Question

Consider the following reaction: $$ \mathrm{CH}_{3} \mathrm{OH}(g) \longrightarrow \mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \quad \Delta H=+90.7 \mathrm{~kJ} $$ (a) Is heat absorbed or released in the course of this reaction? (b) Calculate the amount of heat transferred when \(45.0 \mathrm{~g}\) 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 on reaction is \(25.8 \mathrm{~kJ}\). How many grams of hydrogen gas are produced? What is the value of \(\Delta H\) for the reverse of the previous reaction? (d) How many kilojoules of heat are released when \(50.9 \mathrm{~g}\) of \(\mathrm{CO}(g)\) reacts completely with \(\mathrm{H}_{2}(g)\) to form \(\mathrm{CH}_{3} \mathrm{OH}(g)\) at constant pressure?

Short answer

(a) As the given enthalpy change \(\Delta H\) is positive (+90.7 kJ), heat is absorbed in the course of this reaction. (b) The heat transferred when \(45.0\, g\) of \(\mathrm{CH}_{3}\mathrm{OH}\) decomposes is \(127.3\, kJ\). (c) When the enthalpy change is \(25.8\, kJ\), \(1.15\, g\) of hydrogen gas is produced, and the value of \(\Delta H\) for the reverse reaction is \(-90.7\, kJ\). (d) The heat released when \(50.9\, g\) of \(\mathrm{CO}(g)\) reacts completely is \(164.8\, kJ\).

Step-by-step solution

(a) Determine if heat is absorbed or released

Since the given enthalpy change, \(\Delta H\) for the reaction is positive (+90.7 kJ), it indicates that the reaction is endothermic, meaning heat is absorbed in the course of this reaction.

(b) Calculate the heat transferred when 45.0 g of CH3OH(g) decomposes

First, find the moles of \(\mathrm{CH}_{3}\mathrm{OH}\) present in 45.0 g. The molar mass of \(\mathrm{CH}_{3}\mathrm{OH}\) is: Molar mass = (12.01 + 3 * 1.01 + 1 * 16.00) g/mol = 32.04 g/mol. So, moles of \(\mathrm{CH}_{3}\mathrm{OH}\) = mass / molar mass = \(45.0 g / 32.04 g/mol = 1.404 mol\) The reaction shows that one mole of \(\mathrm{CH}_{3}\mathrm{OH}\) absorbs 90.7 kJ of heat. Thus, for 1.404 moles, the heat transfer would be: \(q = 1.404 \ mol \times 90.7 \ kJ/mol = 127.3 \ kJ\)

(c) Calculate the amount of H2 produced and the enthalpy change of the reverse reaction

From the reaction: \(1 \ mol \textrm{ of } \mathrm{CH}_{3}\mathrm{OH} \longrightarrow 2 \ mol \ \textrm{ of } \mathrm{H}_{2}\) For the enthalpy change of 25.8 kJ, let's find how many moles of \(\mathrm{CH}_{3}\mathrm{OH}\): \(moles = \dfrac{25.8 \ kJ}{90.7\ kJ/mol} = 0.284\textrm{ mol}\) Now we can find moles of \(\mathrm{H}_{2}\) produced: \(moles_{H_{2}} = 2 \times 0.284\textrm{ mol} = 0.568\textrm{ mol}\) Next, let's find the mass of H2 produced: Molar mass of H2 = (2 * 1.01) g/mol = 2.02 g/mol Mass of H2 produced = moles of H2 * molar mass = \(0.568\, mol \times 2.02\, g/mol = 1.15\, g\) For the reverse reaction, the enthalpy change will be the negative of the forward reaction: \(\Delta H_{reverse} = -\Delta H = -90.7\, kJ\)

