The following diagram represents a reaction shown going to completion. Each molecule in the diagram represents 0.1 mol, and the volume of the box is 1.0 L. (d) Assuming that all of the molecules are in the gas phase, calculate n, the change in the number of gas molecules that accompanies the reaction. [Section 15.2]

Verified step by step guidance

1. Identify the number of gas molecules before and after the reaction by counting the number of molecules represented in the diagram for each state.
2. Calculate the initial number of moles of gas molecules (n_initial) by multiplying the number of molecules before the reaction by 0.1 mol, as each molecule represents 0.1 mol.
3. Calculate the final number of moles of gas molecules (n_final) by multiplying the number of molecules after the reaction by 0.1 mol.
4. Determine the change in the number of moles of gas molecules (\(\Delta n\)) by subtracting the initial number of moles from the final number of moles, i.e., \(\Delta n = n_{final} - n_{initial}\).
5. Interpret the result: if \(\Delta n\) is positive, the reaction results in a net increase in the number of gas molecules; if negative, there is a net decrease.

Key Concepts

Mole Concept

The mole is a fundamental unit in chemistry that quantifies the amount of substance. One mole corresponds to approximately 6.022 x 10^23 entities, such as atoms or molecules. In this context, understanding the mole allows us to relate the number of molecules in the reaction to the amount of substance, which is crucial for calculating changes in the number of gas molecules.

Ideal Gas Law

The Ideal Gas Law (PV=nRT) describes the relationship between pressure (P), volume (V), temperature (T), and the number of moles (n) of a gas. This law is essential for understanding gas behavior under various conditions. In this question, it helps in determining how the number of gas molecules changes as the reaction proceeds, especially since the reaction is occurring in a fixed volume.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions based on balanced equations. It allows chemists to predict the quantities of substances consumed and produced. In this scenario, stoichiometry is vital for determining the change in the number of gas molecules, as it provides the ratios needed to relate the initial and final amounts of reactants and products.