Question

For the reaction \(\mathrm{S}(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{SO}_{2}(g), \Delta H=-296 \mathrm{~kJ}\) per mole of \(\mathrm{SO}_{2}\) formed. a. Calculate the quantity of heat released when \(1.00 \mathrm{~g}\) of sulfur is burned in oxygen. b. Calculate the quantity of heat released when 0.501 mole of sulfur is burned in air. c. What quantity of energy is required to break up 1 mole of \(\mathrm{SO}_{2}(g)\) into its constituent elements?

Short answer

a. The heat released when 1.00 g of sulfur is burned in oxygen is 9.24 kJ. b. The heat released when 0.501 mole of sulfur is burned in air is 148 kJ. c. The quantity of energy required to break up 1 mole of SO2(g) into its constituent elements is 296 kJ.

Step-by-step solution

Part a: Calculate heat released for 1.00 g of sulfur

1. Convert grams of sulfur to moles. The molar mass of sulfur is 32.065 g/mol. We have 1.00 g of sulfur, so we need to find the moles of sulfur involved. Moles = mass / molar mass = 1.00 g / 32.065 g/mol = 0.0312 moles 2. Find the heat released per mole of sulfur. We are given that the enthalpy change for the reaction is -296 kJ per mole of SO2 formed. We have an equal ratio of S and SO2, so the enthalpy change will be the same for burning 1 mole of sulfur. 3. Calculate the heat released. Heat released = moles of sulfur * heat per mole of sulfur = 0.0312 moles * -296 kJ/mol = -9.24 kJ The heat released when 1.00 g of sulfur is burned in oxygen is 9.24 kJ.

Part b: Calculate heat released for 0.501 mole of sulfur

1. Find the heat released per mole of sulfur. As discussed in part a, we use the given enthalpy change for this reaction which is -296 kJ per mole of SO2 formed. 2. Calculate the heat released. Heat released = moles of sulfur * heat per mole of sulfur = 0.501 moles * -296 kJ/mol = -148 kJ The heat released when 0.501 mole of sulfur is burned in air is 148 kJ.

Part c: Calculate energy required to break up 1 mole of SO2

1. Find the enthalpy change for the reverse reaction. In the given reaction, S(s)+O2(g) -> SO2(g), the enthalpy change is -296 kJ/mol. For the reverse reaction, SO2(g) -> S(s)+O2(g), the enthalpy change will be the opposite of that. So, ΔH_reverse = +296 kJ/mol. 2. Calculate the energy required. The enthalpy change for breaking up 1 mole of SO2 into its constituent elements, S(s), and O2(g) is the same as the enthalpy change for the reverse reaction. Therefore, the energy required is 296 kJ. The quantity of energy required to break up 1 mole of SO2(g) into its constituent elements is 296 kJ.

Key concepts

Enthalpy Change Calculation

Understanding enthalpy change calculation is key in chemical thermodynamics. Enthalpy, represented by the symbol \(H\), is the measure of total heat content in a system under constant pressure. The enthalpy change \(\Delta H\) of a reaction indicates whether it absorbs (endothermic) or releases (exothermic) heat. A negative \(\Delta H\) signifies an exothermic reaction, releasing heat, as shown in the sulfur burning example, where \(\Delta H=-296 \mathrm{~kJ/mol}\) for \(\mathrm{SO}_{2}\) formed.

For calculations, we scale the \(\Delta H\) value based on the amount of reactant or product. The heat released for a portion of the reactant (like 1.00 gram of sulfur) is determined by first converting the mass to moles, then multiplying by the enthalpy change per mole. Remember, in chemistry, relationships between reactants and products are based on their mole ratios derived from balanced equations.

Molar Mass in Chemistry

The molar mass, given in grams per mole (g/mol), is fundamental in chemistry for converting between the mass of a substance and the amount in moles. It is essentially the mass of one mole of a substance and is used as a conversion factor. In our example, the molar mass of sulfur is \(32.065 \mathrm{g/mol}\), and we used it to convert grams of sulfur to moles.

Always verify the molar mass from a periodic table and use it carefully in calculations, especially when dealing with stoichiometry. The precision in measuring molar mass directly affects the accuracy of calculated quantities, such as the enthalpy change in a chemical reaction.

Stoichiometry

Stoichiometry is the area of chemistry that involves calculating the quantities of reactants and products in a chemical reaction. It's all about the numbers and ratios. The stoichiometry of a balanced chemical equation tells us the proportion in which substances react and form products. For example, the equation \(\mathrm{S}(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{SO}_{2}(g)\) suggests that one mole of sulfur reacts with one mole of oxygen to form one mole of sulfur dioxide.

When performing the enthalpy change calculations, it is crucial to respect these ratios. In our exercise, the stoichiometry indicated that the enthalpy change for burning sulfur is equivalent to that for forming \(\mathrm{SO}_{2}\), ensuring accurate heat quantity calculations.

Chemical Thermodynamics

Chemical thermodynamics revolves around the study of energy and its transformations in chemical processes. One of the core aspects we investigate is the system's enthalpy change during reactions. It integrates concepts of heat transfer and the relationship between various physical properties and heat. It also looks into the spontaneity of reactions, which is influenced by entropy and free energy.

In thermodynamic calculations, such as in the provided exercise, we see the direct application of these principles. We look at enthalpy change not only during a reaction but also consider the reverse process, which gives us insight into the energy required to break bonds in the formation of reactants from products. This duality is critical for a deeper understanding of reactions' energetic profiles.