Question

Water gas is produced from the reaction of steam with coal: $$\mathrm{C}(s)+{\mathrm{H}}_2\mathrm{O}(g)⟶{\mathrm{H}}_2(g)+\mathrm{CO}(g)$$ Assuming that coal is pure graphite, calculate $\mathrm{\Delta }{H}^{\circ }$ for this reaction.

Short answer

The standard enthalpy change for the reaction between graphite and steam to produce water gas is 131.3 kJ/mol. This is calculated using the formula ∆H° = sum of the standard enthalpies of formation of the products − sum of the standard enthalpies of formation of the reactants, and using the given standard enthalpies of formation for CO, H2O, C (graphite), and H2.

Step-by-step solution

1. Gather the relevant data

We need to gather the standard enthalpies of formation for the substances involved in the reaction. For this, we can consult a table of standard enthalpies of formation. We will find the following values: - ∆Hf° (CO) = -110.5 kJ/mol - ∆Hf° (H2O) = -241.8 kJ/mol - ∆Hf° (C, graphite) = 0 kJ/mol (since graphite is the standard state of carbon) - ∆Hf° (H2) = 0 kJ/mol (since H2 is in its standard state)

2. Use the formula to calculate ∆H°

Now that we have the necessary data, we can apply the formula: ∆H° = [∆Hf° (H2) + ∆Hf° (CO)] - [∆Hf° (C, graphite) + ∆Hf° (H2O)] Plugging in the values: ∆H° = [0 + (-110.5)] - [0 + (-241.8)] Calculating the sum: ∆H° = -110.5 + 241.8 ∆H° = 131.3 kJ/mol The standard enthalpy change for the reaction between graphite and steam to produce water gas is 131.3 kJ/mol.

Key concepts

Standard Enthalpy of Formation

The standard enthalpy of formation is a fundamental concept in chemistry that helps us understand how much energy is absorbed or released during the formation of a substance from its elements in their standard states. Standard states refer to the most stable form of an element at 1 atm pressure and a specified temperature, commonly 25°C. For example, the standard state of carbon is graphite. The standard enthalpy of formation, $\mathrm{\Delta }{H}_f^{\circ }$, is usually expressed in kJ/mol indicating how much energy per mol is involved.

• A negative value of $\mathrm{\Delta }{H}_f^{\circ }$ indicates an exothermic reaction, where energy is released.
• A positive value suggests an endothermic process, where energy is absorbed.

In the given exercise, we calculated the standard enthalpy change for a reaction using values from a table of standard enthalpies of formation. It's crucial because it allows prediction and understanding of energy changes in reactions.

Water Gas Reaction

The water gas reaction is an important industrial process where steam reacts with carbon, typically in the form of coke or coal, to produce a mixture known as water gas. The chemical equation for this process is:$$\mathrm{C}(s)+{\mathrm{H}}_2\mathrm{O}(g)\to {\mathrm{H}}_2(g)+\mathrm{CO}(g)$$In simpler terms, this reaction transforms steam (water vapor) and carbon into hydrogen gas and carbon monoxide.

• The produced hydrogen can be used as a cleaner energy source.
• Carbon monoxide can be further processed or used in synthesis gas mixtures.

The enthalpy change for this reaction is crucial for determining the energy efficiency and feasibility of using this method in various applications, especially in chemical and power industries.

Steam with Coal Reaction

When steam reacts with coal, specifically graphite, a unique chemical transformation takes place. This reaction is represented by the equation:$$\mathrm{C}(s)+{\mathrm{H}}_2\mathrm{O}(g)\to {\mathrm{H}}_2(g)+\mathrm{CO}(g)$$In this process:

• The carbon in coal acts as a reducing agent.
• Steam provides the necessary oxygen for this transformation.

This reaction is endothermic, meaning it absorbs heat. That is, energy input is needed to proceed. However, once complete, it produces gases that can be further utilized in generating energy or as feedstock in chemical manufacturing. Understanding the enthalpy change of this reaction helps industries anticipate the energy input required and the potential returns in terms of gaseous product yield.

Graphite as Standard State

Graphite is the standard state for carbon, meaning it is the most stable form of carbon under standard conditions (1 atm pressure and 25°C). When considering reactions involving carbon, it's represented as graphite, with an associated standard enthalpy of formation of zero ($\mathrm{\Delta }{H}_f^{\circ }=0$ kJ/mol). This is a foundational concept when calculating energy changes, like in the water gas reaction.

• Using graphite's enthalpy as zero simplifies calculations and helps establish a reference point.
• It ensures consistency in recording and comparing reaction energetics.

In the context of enthalpy calculations, adopting graphite as the reference ensures that the energies involved reflect true chemical transformations, unaffected by varying elemental states.