Tungsten carbide is very hard and is used to make cutting tools and rock drills. What is the enthalpy of formation (in \(\mathrm{kJ} / \mathrm{mol}\) ) of tungsten carbide? The enthalpy change for this reaction is difficult of measure directly, because the reaction occurs at \(1400^{\circ} \mathrm{C}\). However, the enthalpies of combustion of the elements and of tungsten carbide can be measured easily. \(2 \mathrm{~W}(\mathrm{~s})+3 \mathrm{O}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{WO}_{3}(\mathrm{~s}) ; \Delta H\) \(=-1680.6 \mathrm{~kJ}\) \(\mathrm{C}(\) graphite \()+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{CO}_{2}(\mathrm{~g}) ; \quad \Delta H\) \(=-393.5 \mathrm{~kJ}\) \(2 \mathrm{WC}(\mathrm{s})+5 \mathrm{O}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{WO}_{3}(\mathrm{~s})+2 \mathrm{CO}_{2}(\mathrm{~g})\) \(\Delta H=-2391.6 \mathrm{~kJ}\) (a) \(-38.0\) (b) \(-76.0\) (c) \(-19.0\) (d) \(-1233.8\)

Hess's Law is a cornerstone in chemical thermodynamics, providing a path to calculate the enthalpy change (\f\( \Delta H \f\)) for a reaction when it may be difficult to measure directly. Don't be intimidated by the technical jargon—think of it as a financial ledger, where you can figure out your total spending by tracking individual purchases, whether they are expenses or refunds.

The law states that the total enthalpy change of a complete chemical reaction is the same, no matter how it occurs, provided the initial and final conditions are identical. This means, if a reaction can be expressed as a sequence of steps, the sum of the enthalpy changes of these steps equals the enthalpy change of the overall process.

For example, if you can't measure the enthalpy directly for the formation of a compound like tungsten carbide, Hess's Law allows you to consider the enthalpy changes of combustion for tungsten and carbon, and the enthalpy change of tungsten carbide combustion. By artfully rearranging and summing these reactions, you can deduce the elusive enthalpy of formation. It's like solving a puzzle, where each reaction is a piece that must fit to reveal the big picture—how much energy is required or released to form a compound.

Chemical thermodynamics is the study of the relationship between heat and work with chemical reactions or with physical changes of state within the confines of the laws of thermodynamics. In simple terms, it looks at the energy movement in chemical processes and how it determines the direction and extent of the reactions.

The concept of enthalpy, a key component of thermodynamics, represents the total heat content of a system. It becomes especially relevant when pressure is constant, as in many standard laboratory conditions, because changes in enthalty (\f\( \Delta H \f\)) directly reflect the heat absorbed or released.

Understanding enthalpy is crucial when studying reactions like the formation of tungsten carbide, a compound with significant industrial value due to its hardness. Determining the enthalpy of formation—how much energy is used when creating a substance from its elements in their standard states—can help predict reaction behaviors and guide practical applications in material synthesis.

Stoichiometry, the bread and butter of chemical equations, is all about proportions. It ensures that atoms are conserved throughout the reactions by balancing the number of atoms of each element on both the reactant and product sides. To put it simply, it makes sure you're not magically losing or gaining atoms in a reaction—it's the accountant for atoms.

The power of stoichiometry lies not just in balancing, but also in its ability to quantify relationships in a chemical reaction. By knowing the amounts of reactants, stoichiometry can determine how much product will be made, or vice versa, which is incredibly useful in industrial applications and preparation of reagents in the lab.

When applying Hess's Law, stoichiometry becomes indispensable. You must often reverse and scale chemical equations to find your desired enthalpy of formation, as done for tungsten carbide. Properly applied stoichiometry ensures the underlying conservation of elements and enables the accurate determination of enthalpy changes in a complex network of chemical reactions.