Question

The reaction that produces the water gas mixture, described in Question 6.99, is $$ \mathrm{C}(s)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{CO}(g)+\mathrm{H}_{2}(g) $$ This reaction requires an input of \(131 \mathrm{~kJ}\) of heat for every mole of carbon that reacts. (a) Is this reaction endothermic or exothermic? (b) What is the energy change for this reaction in units of \(\mathrm{kJ} / \mathrm{mol}\) of carbon?

Short answer

The reaction is endothermic because it requires heat from its surroundings and the energy change is +131 kJ per mole of carbon.

Step-by-step solution

Determine the type of reaction

First, understand what it means when a reaction requires heat. If the reaction consumes heat, it is taking in energy from its surroundings. Hence, to determine whether the reaction is endothermic or exothermic, look at whether the reaction requires or releases heat. In this case, the reaction requires an input of 131 kJ of heat for every mole of carbon, which means it's an endothermic reaction as it absorbs heat.

Calculate the energy change in kilojoules per mole

Next, to calculate the energy change for the reaction in the units of kJ/mol, use the given heat input. The amount of heat energy required per mole of Carbon for this reaction is already provided in the question: 131 kJ. This, therefore, is the energy change, per mole, for this reaction. It's important to note that because this is an endothermic reaction (heat is absorbed), this energy change is considered as a positive value.

Key concepts

Chemical Reactions

Understanding chemical reactions is vital for comprehending the transformative processes that substances undergo. A chemical reaction involves the conversion of reactants into products through the breaking and forming of chemical bonds. In this context, we review an example transition:
\[ \text{C}(s)+\text{H}_2 \text{O}(g) \longrightarrow \text{CO}(g)+\text{H}_2(g) \]
The symbol \( s \) denotes a solid, \( g \) is for gases, and the arrow signifies the direction in which the reaction proceeds. The reaction depicts the transformation of solid carbon and water vapor into carbon monoxide and hydrogen gas. It is crucial to note that during a chemical reaction, the total mass of the reactants must be equal to the total mass of the products, this principle is known as the Law of Conservation of Mass.
To provide a clear example for the student, represented in a balanced chemical equation, reveals how atoms are rearranged and conserved through the reaction. This concept directly correlates with the mole concept and enthalpy change, as the quantity of substances and energy involved will influence the reaction dynamics.

Enthalpy Change

Enthalpy change is an essential concept when exploring the energetics of chemical reactions. It represents the heat exchange with the surroundings at constant pressure. Enthalpy change can be either positive or negative, indicating whether the system absorbs or releases heat, respectively.
Reactants and products contain intrinsic energy, and the enthalpy change (\( \Delta H \)) measures the difference in stored chemical energy between them. An endothermic reaction, like the one given in the exercise, requires heat to proceed, thus \( \Delta H \) is positive. In the provided example:
\[ \Delta H = +131 \text{ kJ/mol} \]
This positive sign is indicative of the energy the reactants must absorb from the surroundings to form products. Elaborating further, students should recognize that endothermic reactions often result in cooling of the environment, as the system absorbs heat, while exothermic reactions typically cause the environment to heat up. Understanding enthalpy changes can give students insights into reaction conditions, thermodynamic stability, and predict whether a reaction will occur spontaneously.

Mole Concept

Grasping the mole concept is fundamental in chemistry, as it bridges the microscopic world of atoms and the macroscopic world we can measure. The mole is a unit of measurement used to express the amount of a chemical substance. It corresponds to Avogadro's number (approximately \(6.022 \times 10^{23}\)), which is the number of atoms, ions, or molecules in one mole of substance.
In the context of the exercise, the 'per mole' aspect is crucial. When the problem states that '131 kJ of heat is required for every mole of carbon,' it means for every \(6.022 \times 10^{23}\) atoms of carbon reacting, 131 kJ of energy is absorbed. Thus, the mole concept allows us to use these large numbers in a manageable form, facilitating easier calculations of particles and energy in chemical reactions.
Emphasizing this concept in relation to the given exercise, students can better comprehend that the enthalpy change is not only a sheer figure but is tied to a specific amount of substance – in this case, a mole of carbon atoms. Such understanding invites a deeper insight into the scalability of chemical processes. It illustrates how chemists must calculate precisely to predict the outcomes of reactions, whether they're occurring in a beaker or an industrial reactor.