The commercial production of water gas utilizes the reaction under standard conditions: \(\mathrm{C}+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightarrow \mathrm{H}_{2}+\mathrm{CO}\). The heat required for this endothermic reaction may be supplied by adding a limited amount of air and burning some carbon to \(\mathrm{CO}_{2}\). How many \(\mathrm{g}\) of carbon must be burnt to \(\mathrm{CO}_{2}\) to provide enough heat for the water gas conversion of \(100 \mathrm{~g}\) carbon? Neglect all heat losses to the environment. Also \(\Delta H_{\mathrm{f}}^{2}\) of \(\mathrm{CO}, \mathrm{H}_{2} \mathrm{O}_{(\mathrm{g})}\) and \(\mathrm{CO}_{2}\) are \(-110.53\), \(-241.81\) and \(-393.51 \mathrm{~kJ} / \mathrm{mol}\) respectively.

Enthalpy of formation, represented as \( \Delta H_f^\circ \), is a fundamental concept in thermochemistry relating to the heat change associated with the formation of a compound from its elements in their standard states. In simpler terms, it measures the amount of energy absorbed or released when a compound is created from its elemental parts.

For instance, in the reaction \( \mathrm{C} + \mathrm{H_2O(g)} \rightarrow \mathrm{H_2} + \mathrm{CO} \), we must consider the enthalpy of formation for each product (carbon monoxide and hydrogen gas) and reactants. If the \( \Delta H_f^\circ \) values are negative, it implies that energy is released when a mole of the compound is formed under standard conditions. In our case, \( \Delta H_f^\circ \) for \( \mathrm{CO} \) and \( \mathrm{CO_2} \) is negative, indicating exothermic reactions.

When using \( \Delta H_f^\circ \) for calculations, it's important to remember that the values depend on the temperature and pressure being standard (298 K and 101.3 kPa). Students must also know how to use these values in conjunction with stoichiometry to accurately determine the heat changes in chemical reactions.

Stoichiometry is the field of chemistry that involves calculating the quantities of reactants and products in chemical reactions. It's essentially the math behind chemistry, allowing us to predict how much of each substance is involved in a reaction.

To solve stoichiometric problems, such as determining how many grams of carbon must be burned to supply enough heat for the water gas conversion, one must first convert mass to moles using the molar mass. The molar mass of carbon is \(12.01 \,\text{g/mol}\), and so for \(100 \,\text{g}\) of carbon, you divide by this value to find the moles of carbon involved.

Moles of Carbon for Water Gas Conversion

Using the equation \( \text{mass} = \text{moles} \times \text{molar mass} \), you reverse the process to convert moles back to grams when necessary. By understanding how to balance equations, students can use stoichiometry to ensure that mass and energy are conserved across the reaction and to calculate yields.

Thermochemistry is the study of heat changes that accompany chemical reactions and phase changes. Understanding how energy is transferred, either as heat or work, is essential in predicting the direction and extent of chemical reactions.

In the commercial production of water gas, thermochemistry helps us understand that heat must be continuously supplied for the endothermic reaction to proceed. The reaction requires the input of energy, which, in a practical industrial setting, is supplied by burning a portion of carbon to \( \mathrm{CO_2} \).

According to the law of conservation of energy, the heat released from burning carbon to \( \mathrm{CO_2} \) can be harnessed to fuel the endothermic water gas reaction. This is a clever use of thermochemistry to ensure that energy requirements are met without external energy inputs, hence optimizing the production process.

Chemical reactions are processes where reactants transform into products through the making and breaking of chemical bonds. There are different types of reactions, including synthesis, decomposition, single replacement, double replacement, and combustion, each with unique characteristics.

The water gas conversion is a type of endothermic reaction, meaning it absorbs heat. For this reaction to occur, we need an additional exothermic process – the combustion of carbon to carbon dioxide – to supply the necessary heat. This illustrates the interplay of different chemical reaction types in industrial processes.

Conservation in Chemical Reactions

One must be mindful of conservation principles, such as the conservation of mass and energy. These principles dictate that in a closed system, mass and energy cannot be created or destroyed, only converted. In the example given, burning carbon to \( \mathrm{CO_2} \) conserves energy by channeling it into the generation of water gas, showcasing the practical application of these fundamental chemical principles in real-world scenarios.