Math Problem Statement

Using the table of standard formation enthalpies that you'll find under the ALEKS Data tab, calculate the reaction enthalpy of this reaction under standard conditions: 2HNO2(g)+O2(g)=2HNO3(g) Round your answer to the nearest kJ.

Solution

To calculate the standard reaction enthalpy (ΔH°) for the reaction:

2HNO2(g)+O2(g)2HNO3(g)2\text{HNO}_2(g) + \text{O}_2(g) \rightarrow 2\text{HNO}_3(g)

we'll use the enthalpy of formation (ΔH_f°) values for the substances involved. The reaction enthalpy can be calculated using the following formula:

ΔHreaction=ΔHf(products)ΔHf(reactants)\Delta H^\circ_{\text{reaction}} = \sum \Delta H^\circ_f(\text{products}) - \sum \Delta H^\circ_f(\text{reactants})

  1. Write the expression for the reaction enthalpy: ΔHreaction=2ΔHf(HNO3(g))[2ΔHf(HNO2(g))+ΔHf(O2(g))]\Delta H^\circ_{\text{reaction}} = 2\Delta H^\circ_f(\text{HNO}_3(g)) - \left[2\Delta H^\circ_f(\text{HNO}_2(g)) + \Delta H^\circ_f(\text{O}_2(g))\right]

    Note that for elemental substances in their standard states, such as O2(g)\text{O}_2(g), the enthalpy of formation is zero.

  2. Obtain the standard enthalpy of formation (ΔH_f°) values from the table (units are kJ/mol):

    • ΔHf(HNO3(g))=134.3kJ/mol\Delta H^\circ_f(\text{HNO}_3(g)) = -134.3 \, \text{kJ/mol}
    • ΔHf(HNO2(g))=+33.2kJ/mol\Delta H^\circ_f(\text{HNO}_2(g)) = +33.2 \, \text{kJ/mol}
    • ΔHf(O2(g))=0kJ/mol\Delta H^\circ_f(\text{O}_2(g)) = 0 \, \text{kJ/mol}
  3. Plug the values into the equation:

    ΔHreaction=2(134.3)[2(33.2)+0]\Delta H^\circ_{\text{reaction}} = 2(-134.3) - \left[2(33.2) + 0\right]

  4. Simplify the expression:

    ΔHreaction=268.6(66.4)\Delta H^\circ_{\text{reaction}} = -268.6 - (66.4)

    ΔHreaction=335.0kJ\Delta H^\circ_{\text{reaction}} = -335.0 \, \text{kJ}

So, the reaction enthalpy under standard conditions is −335 kJ.

Would you like more details or clarifications on this?

Here are five related questions you might find useful:

  1. How does the enthalpy of formation relate to bond energy?
  2. What is the significance of a negative reaction enthalpy?
  3. How do changes in temperature affect reaction enthalpy?
  4. What is the difference between enthalpy of formation and enthalpy of combustion?
  5. How do catalysts affect reaction enthalpy?

Tip: Always ensure that you use the correct units when calculating enthalpy changes, as incorrect units can lead to errors in your results.

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Math Problem Analysis

Mathematical Concepts

Thermodynamics
Enthalpy of Formation
Reaction Enthalpy

Formulas

ΔH°_reaction = Σ ΔH°_f(products) - Σ ΔH°_f(reactants)

Theorems

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Suitable Grade Level

Grades 11-12 (Advanced Chemistry)