Question

Use standard enthalpies of formation from Table \(R-11\) on page 975 to calculate \(\Delta H_{\mathrm{rxn}}^{\circ}\) for the following reaction. \(4 \mathrm{NH}_{3}(\mathrm{g})+7 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 4 \mathrm{NO}_{2}(\mathrm{g})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})\)

Short answer

Using Table R-11, we find the standard enthalpies of formation (ΔHfº) for the reactants and products as: ΔHfº(NH₃(g)) = -45.9 kJ/mol, ΔHfº(O₂(g)) = 0 kJ/mol, ΔHfº(NO₂(g)) = 33.2 kJ/mol, and ΔHfº(H₂O(l)) = -285.8 kJ/mol. By applying the stoichiometric coefficients, we can calculate the standard enthalpy change for the given reaction as follows: ΔHₒᵣₓₙ = [4 × ΔHfₒ(NO₂(g)) + 6 × ΔHfₒ(H₂O(l))] - [4 × ΔHfₒ(NH₃(g)) + 7 × ΔHfₒ(O₂(g))] ΔHₒᵣₓₙ = [4 × 33.2 kJ/mol + 6 × (-285.8 kJ/mol)] - [4 × (-45.9 kJ/mol) + 7 × 0 kJ/mol] ΔHₒᵣₓₙ = (-1378 kJ) - (-183.6 kJ) ΔHₒᵣₓₙ = -1194.4 kJ

Step-by-step solution

Find the standard enthalpies of formation of reactants and products

Refer to Table R-11 on page 975 and look up the standard enthalpies of formation (ΔHfₒ) for the following substances: 1. NH₃(g) 2. O₂(g) 3. NO₂(g) 4. H₂O(l)

Apply the stoichiometric coefficients

Multiply the standard enthalpies of formation found in Step 1 by their respective stoichiometric coefficients given in the balanced chemical equation: 4 NH₃(g): 4 × ΔHfₒ(NH₃(g)) 7 O₂(g): 7 × ΔHfₒ(O₂(g)) 4 NO₂(g): 4 × ΔHfₒ(NO₂(g)) 6 H₂O(l): 6 × ΔHfₒ(H₂O(l))

Calculate the enthalpy change of the reaction

Now, use the formula ΔHₒᵣₓₙ = Σ ΔHfₒ(products) - Σ ΔHfₒ(reactants) to calculate the standard enthalpy change of the reaction: ΔHₒᵣₓₙ = [4 × ΔHfₒ(NO₂(g)) + 6 × ΔHfₒ(H₂O(l))] - [4 × ΔHfₒ(NH₃(g)) + 7 × ΔHfₒ(O₂(g))] Make sure to plug in the values of ΔHfₒ found in Step 1 into the equation.

Compute the final answer

Once you have substituted the values, perform the arithmetic operations to find the final value of ΔHₒᵣₓₙ. This will give you the standard enthalpy change for the given reaction.

Key concepts

Enthalpies of Formation

The enthalpy of formation, denoted as \( \Delta H_f^\circ \), is a measure of the energy change when one mole of a substance is formed from its elements in their standard states. It is an essential concept in thermochemistry that helps us understand the energy involved in creating chemical compounds. For instance, the enthalpy of formation for water (\(H_2O(l)\)) reflects the energy change when hydrogen gas and oxygen gas combine to form one mole of liquid water under standard conditions.

Each substance has a unique standard enthalpy of formation, which can either be endothermic (positive value) or exothermic (negative value), indicating whether the process of formation requires or releases energy. These values are typically found in reference tables, like Table R-11 in the mentioned problem.

To better grasp the standard enthalpy change of a reaction, one should consider that this change is actually the difference between the sum of the enthalpies of formation for the products and the reactants. This difference gives us valuable insight into the overall energy exchange during a chemical reaction.

Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction, grounded in the conservation of mass and the coefficients of a balanced chemical equation. It allows us to predict the amounts of substances consumed and produced in a reaction, making it a fundamental concept in chemistry.

For example, in the given chemical equation, \(4 NH_3(g) + 7 O_2(g) \rightarrow 4 NO_2(g) + 6 H_2O(l)\), the stoichiometric coefficients (4, 7, 4, and 6) dictate the proportions in which the reactants combine and the products are formed. These coefficients are crucial when determining the standard enthalpy change of reaction as they provide the necessary multipliers for the enthalpies of formation of each compound involved in the reaction.

By applying stoichiometry, we ensure that the calculated enthalpy change reflects the actual amounts of substances involved in the experimentally observed reaction. Proper use of stoichiometry is key in predicting the energy changes and resource requirements in chemical processes.

Thermochemistry

Thermochemistry is the branch of chemistry that studies the energy and heat associated with chemical reactions and physical transformations. The central concept of thermochemistry is that energy is conserved in all chemical processes, following the first law of thermodynamics. This principle allows scientists to track energy as it flows in and out of systems.

The standard enthalpy change of a reaction (\(\Delta H_{rxn}^\circ\)) is a primary focus within thermochemistry. It represents the heat absorbed or released under standard conditions (1 atm pressure and 25°C) during a chemical reaction. The sign of \(\Delta H_{rxn}^\circ\) indicates whether a reaction is exothermic (negative sign, releasing heat) or endothermic (positive sign, absorbing heat).

Understanding thermochemistry is critical for controlling industrial chemical reactions to optimize energy use and for predicting the spontaneity of reactions. It explains why certain reactions require a heat source to proceed, while others may require cooling to restrain excessively exothermic behaviors that could be hazardous.