Using the table below that shows some values for standard enthalpy changes of combustion, calculate the standard enthalpy change of the reaction, C(s) + 2H2(g) rightwards arrowCH4(g)
Substance
ΔH°f (kJ/mol)
C(s)
−394
CH4(g)
−890
H2(g)
−286
The equation for the reaction is:
C(s) + 2H2(g) → CH4(g)
To calculate the standard enthalpy change of this reaction, we need to first find the enthalpy change for the formation of the products and reactants from their constituent elements.
For CH4(g), the enthalpy change of formation is given as -890 kJ/mol.
For H2(g), the enthalpy change of formation is given as -286 kJ/mol.
For C(s), the enthalpy change of formation is given as -394 kJ/mol.
Using Hess's law, we can relate these formation enthalpies to the enthalpy change of the combustion reaction:
ΔH°combustion = Σ ΔH°f(products) - Σ ΔH°f(reactants)
Substituting the formation enthalpies for the products and reactants, we get:
ΔH°combustion = [ΔH°f(CH4) + 2ΔH°f(H2)] - ΔH°f(C)
ΔH°combustion = [(-890 kJ/mol) + 2(-286 kJ/mol)] - (-394 kJ/mol)
ΔH°combustion = -890 kJ/mol + (-572 kJ/mol) + 394 kJ/mol
ΔH°combustion = -1068 kJ/mol
Therefore, the standard enthalpy change of the reaction C(s) + 2H2(g) → CH4(g) is -1068 kJ/mol.
To calculate the standard enthalpy change of the reaction C(s) + 2H2(g) rightwards arrow CH4(g), we can use the standard formation enthalpies of the substances involved.
The given standard formation enthalpies are:
ΔH°f (C(s)) = -394 kJ/mol
ΔH°f (CH4(g)) = -890 kJ/mol
ΔH°f (H2(g)) = -286 kJ/mol
The reaction equation shows that we have one mole of carbon (C) reacting with two moles of hydrogen gas (H2) to form one mole of methane (CH4).
Since ΔH°f represents the enthalpy change when one mole of a substance is formed from its elements, we need to take into account the stoichiometric coefficients in the reaction equation.
The enthalpy change of the reaction can be calculated using the following equation:
ΔH°rxn = ∑(ΔH°f products) - ∑(ΔH°f reactants)
ΔH°rxn = ΔH°f (CH4(g)) - ΔH°f (C(s)) - 2 × ΔH°f (H2(g))
ΔH°rxn = -890 kJ/mol - (-394 kJ/mol) - 2 × (-286 kJ/mol)
ΔH°rxn = -890 kJ/mol + 394 kJ/mol - 2 × (-286 kJ/mol)
ΔH°rxn = -890 kJ/mol + 394 kJ/mol + 572 kJ/mol
ΔH°rxn = 76 kJ/mol
Therefore, the standard enthalpy change of the reaction C(s) + 2H2(g) rightwards arrow CH4(g) is 76 kJ/mol.