Calculate the enthalpy change for the reaction C(s) + 2 H2(g) → CH4(g) ΔH = ? Given the enthalpy values for the following reactions CH4(g) + 2 O2(g) → CO2(g) + 2 H2O(l) ΔH = −890.4 kJ C(s) + O2(g) → CO2(g) ΔH = −393.5 kJ H2(g) + 1/2 O2(g) → H2O (g) ΔH = −285.8 kJ (a) −1569.7 kJ (b) +211.1 kJ (c) −1855.5 kJ (d) −74.7 kJ

Verified step by step guidance

1. Identify the target reaction and the given reactions. The target reaction is C(s) + 2 H2(g) → CH4(g).
2. Write the given reactions in a way that will help to derive the target reaction. The reactions given are: CH4(g) + 2 O2(g) → CO2(g) + 2 H2O(l), C(s) + O2(g) → CO2(g), and H2(g) + 1/2 O2(g) → H2O(g).
3. Reverse the first given reaction to form CH4(g) from CO2(g) and H2O(l), as it aligns with the products of the target reaction. This changes the sign of ΔH for this reaction.
4. Use the second and third given reactions directly as they provide the necessary reactants (C(s) and H2(g)) for the target reaction.
5. Add the modified first reaction to the second and third reactions, ensuring that all extra reactants and products cancel out, leaving only the desired reactants and products of the target reaction. Sum the ΔH values of these reactions to find the ΔH for the target reaction.

Key Concepts

Enthalpy Change (ΔH)

Enthalpy change, denoted as ΔH, represents the heat content change of a system during a chemical reaction at constant pressure. It can be either exothermic (releasing heat, ΔH < 0) or endothermic (absorbing heat, ΔH > 0). Understanding ΔH is crucial for predicting the energy changes associated with reactions, which is essential for calculating the overall enthalpy change in a reaction pathway.

Hess's Law

Hess's Law states that the total enthalpy change for a reaction is the sum of the enthalpy changes for the individual steps of the reaction, regardless of the pathway taken. This principle allows chemists to calculate the enthalpy change for a reaction that may be difficult to measure directly by using known enthalpy values from related reactions. It is particularly useful in this problem to derive the enthalpy change for the formation of methane from the given reactions.

Standard Enthalpy of Formation

The standard enthalpy of formation is the change in enthalpy when one mole of a compound is formed from its elements in their standard states. For the reaction in question, the standard enthalpy of formation for CH4(g) is indirectly calculated using the enthalpy values of combustion and formation of reactants and products. This concept is vital for determining the ΔH of the reaction involving carbon and hydrogen to form methane.