The explosive nitroglycerin (C₃H₅N₃O₉) decomposes rapidly upon ignition or sudden impact according to the balanced equation: 4 C₃H₅N₃O₉(l) → 12 CO₂(g) + 10 H₂O(g) + 6 N₂(g) + O₂(g) ΔH°_rxn = –5678 kJ Calculate the standard enthalpy of formation (ΔH°_f ) for nitroglycerin.

Verified step by step guidance

1. Step 1: Identify the standard enthalpies of formation (ΔH°f) for all the products and reactants in the balanced equation. The ΔH°f values for CO2(g), H2O(g), N2(g), and O2(g) are -393.5 kJ/mol, -241.8 kJ/mol, 0 kJ/mol, and 0 kJ/mol respectively.
2. Step 2: Calculate the total enthalpy of the products. This is done by multiplying the ΔH°f of each product by its stoichiometric coefficient in the balanced equation and then adding all these values together. For this equation, it would be (12 mol CO2 * -393.5 kJ/mol CO2) + (10 mol H2O * -241.8 kJ/mol H2O) + (6 mol N2 * 0 kJ/mol N2) + (1 mol O2 * 0 kJ/mol O2).
3. Step 3: Calculate the total enthalpy of the reactants. Since we are trying to find the ΔH°f for nitroglycerin, we will represent it as x. For this equation, it would be (4 mol C3H5N3O9 * x kJ/mol C3H5N3O9).
4. Step 4: Set up the equation for the enthalpy of the reaction (ΔH°rxn), which is the total enthalpy of the products minus the total enthalpy of the reactants. So, ΔH°rxn = (enthalpy of products) - (enthalpy of reactants).
5. Step 5: Solve the equation from step 4 for x, which represents the ΔH°f for nitroglycerin. The given ΔH°rxn is -5678 kJ. So, -5678 kJ = (enthalpy of products) - (4 mol C3H5N3O9 * x kJ/mol C3H5N3O9). Solving this equation will give you the ΔH°f for nitroglycerin.

Key Concepts

Standard Enthalpy of Formation (ΔH°f)

The standard enthalpy of formation (ΔH°f) is the change in enthalpy when one mole of a compound is formed from its elements in their standard states. It is a crucial concept in thermodynamics, as it allows for the calculation of the energy changes associated with chemical reactions. For nitroglycerin, this value can be derived from the enthalpy change of the decomposition reaction and the enthalpies of formation of the products.

Hess's Law

Hess's Law states that the total enthalpy change for a reaction is the same, regardless of the number of steps taken to complete the reaction. This principle allows chemists to calculate the enthalpy change of a reaction by using known enthalpy changes of other reactions. In the case of nitroglycerin, Hess's Law can be applied to relate the enthalpy of formation to the enthalpy of the decomposition reaction provided.

Balanced Chemical Equations

A balanced chemical equation represents the conservation of mass in a chemical reaction, showing the relationship between reactants and products. In the case of nitroglycerin's decomposition, the balanced equation provides the stoichiometric coefficients necessary to calculate the enthalpy changes. Understanding how to balance equations is essential for determining the amounts of substances involved and for applying thermodynamic principles correctly.