Problem 44 - Chemistry The Central Science In Si Units

Question

Consider the following reaction: $$ 2 \mathrm{CH}_{3} \mathrm{OH}(g) \longrightarrow 2 \mathrm{CH}_{4}(g)+\mathrm{O}_{2}(g) \quad \Delta H=+252.8 \mathrm{~kJ} $$ (a) Is this reaction exothermic or endothermic? (b) Calculate the amount of heat transferred when \(24.0 \mathrm{~g}\) of \(\mathrm{CH}_{3} \mathrm{OH}(g)\) is decomposed by this reaction at constant pressure. \((\mathbf{c})\) For a given sample of \(\mathrm{CH}_{3} \mathrm{OH},\) the enthalpy change during the reaction is \(82.1 \mathrm{~kJ} .\) How many grams of methane gas are produced? (d) How many kilojoules of heat are released when \(38.5 \mathrm{~g}\) of \(\mathrm{CH}_{4}(g)\) reacts completely with \(\mathrm{O}_{2}(g)\) to form \(\mathrm{CH}_{3} \mathrm{OH}(g)\) at constant pressure?

Step-by-Step Solution

Answer

(a) Endothermic. (b) 94.5 kJ. (c) 10.4 g. (d) 303.4 kJ released.

Step 1: Determine Exothermic or Endothermic

The reaction has an enthalpy change \( \Delta H = +252.8 \text{kJ} \). A positive \( \Delta H \) indicates that the reaction absorbs heat, meaning it is an endothermic reaction.

Step 2: Calculate Moles of CH₃OH in 24.0 g

First, calculate the molar mass of \( \text{CH}_3\text{OH} \). Its molar mass is \( 12.01 + 3\times1.01 + 16.00 + 1.01 = 32.04 \text{ g/mol} \). The moles of \( \text{CH}_3\text{OH} \) in 24.0 g are calculated by: \[ \text{moles} = \frac{24.0 \text{ g}}{32.04 \text{ g/mol}} = 0.749 \text{ moles} \]

Step 3: Calculate Heat for 24.0 g of CH₃OH

The reaction as given decomposes \(2 \text{ moles} \) of \( \text{CH}_3\text{OH} \) and releases \(252.8 \text{kJ} \). Since we have \(0.749 \text{ moles} \) of \( \text{CH}_3\text{OH} \), the heat transferred is: \[ \text{heat} = 0.749 \text{ moles} \times \frac{252.8 \text{kJ}}{2 \text{ moles}} = 94.5 \text{kJ} \]

Step 4: Determine Moles from Given Enthalpy Change

Given that the reaction enthalpy change is \( 82.1 \text{kJ} \), and knowing the heat change per 2 moles of \( \text{CH}_3\text{OH} \) is \(252.8 \text{kJ} \), use the ratio: \[ \text{moles of } \text{CH}_3\text{OH} = \frac{82.1 \text{kJ}}{252.8 \text{kJ}} \times 2 \approx 0.649 \text{ moles} \] of \( \text{CH}_3\text{OH} \).

Step 5: Calculate Produced CH₄ from Moles of CH₃OH

Since 2 moles of \( \text{CH}_3\text{OH} \) produce 2 moles of \( \text{CH}_4 \), \(0.649 \text{ moles} \) of \( \text{CH}_3\text{OH} \) will produce \(0.649 \text{ moles} \) of \( \text{CH}_4 \). The mass of \( \text{CH}_4 \) is calculated as: \[ \text{mass} = 0.649 \text{ moles} \times 16.04 \text{ g/mol} \approx 10.4 \text{ g} \]

Step 6: Determine Heat Released from 38.5 g CH₄ Formation

Find moles of \( \text{CH}_4 \) in 38.5 g using its molar mass (16.04 g/mol): \[ \text{moles} = \frac{38.5 \text{ g}}{16.04 \text{ g/mol}} \approx 2.4 \text{ moles} \]. Since \(2 \text{ moles} \) of \( \text{CH}_4 \) produces \(252.8 \text{kJ} \), \(2.4 \) moles will release: \[ \text{heat} = 2.4 \text{ moles} \times \frac{252.8 \text{kJ}}{2 \text{ moles}} = 303.4 \text{kJ} \].

Key Concepts

Enthalpy Change

Enthalpy change, denoted as \( \Delta H \), is a crucial concept in thermochemistry, representing the heat change during a reaction at constant pressure. The sign of \( \Delta H \) tells us whether a reaction absorbs or releases heat. A positive \( \Delta H \), like in the given reaction \( 2 \mathrm{CH}_3\mathrm{OH}(g) \longrightarrow 2 \mathrm{CH}_4(g) + \mathrm{O}_2(g) \) with \( \Delta H = +252.8 \mathrm{~kJ} \), indicates an endothermic process. This means that the reaction requires energy input from its surroundings.

Understanding enthalpy change is not only about determining the heat exchange; it also involves the balance between breaking and forming bonds.

• Breaking chemical bonds requires energy, which contributes to an endothermic reaction.
• Forming new bonds releases energy, typically associated with exothermic reactions, which are characterized by a negative \( \Delta H \).

The study of enthalpy enables chemists to predict how reactions interact with their environment, which is essential for applications requiring temperature control or energy usage.

Mole Calculations

Mole calculations are fundamental in chemistry for quantifying substances involved in reactions. The mole is a unit that represents a specific number of particles, usually atoms or molecules. To find moles, you divide the mass of the substance by its molar mass. For example, calculating the moles of \( \text{CH}_3\text{OH} \) given a mass of 24.0 g:
The molar mass is calculated as follows: Carbon: \( 12.01 \text{ g/mol} \), Hydrogen: \( 1.01 \times 4 = 4.04 \text{ g/mol} \), Oxygen: \( 16.00 \text{ g/mol} \). Adding these gives \( 32.04 \text{ g/mol} \).

The number of moles is calculated by: \[ \text{moles} = \frac{24.0 \text{ g}}{32.04 \text{ g/mol}} \approx 0.749 \text{ moles} \]This step is critical for determining the scale of reactions and associating it with energy transfer through enthalpy change.

Specific to this exercise, understanding mole calculations assists in finding the amount of heat energy exchanged and the quantities of products formed in reactions, making it a vital skill for solving thermochemistry problems.

Endothermic Reactions

Endothermic reactions are those that absorb energy from their surroundings, resulting in a positive enthalpy change (\( \Delta H > 0 \)). In the context of the given chemical equation, the reaction of \( 2 \mathrm{CH}_3\mathrm{OH}(g) \) forming \( 2 \mathrm{CH}_4(g) \) and \( \mathrm{O}_2(g) \) with \( \Delta H = +252.8 \mathrm{~kJ} \) is explicitly endothermic.

Key characteristics of endothermic reactions include:

• The surroundings feel colder as they lose heat to the reaction.
• The system (i.e., the reactants) gains energy, causing the enthalpy of the products to be higher than the reactants.

These reactions can occur naturally or be initiated by supplying external energy, such as heat or light. A classic example besides chemical decomposition is the melting of ice, where energy is absorbed to break hydrogen bonds.

Understanding endothermic reactions is fundamental in fields where controlled energy absorption is crucial, such as materials science and environmental engineering. Recognizing the role of endothermic processes aids in designing reactions that can harness or mitigate energy absorption effectively.