A sample of gas has an initial volume of 14.1 L at a pressure of 1.05 atm. If the sample is compressed to a volume of 10.1 L (at constant temperature), what is its pressure?

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Identify the gas law applicable to the problem. Since the temperature is constant, use Boyle's Law, which states that \( P_1V_1 = P_2V_2 \).

List the known values: initial volume \( V_1 = 14.1 \text{ L} \), initial pressure \( P_1 = 1.05 \text{ atm} \), and final volume \( V_2 = 10.1 \text{ L} \).

Rearrange Boyle's Law to solve for the final pressure \( P_2 \): \( P_2 = \frac{P_1V_1}{V_2} \).

Substitute the known values into the equation: \( P_2 = \frac{1.05 \text{ atm} \times 14.1 \text{ L}}{10.1 \text{ L}} \).

Calculate the expression to find the final pressure \( P_2 \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Boyle's Law

Boyle's Law states that the pressure of a gas is inversely proportional to its volume when the temperature is held constant. This means that if the volume decreases, the pressure increases, and vice versa. Mathematically, it can be expressed as P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. While this question specifically uses Boyle's Law, understanding the Ideal Gas Law provides a broader context for gas behavior under various conditions, including how changes in one variable affect others.

Units of Pressure

Pressure is commonly measured in units such as atmospheres (atm), pascals (Pa), or millimeters of mercury (mmHg). In this question, pressure is given in atmospheres, which is a standard unit in gas law calculations. Understanding how to convert between these units can be crucial when solving problems involving gas behavior.

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