Ch.5 - Gases

Tro - Chemistry: A Molecular Approach 4th Edition

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Tro 4th Edition

Ch.5 - Gases

Problema 31

Capitolo 5, Problema 31

A sample of gas has an initial volume of 5.6 L at a pressure of 735 mmHg. If the volume of the gas is increased to 9.4 L, what is its pressure?

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Identify the initial conditions: initial volume \( V_1 = 5.6 \text{ L} \) and initial pressure \( P_1 = 735 \text{ mmHg} \).

Identify the final condition: final volume \( V_2 = 9.4 \text{ L} \).

Use Boyle's Law, which states that for a given amount of gas at constant temperature, the pressure of a gas is inversely proportional to its volume: \( P_1 V_1 = P_2 V_2 \).

Rearrange the equation to solve for the final pressure \( P_2 \): \( P_2 = \frac{P_1 V_1}{V_2} \).

Substitute the known values into the equation: \( P_2 = \frac{735 \text{ mmHg} \times 5.6 \text{ L}}{9.4 \text{ L}} \).

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Boyle's Law

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

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Boyle's Law

Units of Pressure

Pressure is commonly measured in various units, including atmospheres (atm), pascals (Pa), and millimeters of mercury (mmHg). Understanding these units is crucial for solving gas law problems, as they must be consistent throughout calculations. In this question, the initial pressure is given in mmHg, which is a standard unit for measuring gas pressure.

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Pressure Units

Gas Laws and Ideal Gas Behavior

Gas laws describe the behavior of gases under various conditions of pressure, volume, and temperature. The ideal gas law, PV = nRT, relates these variables for an ideal gas. While this question specifically uses Boyle's Law, understanding the ideal gas behavior helps in grasping how real gases approximate these laws under certain conditions, such as low pressure and high temperature.

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Ideal Gas Law Formula

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