We can use Hess's law to calculate enthalpy changes that cannot be measured. One such reaction is the conversion of methane to ethane: 2 CH4(g) → C2H6(g) + H2(g) Calculate the ΔH° for this reaction using the following thermochemical data: CH4(g) + 2 O2(g) → CO2(g) + 2 H2O(l) ΔH° = -890.3 kJ 2 H2(g) + O2(g) → 2 H2O(l) H° = -571.6 kJ 2 C2H6(g) + 7 O2(g) → 4 CO2(g) + 6 H2O(l) ΔH° = -3120.8 kJ

Verified step by step guidance

Identify the target reaction: 2 CH4(g) → C2H6(g) + H2(g).

Write the given reactions and their enthalpy changes: (1) CH4(g) + 2 O2(g) → CO2(g) + 2 H2O(l), ΔH° = -890.3 kJ; (2) 2 H2(g) + O2(g) → 2 H2O(l), ΔH° = -571.6 kJ; (3) 2 C2H6(g) + 7 O2(g) → 4 CO2(g) + 6 H2O(l), ΔH° = -3120.8 kJ.

Reverse reaction (3) to match the formation of C2H6(g) and adjust the enthalpy change: 4 CO2(g) + 6 H2O(l) → 2 C2H6(g) + 7 O2(g), ΔH° = +3120.8 kJ.

Use Hess's Law to combine the reactions: (1) and (2) as given, and the reversed (3), ensuring that the intermediates (CO2 and H2O) cancel out to yield the target reaction.

Sum the enthalpy changes of the adjusted reactions to find the ΔH° for the target reaction.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Hess's Law

Hess's Law states that the total enthalpy change for a chemical reaction is the same, regardless of the number of steps taken to complete the reaction. This principle allows us to calculate the enthalpy change of a reaction by using the enthalpy changes of related reactions, making it particularly useful for reactions that are difficult to measure directly.

Enthalpy (ΔH)

Enthalpy is a thermodynamic quantity that represents the total heat content of a system. It is often expressed as ΔH, which indicates the change in enthalpy during a reaction. A negative ΔH value signifies that the reaction is exothermic, releasing heat, while a positive ΔH indicates an endothermic reaction, absorbing heat.

Thermochemical Equations

Thermochemical equations are balanced chemical equations that include the enthalpy change associated with the reaction. These equations provide essential information about the energy changes that occur during chemical reactions, allowing chemists to predict the heat absorbed or released when reactants are converted to products.

Recommended video:

Guided course

01:13

Thermochemical Equations

Related Practice

Textbook Question

From the following data for three prospective fuels, calculate which could provide the most energy per unit mass and per unit volume:

Textbook Question

When magnesium metal is burned in air (Figure 3.6), two products are produced. One is magnesium oxide, MgO. The other is the product of the reaction of Mg with molecular nitrogen, magnesium nitride. When water is added to magnesium nitride, it reacts to form magnesium oxide and ammonia gas. (e) The standard enthalpy of formation of solid magnesium nitride is -461.08 kJ>mol. Calculate the standard enthalpy change for the reaction between magnesium metal and ammonia gas.

Textbook Question

(b) Assuming that there is an uncertainty of 0.002 °C in each temperature reading and that the masses of samples are measured to 0.001 g, what is the estimated uncertainty in the value calculated for the heat of combustion per mole of caffeine?