Problem 64 - Chemistry The Central Science In Si Units

Question

From the enthalpies of reaction $$ 2 \mathrm{C}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}(g) \quad \Delta H=-221.0 \mathrm{~kJ} $$ \(2 \mathrm{C}(s)+\mathrm{O}_{2}(g)+4 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{CH}_{3} \mathrm{OH}(g) \quad \Delta H=-402.4 \mathrm{~kJ}\) calculate \(\Delta H\) for the reaction $$ \mathrm{CO}(g)+2 \mathrm{H}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(g) $$

Step-by-Step Solution

Step 1: Write Known Reactions

We are given two reactions with known enthalpies. Firstly,\[ 2 \mathrm{C}(s) + \mathrm{O}_2(g) \rightarrow 2 \mathrm{CO}(g) \quad \Delta H = -221.0 \, \text{kJ} \]Secondly,\[ 2 \mathrm{C}(s) + \mathrm{O}_2(g) + 4 \mathrm{H}_2(g) \rightarrow 2 \mathrm{CH}_3\mathrm{OH}(g) \quad \Delta H = -402.4 \, \text{kJ} \]

Key Concepts

The Basics of Thermochemistry

Thermochemistry is a fascinating branch of chemistry that deals with the heat energy involved in chemical reactions. It's all about understanding how energy is released or absorbed during these reactions.
In thermochemistry, one of the most important concepts is enthalpy, often denoted as \( \Delta H \). Enthalpy changes tell us about the heat content of a system. It's a valuable measure for determining how much energy a reaction requires or releases.
When the enthalpy change or \( \Delta H \) is negative, the reaction releases energy to the surroundings, known as an exothermic reaction. Conversely, if \( \Delta H \) is positive, the reaction absorbs energy, making it endothermic. Understanding the enthalpy change helps predict whether a reaction is viable for processes like fuel combustion or biological energy transformations.
Key points in thermochemistry:

• Energy changes are measured in kilojoules (kJ).
• Enthalpy changes give insight into the heat involved during a reaction.
• Thermochemistry plays a crucial role in industry, energy production, and environmental science.

Let's dive deeper into how our exercise relates to these concepts by exploring Hess's Law.

Explaining Hess's Law

Hess's Law is a useful principle in thermochemistry that allows us to determine the enthalpy change of a reaction even if it can't be measured directly. The law states: The total enthalpy change of a chemical reaction is the same, no matter how many different steps occur in the reaction.
This principle relies on the idea that enthalpy is a state function, meaning its value depends only on the initial and final states, not on the path taken.
In our original exercise, Hess's Law is used to find the enthalpy change, \( \Delta H \), for the formation of methanol (\( \text{CH}_3 ext{OH} \)) from carbon monoxide (\( \text{CO} \)) and hydrogen (\( \text{H}_2 \)). To calculate this, we use two known reactions:

• The formation of carbon monoxide from carbon.
• The formation of methanol directly from carbon.

By rearranging these known reactions and their enthalpies, we can find the enthalpy change for the target reaction. It's like using a map: no matter which route you take, the start and end points define the journey.
Hess's Law is particularly valuable because it:

• Helps design industrial processes with precise energy requirements.
• Enables calculations for reactions that can't be observed directly.
• Supports environmental applications in assessing reaction energy changes.

Understanding and applying Hess's Law can greatly enhance problem-solving skills in thermochemistry.

Understanding Chemical Reactions

Chemical reactions are processes where substances, called reactants, transform into new substances, known as products. These transformations involve breaking and forming chemical bonds, and are often accompanied by energy changes.
Key components of chemical reactions include:

• Reactants: Substances that start the reaction.
• Products: New substances formed in the reaction.
• Reaction conditions: Variables like temperature and pressure that can affect the reaction's course.

Energy plays a crucial role, as bonds require energy to break and release energy on forming new bonds. This energy change is directly linked to the reaction's enthalpy \( \Delta H \).
In our specific exercise, we are focused on a reaction producing methanol from carbon monoxide and hydrogen. This involves combining hydrogen molecules with carbon monoxide, creating a new compound. Understanding chemical reactions is essential in fields such as:

• Pharmaceuticals: Developing new drugs.
• Energy: Creating more efficient processes for generating and using energy.
• Agriculture: Developing fertilizers that increase crop yields.

Grasping the essentials of chemical reactions equips students to predict the behavior of substances and energy in various scientific and real-world applications.