Math Problem Statement

Calculate the enthalpy change (ΔH) for the combustion reaction: C4H4(g) + 2H2(g) → C4H8(g), using the enthalpies of combustion for C4H4 (-2341 kJ/mol), C4H8 (-2755 kJ/mol), and H2 (-286 kJ/mol).

Solution

The image contains a problem regarding the enthalpy change (ΔH\Delta H) for a reaction involving combustion. Here's the transcription of the problem for clarity:


Problem Statement:

Combustion reactions involve reacting a substance with oxygen. When compounds containing carbon and hydrogen are combusted, carbon dioxide and water are the products. Using the enthalpies of combustion for:

  • C4H4C_4H_4: 2341kJ/mol-2341 \, \text{kJ/mol},
  • C4H8C_4H_8: 2755kJ/mol-2755 \, \text{kJ/mol},
  • H2H_2: 286kJ/mol-286 \, \text{kJ/mol},

calculate ΔH\Delta H for the reaction:

C4H4(g)+2H2(g)C4H8(g)C_4H_4 (g) + 2H_2 (g) \rightarrow C_4H_8 (g)


Solution:

The enthalpy change (ΔH\Delta H) for the reaction is calculated using the formula:

ΔH=(sum of enthalpies of products)(sum of enthalpies of reactants)\Delta H = \text{(sum of enthalpies of products)} - \text{(sum of enthalpies of reactants)}

Step 1: Write down the enthalpies for the given compounds:

  • C4H4C_4H_4: 2341kJ/mol-2341 \, \text{kJ/mol} (reactant)
  • H2H_2: 286kJ/mol-286 \, \text{kJ/mol} (reactant; 2 moles, so multiply by 2)
  • C4H8C_4H_8: 2755kJ/mol-2755 \, \text{kJ/mol} (product)

Step 2: Substitute into the formula:

[ \Delta H = \left[ \Delta H(C_4H_8) \right] - \left[ \Delta H(C_4H_4) + 2 \cdot \Delta H(H_2) \right] ]

Substitute the values: [ \Delta H = \left[ -2755 \right] - \left[ -2341 + 2 \cdot (-286) \right] ]

Step 3: Simplify: ΔH=2755[2341572]\Delta H = -2755 - \left[ -2341 - 572 \right] ΔH=2755(2913)\Delta H = -2755 - (-2913) ΔH=2755+2913\Delta H = -2755 + 2913 ΔH=158kJ\Delta H = 158 \, \text{kJ}

Final Answer:

ΔH=158kJ\Delta H = 158 \, \text{kJ}


Do you want further details or additional examples?

Related Questions:

  1. What is the significance of negative and positive values of ΔH\Delta H?
  2. How would the calculation change if one of the substances was in a different phase?
  3. How are enthalpy changes measured experimentally?
  4. What is the role of stoichiometry in enthalpy calculations?
  5. Can this reaction be considered endothermic or exothermic? Why?

Tip:

Always ensure the phases of reactants and products match the provided enthalpy values, as phase changes can affect the enthalpy significantly.

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Math Problem Analysis

Mathematical Concepts

Thermodynamics
Chemical Reactions
Enthalpy Change

Formulas

ΔH = Σ(enthalpies of products) - Σ(enthalpies of reactants)

Theorems

Hess's Law

Suitable Grade Level

Grades 10-12 (High School Chemistry)