Problem 2 - Chemistry Matter and Change

Question

The pressure of a sample of helium in a 1.00-L container is 0.988 atm. What is the new pressure if the sample is placed in a 2.00-L container?

Step-by-Step Solution

Answer

The new pressure of the helium gas when it is placed in a 2.00-L container is 0.494 atm.

Step 1: Identify the given variables

The initial pressure of the helium gas (P1) is 0.988 atm, and the initial volume (V1) is 1.00 L. The final volume (V2) is 2.00 L. Our goal is to find the final pressure (P2).

Step 2: Apply Boyle's Law formula

We can use the formula for Boyle's Law, which is P1V1 = P2V2. We will be solving for P2, the final pressure.

Step 3: Plug in the given values

Let's plug in the values that we have into the formula: \(0.988 atm \times 1.00 L = P2 \times 2.00 L\)

Step 4: Solve for P2

Now, we need to solve for P2. Divide both sides of the equation by 2.00 L: \(\frac{0.988 atm \times 1.00 L}{2.00 L} = P2\)

Step 5: Calculate the final pressure

Now we can calculate the final pressure: \(P2 = \frac{0.988 atm}{2} = 0.494 atm\)

Step 6: State the answer

So, the new pressure of the helium gas when it is placed in a 2.00-L container is 0.494 atm.

Key Concepts

Gas Laws

Understanding the behavior of gases is a foundational aspect of chemistry and physics. Gas laws provide scientists and engineers with tools to predict how gases will react under different conditions. By studying the relationships between volume, temperature, pressure, and amount of a gas, we can understand and manipulate the behavior of gases for various applications. These laws are not just theoretical; they are used in everyday life, from inflating tires to breathing with scuba diving equipment.

Pressure-Volume Relationship

Boyle's Law is at the heart of the pressure-volume relationship in gases. It states that for a fixed quantity of gas kept at a constant temperature, the pressure of the gas is inversely proportional to its volume. This means as the volume of the gas decreases, its pressure increases and vice versa, assuming the temperature remains the same. In the context of our helium gas problem, when the volume of the gas was doubled from 1.00 L to 2.00 L, Boyle's Law predicted that the pressure would halve, which is exactly what we found in the exercise.

Helium Gas Behavior

Helium gas, like all gases, follows the gas laws which describe its behavior under various conditions. One of the unique properties of helium is its low density and the fact that it's inert, which means it doesn't react with other substances easily. This characteristic makes helium an ideal gas to study in controlled experiments since its behavior will be predictable and consistent. Additionally, being a noble gas, helium's behavior is a good approximation for an ideal gas, which assumes no intermolecular forces and molecules that do not occupy space, providing a simplified model for understanding gas behavior.

Chemistry Problem Solving

To proficiently solve chemistry problems, one must be systematic and understand the concepts involved. First, clearly identify the known and unknown variables before applying the relevant principles or laws. In our exercise, we defined the initial and final conditions for volume and pressure and systematically applied Boyle's Law to find the unknown pressure. Next, use algebraic methods to rearrange and solve the equations. Finally, always reflect on the answer to ensure that it makes sense both mathematically and physically, checking if it aligns with the principles used.