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. (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 \(\mathrm{CH}_{3} \mathrm{OH}(\mathrm{g})\) at constant pressure? 5.45 When solutions containing silver ions and chloride ions are mixed, silver chloride precipitates: $$ \mathrm{Ag}^{+}(a q)+\mathrm{Cl}^{-}(a q) \longrightarrow \operatorname{AgCl}(s) \quad \Delta H=-65.5 \mathrm{~kJ} $$ (a) Calculate \(\Delta H\) for the production of \(0.450 \mathrm{~mol}\) of \(\mathrm{AgCl}\) by this reaction. (b) Calculate \(\Delta H\) for the production of \(9.00 \mathrm{~g}\) of \(\mathrm{AgCl}\). (c) Calculate \(\Delta H\) when \(9.25 \times 10^{-4} \mathrm{~mol}\) of \(\mathrm{AgCl}\) dissolves in water.

Short answer

The reaction is endothermic. (b) 94.6 kJ of heat is transferred when 24.0 g of CH₃OH is decomposed. (c) 10.4 g of methane gas is produced when the enthalpy change is 82.1 kJ. (d) 151.7 kJ of heat is released when 38.5 g of CH₄ reacts completely with O₂.

Step-by-step solution

(a) Exothermic or Endothermic Reaction

The enthalpy change of the reaction, ΔH, is positive, which means the reaction is endothermic. An endothermic reaction absorbs heat from the surroundings.

(b) Heat Transferred for 24.0 grams of CH3OH

We will first convert the mass of CH3OH to moles and then use the stoichiometry of the reaction to calculate the heat transferred. 1. Convert mass of CH3OH to moles: Molar mass of CH3OH = 12.01 (C) + 3×1.01 (H) + 1.01 (H) + 16.00 (O) = 32.04 g/mol Moles of CH3OH = \(\frac{24.0~g}{32.04~g/mol}\) = 0.749 moles 2. Calculate the heat transferred: ΔH is given per 2 moles of CH3OH, so we need to find the heat transferred for 0.749 moles of CH3OH. Heat transferred = ΔH × \(\frac{0.749~mol}{2~mol} = 252.8~kJ × \frac{0.749}{2} = 94.6~kJ\)

(c) Methane Gas Produced

We are given the enthalpy change during the reaction as 82.1 kJ. We will use this to find the moles of CH4 produced and then convert it to grams. 1. Calculate moles of CH4 produced: Moles of CH4 = \(\frac{82.1~kJ}{252.8~kJ/2~mol}\) = 0.650 moles 2. Convert moles of CH4 to grams: Molar mass of CH4 = 12.01 (C) + 4x1.01 (H) = 16.04 g/mol Mass of CH4 = 0.650 moles × 16.04 g/mol = 10.4 grams

(d) Heat Released for 38.5 grams of CH4

We will first convert the mass of CH4 to moles, and then using the stoichiometry of the reaction, calculate the heat released. 1. Convert mass of CH4 to moles: Moles of CH4 = \(\frac{38.5~g}{16.04~g/mol}\) = 2.40 moles 2. Calculate heat released: Heat released = ΔH × \(\frac{2.40~mol}{4~mol} = -252.8~kJ × \frac{2.40}{4} = - 151.7~kJ\) The negative sign indicates heat is released.

Key concepts

Endothermic Reaction

An endothermic reaction is one where energy is absorbed from the surroundings. This type of reaction results in a positive change in enthalpy (ΔH).
When we look at the given exercise, the reaction between methanol (CH₃OH) and oxygen is characterized by ΔH = +252.8 kJ, which is indeed positive. This confirms that the reaction is endothermic.

• Energy Absorption: Endothermic reactions require input energy to proceed, often making them non-spontaneous under normal conditions without an external energy source.
• Enthalpy Change: Since ΔH is positive, the reactants absorb heat, storing it within the chemical bonds of the products.

In such reactions, temperature of the immediate surroundings usually drops because the system absorbs heat from it. Recognizing endothermic reactions is crucial for understanding energy changes in thermodynamics and chemical reactions.

Stoichiometry

Stoichiometry deals with the quantitative relationships between reactants and products in a chemical reaction. It helps us calculate the amount of substances consumed and formed.
In the exercise, stoichiometry is used to determine the heat transfer when a certain amount of methanol is decomposed.

• Mole Conversion: For example, converting grams of CH₃OH to moles using its molar mass helps in calculating how the amount of reactant relates to other substances involved in the reaction.
• Heat Calculation: Once moles are known, stoichiometry helps relate moles of a substance to the heat change using the reaction's enthalpy values. For this particular reaction, the heat absorbed is proportional to the moles of CH₃OH decomposed.
• Mass-to-Mass Calculations: Converting moles back to mass, as demonstrated in the problem, allows us to understand the practical quantities of substances needed or produced.

Mastering stoichiometry is essential for solving chemical equations and ensures accurate predictions in laboratory experiments and industrial processes.

Heat Transfer

Heat transfer in chemical reactions is the movement of thermal energy as a reaction proceeds. It can involve energy absorption or release, affecting the environment and the system.
For example, in our exercise, the heat transfer calculation involves finding how much energy is shifted based on the reaction's stoichiometry.

• Energy Balance: Knowing the total ΔH helps in understanding how much energy was gained or lost by the system and the surroundings.
• Calculation of Heat: The calculation of transferred heat (94.6 kJ) when 24.0 grams of methanol decomposes showcases practical applications of these concepts.
  • In case of endothermic reactions, such as this decomposition, the system absorbs heat, measured by the positive ΔH.
  • For exothermic processes (not in this reaction), heat is released, resulting in a negative ΔH.
• Thermodynamic Applications: Heat transfer tells us how energy is conserved or lost in reactions, crucial for designing reactors and managing chemical processes.

Understanding heat transfer allows chemists to control reactions better and optimize conditions for efficiency and safety.