A 14.58 g quantity of N2O4 was placed in a 1.000-L reaction vessel at 400 K. The N2O4 decomposed to an equilibrium mix- ture of N2O4 and NO2 that had a total pressure of 9.15 atm.(b) How much heat (in kilojoules) was absorbed when the N2O4 decomposed to give the equilibrium mixture? (Stan- dard heats of formation may be found in Appendix B.)

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Step 1: Write down the balanced chemical equation for the decomposition of N2O4. It is N2O4(g) ⇌ 2NO2(g).

Step 2: Use the ideal gas law (PV=nRT) to calculate the number of moles of N2O4 initially present and the total number of moles at equilibrium. Remember that R is the ideal gas constant (0.0821 L·atm/K·mol), T is the temperature in Kelvin, and P is the pressure in atm.

Step 3: Calculate the change in the number of moles for N2O4 and NO2. This will give you the number of moles of N2O4 that decomposed and the number of moles of NO2 that were formed.

Step 4: Use the standard heats of formation (ΔHf°) values from Appendix B to calculate the heat of reaction (ΔH°) for the decomposition of N2O4. The heat of reaction can be calculated using the equation ΔH° = Σ ΔHf°(products) - Σ ΔHf°(reactants), where the sum is over all products and reactants.

Step 5: Multiply the heat of reaction (ΔH°) by the change in the number of moles of N2O4 to find the total heat absorbed when the N2O4 decomposed to give the equilibrium mixture. Remember to convert the heat to kilojoules if necessary.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Equilibrium and Le Chatelier's Principle

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products. Le Chatelier's Principle states that if a system at equilibrium is disturbed, it will shift in a direction that counteracts the disturbance. Understanding this principle is crucial for predicting how changes in conditions (like temperature or pressure) affect the equilibrium position.

Standard Enthalpy of Formation

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. This value is essential for calculating the heat absorbed or released during a reaction using Hess's Law, which states that the total enthalpy change for a reaction is the sum of the enthalpy changes for individual steps of the reaction.

Ideal Gas Law and Partial Pressures

The Ideal Gas Law (PV=nRT) relates the pressure, volume, temperature, and number of moles of a gas. In this context, understanding how to calculate the partial pressures of gases in a mixture is important for determining the total pressure and the equilibrium concentrations of the gases involved. This knowledge is necessary for applying the equilibrium constant expression and calculating the heat of the reaction.

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Textbook Question

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