Question

A balloon contains 0.158 mol of gas and has a volume of 2.46 L. If we add 0.113 mol of gas to the balloon (at the same temperature and pressure), what is its final volume?

Short answer

The final volume of the gas in the balloon is 3.69 L.

Step-by-step solution

Understand the gas law relationship

The problem involves a situation where the amount of gas in a balloon changes, but the temperature and pressure remain constant. According to Avogadro's Law, at constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of gas present. The mathematical relationship is given by V1/n1 = V2/n2, where V1 is the initial volume, n1 is the initial number of moles, V2 is the final volume, and n2 is the final number of moles.

Calculate the final number of moles (n2)

To find the final number of moles, add the additional moles to the initial moles: n2 = n1 + added moles = 0.158 mol + 0.113 mol.

Calculate the final volume (V2)

Use the equation from Avogadro's Law to solve for the final volume. Rearrange the equation to solve for V2: V2 = (V1 * n2) / n1. Substitute the known values into the equation to find V2.

Key concepts

Gas Laws

Gas laws are fundamental principles that describe the behavior of gases and how they interact with changes in temperature, volume, and pressure. One of the simplest and most vital of these principles is Avogadro's Law, which states that at a constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of the gas present. This relationship allows for predictions on how changes in the amount of gas (in moles) will affect its volume.

Understanding this law is crucial when dealing with problems like the balloon exercise. It allows us to find the final volume of gas once we know the initial volume and the change in the number of moles. This concept forms an integral part of the gas laws, which also include Boyle's Law (pressure-volume relationship), Charles' Law (volume-temperature relationship), and the Combined Gas Law, which is a combination of the first two.

Mole Concept

The mole concept is a bridge between the microscopic world of atoms and molecules and the macroscopic world we observe. It is defined as the amount of substance that contains as many elementary entities (e.g., atoms, molecules, ions, electrons) as there are atoms in 12 grams of carbon-12. This number is Avogadro's number, approximately equal to \(6.02 \times 10^{23}\).

When we measure substances in moles, we can directly relate the mass of a substance to its chemical entities; this is invaluable in chemistry. In the context of our balloon example, understanding that moles represent a quantity of gas particles helps us apply Avogadro's Law to predict the change in volume with the addition of a known amount of gas, measured in moles.

Stoichiometry

Stoichiometry is a section of chemistry that deals with the quantities of substances involved in chemical reactions. It is based on the conservation of mass and the concept of the mole. Through stoichiometry, we can calculate the amounts of reactants needed or products formed in a chemical reaction.

Applying stoichiometry helps us to make connections between the reactants and products through balanced chemical equations. In practical applications, like calculating the volume change of a gas in a reaction, stoichiometry provides the tools to predict the outcomes based on the mole ratios outlined in the balanced equation. Hence, when we add or remove moles of gas during a chemical reaction, stoichiometry guides us to quantify these changes accurately.

Chemistry Education

Chemistry education aims to impart comprehensive knowledge and understanding of chemical principles and their real-world applications. Effective chemistry education uses clear explanations, practical examples, and interactive experiences to enhance learning and comprehension.

In the case of the balloon exercise, a chemistry educator would facilitate understanding by breaking down Avogadro's Law and explaining the mole concept and stoichiometry, making these complex ideas accessible. Through well-structured problems and step-by-step solutions, educators help students build a solid foundation to tackle more complex chemistry challenges with confidence. Equipping students with these skills is essential for their success in chemistry and related scientific fields.