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 of \(\mathrm{CH}_{3} \mathrm{OH}(g)\) is decomposed by this reaction at constant pressure. (c) For a given sample of \(\mathrm{CH}_{3} \mathrm{OH},\) the enthalpy change during the reaction is 82.1 kJ. How many grams of methane gas are produced? (\mathbf{d} ) How many kilojoules of heatare 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?

Short answer

(a) The reaction is endothermic since ΔH = +252.8 kJ. (b) When 24.0 g of CH3OH is decomposed, the heat transferred is 188.793 kJ. (c) In the given reaction, 10.43 grams of methane gas are produced when the enthalpy change is 82.1 kJ. (d) When 38.5 g of CH4 reacts completely with O2 to form CH3OH at constant pressure, 303.077 kJ of heat are released.

Step-by-step solution

a) Identify if the reaction is exothermic or endothermic

If the enthalpy change, ΔH, is positive, the reaction is endothermic (absorbs heat). If the enthalpy change is negative, the reaction is exothermic (releases heat). The given enthalpy change for the reaction is: ΔH = +252.8 kJ Since the enthalpy change is positive, the reaction is endothermic.

b) Calculate the heat transferred for decomposing 24.0 g of CH3OH

First, we need to determine the moles of CH3OH. The molar mass of CH3OH is calculated as follows: Molar mass of CH3OH = (12.01 g/mol (C)) + (4 × 1.01 g/mol (H)) + (16.00 g/mol (O)) Molar mass of CH3OH = 32.05 g/mol Now, we will convert the given mass of CH3OH (24.0 g) to moles: Moles of CH3OH = (24.0 g) / (32.05 g/mol) = 0.748 mol Next, we will use the stoichiometry of the reaction to determine the moles of CH3OH participating in the reaction: 2 moles of CH3OH produce 252.8 kJ of heat 0.748 moles of CH3OH will produce ΔH = (0.748 mol) × (252.8 kJ / 2 mol) = 188.793 kJ So, the heat transferred when 24.0 g of CH3OH is decomposed is 188.793 kJ.

c) Find grams of methane produced given enthalpy change

Given that the enthalpy change during the reaction is 82.1 kJ, we can find out how many moles of CH3OH reacted: 82.1 kJ = (x moles CH3OH) × (252.8 kJ/2 mol CH3OH) x = (82.1 kJ) × (2 mol CH3OH / 252.8 kJ) = 0.650 mol of CH3OH Now, we use the stoichiometry of the reaction (2 moles CH3OH produce 2 moles CH4) to determine the moles of CH4 produced: 0.650 mol CH3OH produce 0.650 mol CH4 Finally, we convert the moles of CH4 to grams. The molar mass of CH4 is: Molar mass of CH4 = (12.01 g/mol (C)) + (4 × 1.01 g/mol (H)) = 16.05 g/mol Grams of CH4 = (0.650 mol) × (16.05 g/mol) = 10.43 g So, 10.43 grams of methane gas are produced.

d) Calculate heat released when 38.5 g of CH4 reacts with O2

This part of the problem is essentially the reverse reaction, which would have the opposite sign for the enthalpy change: $$2 \mathrm{CH}_{4} (g) + \mathrm{O}_{2} (g) \longrightarrow 2 \mathrm{CH}_{3} \mathrm{OH} (g) \quad \Delta H = -252.8 \mathrm{kJ}$$ First, we will convert the given mass of CH4 (38.5 g) to moles: Moles of CH4 = (38.5 g) / (16.05 g/mol) = 2.399 mol Now we use the stoichiometry of the reversed reaction to determine the heat released: 2 moles of CH4 react to release 252.8 kJ 2.399 moles of CH4 release ΔH = (2.399 mol) × (252.8 kJ / 2 mol) = 303.077 kJ So, 303.077 kJ of heat are released when 38.5 g of CH4 reacts completely with O2 to form CH3OH at constant pressure.

Key concepts

Enthalpy Change

Enthalpy change is an essential concept in thermochemistry, as it determines whether a chemical reaction absorbs or releases heat. In this exercise, the given reaction of converting methanol (\( \text{CH}_3\text{OH}(g) \)) into methane (\( \text{CH}_4(g) \)) and oxygen (\( \text{O}_2(g) \) ) shows an enthalpy change (\( \Delta H \)) of +252.8 kJ. A positive \( \Delta H \) signifies that the reaction is endothermic.

In an endothermic reaction, the system absorbs heat from the surroundings. This means that products have higher energy than the reactants, leading to a net intake of energy as bonds are broken and formed. Understanding enthalpy change helps in predicting reaction feasibility and stability, which are crucial in practical and industrial applications.

Exothermic and Endothermic Reactions

Chemical reactions can either release or absorb heat, making them exothermic or endothermic, respectively. In our exercise, the reaction is classified as endothermic because the enthalpy change is positive (+252.8 kJ). This means the reaction requires energy input to proceed.

Exothermic reactions, on the other hand, have a negative enthalpy change (\( \Delta H \)) and release heat to the surroundings, making the products less energetic than the reactants. Examples include the combustion of fuels and various oxidation reactions.

Knowing the type of reaction is vital as it influences reaction conditions. In endothermic reactions, for instance, external heat might be needed to maintain the reaction at a desired rate.

Stoichiometry

Stoichiometry is the study of quantitative relationships between reactants and products in a chemical reaction. In this exercise, stoichiometry is used to link the measured enthalpy change to the quantities of substances involved.

For the given reaction: \( 2 \text{CH}_3\text{OH}(g) \longrightarrow 2 \text{CH}_4(g) + \text{O}_2(g) \), stoichiometry tells us that 2 moles of \( \text{CH}_3\text{OH} \) produce the specified enthalpy change of +252.8 kJ.

• From this, we can calculate the heat involved when non-standard amounts react, such as 24.0 g of \( \text{CH}_3\text{OH} \).
• It also helps in determining the amount of methane produced from an energy change, as seen when 82.1 kJ corresponds to 10.43 g of methane.

Stoichiometry involves balancing equations and using the mole concept, making it a core skill in chemistry for predicting how much of each substance is required or produced in a reaction.

Heat Transfer Calculations

Heat transfer calculations are crucial in understanding how energy moves within a chemical system. In the context of this exercise, we have calculated the heat involved in various scenarios.

For decomposing 24.0 g of \( \text{CH}_3\text{OH} \), we determined the heat transferred using stoichiometry and molar masses:\[188.793 \text{ kJ}.\]

When 38.5 g of \( \text{CH}_4 \) reacts completely, the reversed reaction's enthalpy is used to find 303.077 kJ of heat released. These calculations require:

• Converting mass to moles using molar mass.
• Applying stoichiometric relationships to link heat change with moles of reactants or products.

Heat transfer calculations not only measure energy changes but also help in determining reaction efficiency and understanding thermodynamic principles in chemical processes.