Question

Hydrogen gas is being considered as a fuel for automobiles. There are many chemical means for producing hydrogen gas from water. One of these reactions is $$\mathrm{C}(s)+{\mathrm{H}}_2\mathrm{O}(g)⟶\mathrm{CO}(g)+{\mathrm{H}}_2(g)$$ In this case the form of carbon used is graphite. a. Calculate $\mathrm{\Delta }{H}^{\circ }$ and $\mathrm{\Delta }{S}^{\circ }$ for this reaction using data from Appendix $4.$ b. At what temperatures is this reaction spontaneous? Assume $\mathrm{\Delta }{H}^{\circ }$ and $\mathrm{\Delta }{S}^{\circ }$ do not depend on temperature.

Short answer

The standard enthalpy change (ΔH°) for the given reaction is 131.296 kJ/mol, and the standard entropy change (ΔS°) is 133.760 J/(mol * K). The reaction is spontaneous for temperatures greater than 981.74 K.

Step-by-step solution

Calculate ΔH° and ΔS°

We have the following reaction: $C(s)+H_{2}O(g)\to CO(g)+H_2(g)$ Using the thermodynamic data in Appendix 4, we can calculate ΔH° and ΔS° based on the values for each of the constituent species. The standard enthalpy change (ΔH°) and the standard entropy change (ΔS°) can be calculated using the following formulae: ΔH° = Σ (ΔH_product°) - Σ (ΔH_reactant°) ΔS° = Σ (ΔS_product°) - Σ (ΔS_reactant°) From Appendix 4, we have: ΔH° and ΔS° for C(s): 0 kJ/mol, 5.74 J/(mol * K) ΔH° and ΔS° for H2O(g): -241.826 kJ/mol, 188.84 J/(mol * K) ΔH° and ΔS° for CO(g): -110.530 kJ/mol, 197.66 J/(mol * K) ΔH° and ΔS° for H2(g): 0 kJ/mol, 130.68 J/(mol * K) Now, we can plug these values into the respective formulae and calculate ΔH° and ΔS° for the overall reaction. ΔH° = [(-110.530) + (0)] - [(0) + (-241.826)] = 131.296 kJ/mol ΔS° = [(197.66) + (130.68)] - [(5.74) + (188.84)] = 133.760 J/(mol * K)

Determining spontaneous reaction temperature

A reaction is spontaneous if ΔG° < 0, where ΔG° is the standard Gibbs free energy change. We can use the following formula to find ΔG°: ΔG° = ΔH° - T * ΔS° Assuming ΔH° and ΔS° do not depend on temperature, to find the temperature range where the reaction is spontaneous, we solve for T: ΔG° < 0 => ΔH° - T * ΔS° < 0 => T > (ΔH° / ΔS°) T > (131.296 kJ/mol) / (133.760 J/(mol * K)) => T > (131296 J/mol) / (133.760 J/(mol * K)) T > 981.74 K The reaction is spontaneous for temperatures greater than 981.74 K.

Key concepts

Gibbs Free Energy

Gibbs Free Energy ($\mathrm{\Delta }G$) is a fundamental concept in chemistry that determines the spontaneity of a reaction. It combines enthalpy ($\mathrm{\Delta }H$) and entropy ($\mathrm{\Delta }S$) into a single value that predicts whether a reaction will occur without the input of additional energy. The formula for Gibbs Free Energy is:$$\mathrm{\Delta }G=\mathrm{\Delta }H-T\cdot \mathrm{\Delta }S$$Where $T$ is the temperature in Kelvin. A negative $\mathrm{\Delta }G$ indicates that the reaction is spontaneous and can proceed on its own. On the other hand, a positive $\mathrm{\Delta }G$ suggests that the reaction requires energy input to occur. This balance between entropy and enthalpy helps chemists predict how chemical reactions are likely to proceed under various conditions.

Enthalpy and Entropy

In thermodynamics, enthalpy ($\mathrm{\Delta }H$) is the measure of the total heat content of a system. It provides insight into the energy changes that occur during a chemical reaction. A negative $\mathrm{\Delta }H$ generally suggests an exothermic reaction, releasing heat, while a positive $\mathrm{\Delta }H$ indicates an endothermic reaction, absorbing heat.Entropy ($\mathrm{\Delta }S$) is a measurement of the disorder or randomness in a system. Increased entropy suggests that a system's energy is more spread out, which often aligns with natural processes. For reactions to be spontaneous, the change in entropy and enthalpy needs to work together to lower the free energy of the system. This balance is crucial in determining whether a chemical process, like hydrogen production, will occur naturally or needs external energy inputs.

Spontaneity of Reactions

A reaction's spontaneity is essential for determining its viability without external energy. A spontaneous reaction has a negative Gibbs Free Energy ($\mathrm{\Delta }G<0$), implying it moves forward without energy input. It doesn't necessarily mean the reaction happens instantly or explosively but rather that it is thermodynamically favorable.Factors affecting spontaneity:

• Temperature: Higher temperatures can influence $\mathrm{\Delta }G$ by increasing the effect of entropy on free energy.
• Enthalpy: Endothermic reactions ($\mathrm{\Delta }H>0$) may need very favorable entropy or high temperatures to become spontaneous.
• Entropy: Reactions that increase entropy are more likely to be spontaneous.

For the reaction: $C(s)+H_{2}O(g)\to CO(g)+H_2(g)$, it becomes spontaneous at temperatures above 981.74 K as calculated by evaluating $\mathrm{\Delta }G$.

Hydrogen Production

Hydrogen production is an area of intense research due to hydrogen's potential as a clean fuel. Among various methods to produce hydrogen, reactions involving water and carbon-based materials, such as the reaction being studied, are significant because they can use widely available resources.This particular reaction involves transforming graphite and steam into carbon monoxide and hydrogen gas. Such reactions are vital in producing hydrogen for fuel cells, which can provide energy without producing carbon dioxide. The key to these reactions is finding conditions under which they are spontaneous and energy-efficient. Understanding $\mathrm{\Delta }G$, $\mathrm{\Delta }H$, and $\mathrm{\Delta }S$ helps identify the parameters required for optimizing hydrogen production processes.

Chemical Reactions

Chemical reactions are core processes in chemistry where substances transform into different materials. A reaction's likelihood depends on a myriad of factors, including $\mathrm{\Delta }G$, which indicates spontaneity, and whether energy or catalysts are present.Key Characteristics:

• Reactants and Products: What materials change and the substances they become.
• Energy Changes: Determining if a reaction absorbs or releases heat ($\mathrm{\Delta }H$).
• Disorder: Changes in entropy that signify if a reaction may occur ($\mathrm{\Delta }S$).

The specific reaction of forming hydrogen from water using carbon showcases these principles. By breaking bonds in the reactants and forming new bonds in the products, energy and entropy dictate the feasibility of the desired transformation. Understanding these concepts is vital for advancements in chemical research and technology.