(d) Calculate the heat released when 50.9 g of CO(g) reacts completely

First, find how many moles of CO are present: Molar mass of CO = (12.01 + 1 * 16.00) g/mol = 28.01 g/mol Moles of CO = mass / molar mass = \(50.9\, g / 28.01\, g/mol = 1.818\, mol\) The reverse reaction is \(\mathrm{CO}(g) + 2\ \mathrm{H}_{2}(g) \longrightarrow \mathrm{CH}_{3}\mathrm{OH}(g)\) with \(\Delta H = -90.7\, kJ\). For every mole of CO consumed, the heat released will be 90.7 kJ. Thus, for 1.818 moles, heat released would be: \(q = 1.818\, mol \times 90.7\, kJ/mol = 164.8\, kJ\)

Key concepts

Thermochemistry

Thermochemistry is a branch of physical chemistry that involves the study of heat energy associated with chemical reactions and physical transformations. A key concept in thermochemistry is the enthalpy change (\r\( \Delta H \)), which represents the heat absorbed or released during a reaction at constant pressure. An enthalpy change can be categorized as either exothermic, where heat is released (\r\( \Delta H < 0 \)), or endothermic, where heat is absorbed (\r\( \Delta H > 0 \)). Understanding enthalpy changes is crucial for calculating the energy required for a reaction or the energy produced by a reaction, and this information is essential for various applications, including energy production, material synthesis, and temperature control in chemical processes.

To calculate the enthalpy change in a reaction, the amount of substance participating in the reaction (usually in moles) is multiplied by the per-mole enthalpy change. This calculation is integral to understanding both the theoretical and practical aspects of energy management in chemical reactions.

Endothermic Reactions

Endothermic reactions are chemical processes that absorb energy from the surroundings in the form of heat. This absorption of heat results in a temperature decrease in the environment unless the system is continually supplied with energy to maintain constant temperature conditions. The characteristic feature of an endothermic reaction is a positive value for the enthalpy change (\r\( \Delta H > 0 \)). An example of such a reaction is the decomposition of methanol (\r\( \mathrm{CH}_{3} \mathrm{OH}(g) \)) into carbon monoxide (\r\( \mathrm{CO}(g) \)) and hydrogen gas (\r\( \mathrm{H}_{2}(g) \)), where heat is absorbed and the value of \r\( \Delta H \) is expressed as +90.7 kJ.

Students learning about endothermic reactions should also understand that these reactions require continuous input of energy to proceed, and they play a vital role in various natural and industrial processes, such as photosynthesis and the production of certain pharmaceuticals.

Molar Mass Calculation

The molar mass of a substance is the mass in grams of one mole of that substance. It is a critical factor in stoichiometric calculations as it allows chemists to convert between mass and moles of a substance. Calculating molar mass involves summing the atomic masses of all the atoms in a given formula unit or molecule. Atomic masses are usually found on the periodic table and are expressed in atomic mass units (amu). For example, the molar mass of methanol (\r\( \mathrm{CH}_{3} \mathrm{OH} \)) is calculated by adding the atomic masses of carbon (12.01 amu), hydrogen (3 times 1.01 amu), and oxygen (16.00 amu), resulting in a molar mass of 32.04 g/mol.

It is essential for students to comprehend this concept, as it enables them to relate the microscopic (atomic or molecular) scale to the macroscopic scale that can be measured in the laboratory. Precise knowledge of molar masses is indispensable for accurate chemical quantitation and the preparation of reaction mixtures.

Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It is derived from the balanced chemical equation and is founded on the conservation of mass and the concept of the mole. Stoichiometry requires the knowledge of molar masses and the concept of the mole ratio, which relates the proportions of reactants and products. For instance, the decomposition of methanol reaction shows a mole ratio of 1 mole of methanol to 1 mole of carbon monoxide to 2 moles of hydrogen gas.

By using stoichiometry, one can determine the amount of reactants needed to produce a desired amount of product or the amount of product that can be produced from given reactants. It's a foundational tool in chemistry that enables predictions about the outcomes of reactions. For example, if a certain amount of heat is released or absorbed in a reaction, stoichiometry can help us calculate how much reactant was involved or how much product was created, as seen in various steps of the exercise provided.