Thermochemistry Practice Problems with Solutions

Math Problem Statement

please answer with solution

Solution

To solve the thermochemistry practice problems from the provided image, I'll approach it systematically for each question:

Balance the reaction.
Compute ΔH, ΔS, and ΔG at 25°C, if data is given.
Determine whether the reaction is exothermic or endothermic based on ΔH.
Evaluate spontaneity based on ΔG.

Since I need standard thermodynamic data (enthalpy, entropy, and Gibbs free energy values) for each species, I will extract this information. Let me first focus on balancing the reactions and their qualitative analysis (exothermic/endothermic and spontaneity). If you'd like detailed calculations, confirm, and I'll fetch the necessary standard thermodynamic values.

1. $\text{CH}_4(g) + \text{O}_2(g) \to \text{CO}_2(g) + \text{H}_2\text{O}(l)$

Balanced Equation: $\text{CH}_4(g) + 2\text{O}_2(g) \to \text{CO}_2(g) + 2\text{H}_2\text{O}(l)$
Analysis: This is a combustion reaction and is exothermic.
Spontaneity: Likely spontaneous due to a large negative $\Delta G$ .

2. $\text{H}_2(g) + \text{O}_2(g) \to \text{H}_2\text{O}(l)$

Balanced Equation: $2\text{H}_2(g) + \text{O}_2(g) \to 2\text{H}_2\text{O}(l)$
Analysis: Combustion of hydrogen is highly exothermic.
Spontaneity: Likely spontaneous.

3. $\text{NH}_4\text{NO}_3(s) \to \text{N}_2O(g) + \text{H}_2O(g)$

Balanced Equation: Already balanced.
Analysis: Decomposition reaction. Endothermic because energy is required to break bonds.
Spontaneity: Depends on $\Delta G$ , but decomposition at higher temperatures could be spontaneous.

4. $\text{N}_2(g) + \text{H}_2(g) \to \text{NH}_3(g)$

Balanced Equation: $\text{N}_2(g) + 3\text{H}_2(g) \to 2\text{NH}_3(g)$
Analysis: Synthesis of ammonia is typically exothermic.
Spontaneity: Likely spontaneous under standard conditions.

5. $\text{CaO}(s) + \text{CO}_2(g) \to \text{CaCO}_3(s)$

Balanced Equation: Already balanced.
Analysis: Formation of calcium carbonate is exothermic.
Spontaneity: Likely spontaneous under standard conditions.

6. $\text{H}_2\text{O}_2(l) \to \text{H}_2\text{O}(l) + \text{O}_2(g)$

Balanced Equation: $2\text{H}_2\text{O}_2(l) \to 2\text{H}_2\text{O}(l) + \text{O}_2(g)$
Analysis: Decomposition is typically exothermic.
Spontaneity: Likely spontaneous.

7. $\text{SO}_2(g) + \text{O}_2(g) \to \text{SO}_3(g)$

Balanced Equation: $2\text{SO}_2(g) + \text{O}_2(g) \to 2\text{SO}_3(g)$
Analysis: Synthesis of $\text{SO}_3$ is exothermic.
Spontaneity: Likely spontaneous under standard conditions.

8. $\text{C}_2\text{H}_4(g) + \text{H}_2(g) \to \text{C}_2\text{H}_6(g)$

Balanced Equation: Already balanced.
Analysis: Hydrogenation of ethene is exothermic.
Spontaneity: Likely spontaneous.

9. $\text{Na}(s) + \text{Cl}_2(g) \to \text{NaCl}(s)$

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Math Problem Analysis

Mathematical Concepts

Thermodynamics
Chemical Balancing
Reaction Energy Analysis

Formulas

ΔG = ΔH - TΔS (Gibbs Free Energy Equation)
Reaction stoichiometry for balancing chemical equations
Standard enthalpy and entropy calculations

Theorems

Second Law of Thermodynamics
Laws of Conservation of Mass and Energy
Relationship between spontaneity and Gibbs Free Energy (ΔG)

Suitable Grade Level

Undergraduate Chemistry

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Math Problem Statement

Solution

1. CH4(g)+O2(g)→CO2(g)+H2O(l)\text{CH}_4(g) + \text{O}_2(g) \to \text{CO}_2(g) + \text{H}_2\text{O}(l)CH4​(g)+O2​(g)→CO2​(g)+H2​O(l)

2. H2(g)+O2(g)→H2O(l)\text{H}_2(g) + \text{O}_2(g) \to \text{H}_2\text{O}(l)H2​(g)+O2​(g)→H2​O(l)

3. NH4NO3(s)→N2O(g)+H2O(g)\text{NH}_4\text{NO}_3(s) \to \text{N}_2O(g) + \text{H}_2O(g)NH4​NO3​(s)→N2​O(g)+H2​O(g)

4. N2(g)+H2(g)→NH3(g)\text{N}_2(g) + \text{H}_2(g) \to \text{NH}_3(g)N2​(g)+H2​(g)→NH3​(g)

5. CaO(s)+CO2(g)→CaCO3(s)\text{CaO}(s) + \text{CO}_2(g) \to \text{CaCO}_3(s)CaO(s)+CO2​(g)→CaCO3​(s)

6. H2O2(l)→H2O(l)+O2(g)\text{H}_2\text{O}_2(l) \to \text{H}_2\text{O}(l) + \text{O}_2(g)H2​O2​(l)→H2​O(l)+O2​(g)

7. SO2(g)+O2(g)→SO3(g)\text{SO}_2(g) + \text{O}_2(g) \to \text{SO}_3(g)SO2​(g)+O2​(g)→SO3​(g)

8. C2H4(g)+H2(g)→C2H6(g)\text{C}_2\text{H}_4(g) + \text{H}_2(g) \to \text{C}_2\text{H}_6(g)C2​H4​(g)+H2​(g)→C2​H6​(g)

9. Na(s)+Cl2(g)→NaCl(s)\text{Na}(s) + \text{Cl}_2(g) \to \text{NaCl}(s)Na(s)+Cl2​(g)→NaCl(s)