Question

Use the following thermochemical equation to calculate how much heat in kilojoules is evolved or absorbed in each of the following processes.$$ 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l) \quad \Delta H^{\circ}=-571.6 \mathrm{~kJ}$$ (a) \(10.00 \mathrm{~g}\) of gaseous hydrogen burns in excess oxygen. (b) \(5.500 \mathrm{~mol}\) of liquid water are converted to hydrogen and oxygen gas.

Short answer

In part (a), 1414.47 kJ of heat is evolved. In part (b), 1571.9 kJ of heat is absorbed.

Step-by-step solution

Calculate Moles of Hydrogen

First, find the number of moles of hydrogen gas (\( \mathrm{H}_2 \)) in 10.00 g. The molar mass of \( \mathrm{H}_2 \) is approximately 2.02 g/mol. Use the formula: \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \).\[ \text{moles of } \mathrm{H}_2 = \frac{10.00 \text{ g}}{2.02 \text{ g/mol}} \approx 4.95 \text{ moles} \]

Determine Heat Evolved for Hydrogen Combustion

Using the provided thermochemical equation, 2 moles of \( \mathrm{H}_2 \) release 571.6 kJ. Determine the heat evolved for 4.95 moles. \[ \Delta H = -571.6 \text{ kJ} \times \frac{4.95}{2} = -1414.47 \text{ kJ} \] Thus, 1414.47 kJ of heat is evolved.

Use Hess's Law for Water Decomposition

The reverse reaction, formation of \( \mathrm{H}_2 \) and \( \mathrm{O}_2 \) from \( \mathrm{H}_2\mathrm{O} \), has the same magnitude of \( \Delta H \), but opposite in sign. For the decomposition of water, \( \Delta H = +571.6 \text{ kJ} \) per 2 moles of \( \mathrm{H}_2\mathrm{O} \).

Determine Heat Absorbed for Water Decomposition

Given 5.500 moles of water, calculate the heat absorbed using the relation from Step 3. \[ \Delta H = +571.6 \text{ kJ} \times \frac{5.500}{2} = +1571.9 \text{ kJ} \] Thus, 1571.9 kJ of heat is absorbed.

Key concepts

Heat Calculation

Heat calculation involves determining the amount of heat energy either released or absorbed during a chemical reaction. This is often expressed in the units of kilojoules (kJ). To calculate heat, we frequently rely on thermochemical equations, which provide information about the energy changes associated with chemical reactions.

• When we deal with substance quantities, like moles in a reaction, we make use of conversion factors presented in the thermochemical equation.
• In the given problem, the equation shows an enthalpy change, \( \Delta H \), of \(-571.6 \text{ kJ} \) for every 2 moles of \( \mathrm{H}_2 \) reacting.
• To find out how much heat corresponds to a different quantity of reactants, you calculate it proportionally.

Understanding these calculations is fundamental because it connects the world of theoretical chemistry to practical applications, such as energy production and consumption.

Hess's Law

Hess's Law is a principle in chemistry that states the total enthalpy change during the complete course of a chemical reaction is the same, regardless of the steps or intermediates involved. This is because enthalpy is a state function, depending only on initial and final states and not on the path taken.

• In practical terms, if you can break down a reaction into multiple steps for which you know the energies, you can sum these energies to get the overall enthalpy change.
• In the process given, we use Hess's Law to determine energy changes when water decomposes into hydrogen and oxygen. This reaction is the reverse of the combustion one, hence the sign of \( \Delta H \) inverts.
• The computations remain consistent with the original enthalpy values, irrespective of the reaction pathway chosen.

Hess's Law is particularly useful when direct measuring of enthalpy change is difficult, allowing indirect calculation by summing component reactions.

Moles and Molar Mass

Understanding moles and molar mass is foundational for calculating the quantities in chemical reactions. The mole is a unit that measures the amount of substance, giving chemists a way to 'count' atoms or molecules by weighing them. Molar mass, expressed in grams per mole (g/mol), is the mass of one mole of a substance.

• To convert from mass to moles, you divide the mass of the substance by its molar mass.
• In the example, 10.00 g of \( \mathrm{H}_2 \) are converted to moles using the molar mass of hydrogen, approximately 2.02 g/mol.
• This conversion is vital for stoichiometric calculations in reactions, allowing the determination of the proportion of reactants to products.

Grasping these concepts facilitates our understanding of chemical equations and our ability to perform chemical reactions accurately in the laboratory.

Exothermic and Endothermic Reactions

Chemical reactions are classified as either exothermic or endothermic based on their heat exchange with the surroundings. Exothermic reactions release heat, which can be observed as a rise in temperature of its surroundings, while endothermic reactions absorb heat, resulting in a decrease in temperature in the surrounding environment.

• The exercise illustrates both reaction types: burning hydrogen in oxygen (an exothermic reaction) and splitting water into hydrogen and oxygen (an endothermic reaction).
• For exothermic reactions, \( \Delta H \) is negative because the system loses heat. Conversely, for endothermic reactions, \( \Delta H \) is positive since the system absorbs heat.
• Understanding these reactions is essential in fields like energy production, where maximizing heat release or absorption is critical.

Knowing whether a reaction is exothermic or endothermic helps in predicting energy flow, which is crucial for designing practical applications and safety protocols.