of chemical reactions can be manipulated mathematically to determine \( \Delta H \) for complicated reactions. This is achieved by adding or subtracting known enthalpy changes of simpler reactions. In the context of our exercise, we used this rule to deduce the enthalpy change for forming hydrogen peroxide from hydrogen and oxygen. By reversing and scaling reactions, enthalpy changes can blend to reach the desired result.

Hydrogen Peroxide Formation

Hydrogen peroxide (\( \text{H}_2\text{O}_2 \)) is a valuable chemical, widely used for cleaning purposes, bleaching, and as an antiseptic due to its oxidizing properties. Understanding the formation of hydrogen peroxide from hydrogen (\( \text{H}_2 \)) and oxygen (\( \text{O}_2 \)) involves an analysis of the thermodynamic principles of the chemical reactions.
The overall reaction can be written as:- \( \text{H}_2(g) + \text{O}_2(g) \rightarrow \text{H}_2\text{O}_2(l) \)
Hess's Law enables us to calculate the enthalpy change for this process using known reactions and their respective enthalpy changes. By carefully reversing and adjusting the coefficients of given reactions, we can isolate the formation of \( \text{H}_2\text{O}_2(l) \), facilitating the calculation of its enthalpy change. This method helps us understand how energy is transferred or converted in forming \( \text{H}_2\text{O}_2 \) from its constituent elements.

Chemical Thermodynamics

Chemical thermodynamics is the study of heat and energy changes associated with chemical reactions. It provides insights into how and why chemical reactions occur, based on principles like Hess's Law and the first law of thermodynamics (conservation of energy).
Key concepts of chemical thermodynamics include:

• Enthalpy (\( \Delta H \)): Heat content change at constant pressure
• Entropy (\( \Delta S \)): Measure of disorder or randomness
• Gibbs Free Energy (\( \Delta G \)): Determines whether a reaction will occur spontaneously

Specifically, Hess's Law, a direct application of the enthalpy concept, allows the calculation of unknown enthalpy changes by summing known values from multiple reactions. The principle is particularly useful in predicting the energy changes in processes where direct calorimetric measurement might be challenging. In the realm of chemical thermodynamics, Hess's Law exemplifies the practical use of theoretical principles to solve real-world chemical problems, like calculating the energy involved in making hydrogen peroxide.