calculations

Standard Enthalpies of Formation

• Definition: Standard enthalpy of formation ($\Delta H_f^\circ$) is the change in enthalpy when 1 mole of a compound is formed from its elements in their standard states.

Formation Reactions

• Example Formation Equations:

  • For MgCO3(s): Balance equation from elements in standard states.

  • For C6H12O6(s): Same process as MgCO3.

• Other examples: Formation equations for NaCl(s) and Pb(NO3)2(s).

Calculation of Standard Enthalpy Change

• Any reaction can be expressed as the sum of formation reactions for reactants/products:

  • $\Delta H^\circ<em>{reaction} = \Sigma n \Delta H</em>f^\circ (products) - \Sigma n \Delta H_f^\circ (reactants)$

  • Where $\Sigma$ means sum and n is the coefficient.

Examples of Reactions and Enthalpy Values

• Specific reactions along with their enthalpy changes:

  • CH4(g) + 2 O2(g) → CO2(g) + 2 H2O(g)

  • $\Delta H^\circ = -802.5 kJ$

  • Look for values for formation reactions like:

  • $\Delta H<em>f^\circ(\text{CH}</em>4) = -74.6 kJ/mol$

  • $\Delta H<em>f^\circ(\text{CO}</em>2) = -393.5 kJ/mol$

  • $\Delta H<em>f^\circ(\text{H}</em>2O) = -241.8 kJ/mol$

Thermite Reaction

• Highly exothermic; calculate $\Delta H^\circ$ using formation values.

Energy Calculations for Combustion

• Given energy can determine mass of octane:

  • Combustion reaction for octane: Write balanced equation.

  • $\text{Molar Mass of C}<em>8\text{H}</em>{18} = 114.22 g/mol$

• Energy relation: Convert energy from kJ to kg of octane using formation enthalpy.

Stoichiometric Relationships in Combustion

• For each fuel's combustion, derive fuel efficiency based on CO2 emissions and energy output:

  • C: 1 mol CO2: -393.5 kJ

  • CH4: 1 mol CO2: -802.3 kJ

  • C8H18: 8 mol CO2: -5074.1 kJ

• Conversion of kg CO2 to moles followed by energy calculation based on enthalpy.

• Best fuel: Natural gas (CH4) provides the most energy per kg CO2.