Problem 49 - Chemistry: Atoms First

Question

When 2.50 g of methane burns in oxygen, 125 kJ of heat is produced. What is the enthalpy of combustion per mole of methane under these conditions?

Step-by-Step Solution

Answer

The enthalpy of combustion per mole of methane under these conditions is approximately 802.31 kJ/mol.

Step 1: Identify the given information

First, determine the given information from the exercise. The mass of methane that was burned is 2.50 g, and the energy released is 125 kJ.

Step 2: Calculate moles of methane

Calculate the number of moles of methane burned using the molar mass of methane (CH4), which is approximately 16.04 g/mol. This is done by dividing the mass of methane by its molar mass: number of moles = \( \frac{mass}{molar\ mass} \) = \( \frac{2.50\ g}{16.04\ g/mol} \).

Step 3: Determine the enthalpy of combustion per mole

With the amount of heat released and the number of moles of methane calculated, find the enthalpy of combustion per mole of methane by dividing the energy released by the number of moles: \( \Delta H \) per mole = \( \frac{Energy\ released}{Number\ of\ moles} \).

Step 4: Perform the calculations

Perform the actual calculations from the previous steps: number of moles = \( \frac{2.50}{16.04} \) = 0.1558 mol (rounded to 4 decimal places). Then calculate the enthalpy of combustion per mole: \( \Delta H \) per mole = \( \frac{125\ kJ}{0.1558\ mol} \) = 802.31 kJ/mol (rounded to 2 decimal places).

Key Concepts

Stoichiometry

Understanding stoichiometry is fundamental when exploring chemical reactions and, in particular, when calculating the enthalpy of combustion. Stoichiometry refers to the calculation of reactants and products in chemical reactions. It is the 'recipe' for a chemical reaction, dictating the proportionate amounts of substances needed.

For instance, when burning methane (CH4), stoichiometry helps us determine how much methane reacts with oxygen to produce carbon dioxide and water, releasing energy. In the textbook exercise, we saw the importance of stoichiometry when the mass of methane (2.50 g) was converted to moles. Without stoichiometry, we wouldn't know how that mass relates to the energy released.

It's like baking: knowing the exact amount of each ingredient necessary to achieve the desired outcome. Similarly, in stoichiometry, our 'ingredients' are the masses and moles of reactants and products; our 'desired outcome' is understanding the reaction's energetics, in this case, the enthalpy of combustion.

Chemical Thermodynamics

Chemical thermodynamics is the branch of science that deals with the relationship between heat and other forms of energy in chemical processes. It's crucial for interpreting the enthalpy of combustion—a key thermodynamic quantity that reflects the total heat exchanged in a chemical reaction when substances burn in an environment at constant pressure.

In our example, when 2.50 g of methane is burned, the energy released is quantified as 125 kJ. Chemical thermodynamics tells us that this 'heat content' change, as gases react with oxygen, is the reaction's enthalpy change, denoted as \( \Delta H \).

Unraveling this part of chemical thermodynamics allows us to connect the dots between the microscopic (molecular) level and the macroscopic phenomena we can measure, like temperature change and heat production, making it indispensable for understanding energy flow in reactions.

Energy in Chemical Reactions

When we discuss energy in chemical reactions, we're chiefly talking about how energy is transferred during the process of breaking and forming chemical bonds. All chemical reactions involve changes in energy, and these are generally categorized as either exothermic (releasing heat) or endothermic (absorbing heat).

The combustion of methane is an exemplary exothermic reaction, turning chemical potential energy stored in methane's bonds into kinetic energy, which we detect as heat and light. The 'enthalpy of combustion' is a specific term for the energy change that occurs when a substance combusts in oxygen.

In the example, a known mass of methane (2.50 g) combusted to release 125 kJ of energy. By understanding how to relate mass to moles (stoichiometry), and considering the principles of chemical thermodynamics, we can express this energy release on a per-mole basis, which is vital for chemists to compare the energy profiles of different reactions and fuels.