Question

The pressure exerted on a 240.0 mL sample of hydrogen gas at constant temperature is increased from 0.428 atm to 0.724 atm. What will the final volume of the sample be?

Short answer

The final volume is approximately 141.86 mL.

Step-by-step solution

- Understand the Problem

We are given a change in pressure of a gas at constant temperature and need to find the final volume. This involves Boyle's Law which states that at constant temperature, the pressure of a gas times its volume is constant.

- Write Boyle's Law

Boyle's Law is given by \[ P_1 V_1 = P_2 V_2 \] where \( P_1 \) and \( V_1 \) are the initial pressure and volume, and \( P_2 \) and \( V_2 \) are the final pressure and volume respectively.

- Identify Given Values

From the problem, we know: \( P_1 = 0.428 \text{ atm} \) \( V_1 = 240.0 \text{ mL} \) \( P_2 = 0.724 \text{ atm} \)

- Rearrange the Equation to Solve for \( V_2 \)

Rearrange Boyle's Law to solve for the final volume \( V_2 \). \[ V_2 = \frac{P_1 V_1}{P_2} \]

- Substitute Values into Equation

Substitute the known values into the equation: \[ V_2 = \frac{0.428 \text{ atm} \times 240.0 \text{ mL}}{0.724 \text{ atm}} \]

- Calculate the Final Volume

Perform the calculation: \[ V_2 = \frac{102.72 \text{ atm mL}}{0.724 \text{ atm}} \approx 141.86 \text{ mL} \]

Key concepts

Gas Laws

Gas laws are fundamental principles that describe how gases behave under different conditions of temperature, pressure, and volume. These laws help us understand and predict changes in gas behavior.

Boyle's Law is one of the key gas laws you need to know. It tells us how pressure and volume of a gas are related when temperature is kept constant. Charles's Law and Avogadro's Law are other important gas laws, but they focus on temperature-volume and volume-molecule relationships respectively.

Knowing these laws can be very useful in solving everyday problems involving gases, such as inflating balloons or understanding how air pressure affects weather patterns.

Pressure-Volume Relationship

The pressure-volume relationship of gases is well described by Boyle's Law. This law states that the product of the pressure of a gas and its volume remains constant when the temperature stays the same.
In other words, when you increase the pressure on a given amount of gas, its volume decreases, provided the temperature does not change.

Mathematically, Boyle's Law is represented as:

- For example, if the initial pressure ( ) is increased, the volume ( ) will decrease. Conversely, if the pressure is decreased, the volume will increase.

Constant Temperature

Keeping the temperature constant is crucial when applying Boyle's Law. This is because temperature influences the energy and movement of gas molecules.
When temperature is constant, we assume the kinetic energy of the gas molecules remains the same. This allows us to focus solely on the pressure and volume changes.

In real-world applications, it can be challenging to maintain a constant temperature. However, understanding this concept will help you make more accurate predictions in controlled environments such as laboratories or specific industrial processes.