A sample of gas has an initial volume of 4.20 L at a pressure of 755 mmHg. If the volume of the gas is increased to 7.10 L (at constant temperature), what is its pressure?

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Identify the initial conditions: initial volume \( V_1 = 4.20 \text{ L} \) and initial pressure \( P_1 = 755 \text{ mmHg} \).

Identify the final condition: final volume \( V_2 = 7.10 \text{ L} \).

Recognize that the temperature is constant, so Boyle's Law applies: \( P_1 V_1 = P_2 V_2 \).

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

Substitute the known values into the equation to find \( P_2 \).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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 of a gas increases, its pressure decreases, and vice versa. Mathematically, it can be expressed as P1V1 = P2V2, where P and V represent pressure and volume, respectively, and the subscripts denote initial and final states.

Gas Laws

Gas laws describe the behavior of gases in relation to pressure, volume, and temperature. They include several key principles, such as Boyle's Law, Charles's Law, and Avogadro's Law, which together help predict how gases will respond to changes in their environment. Understanding these laws is essential for solving problems involving gas behavior.

Units of Pressure

Pressure is a measure of force applied per unit area and can be expressed in various units, including atmospheres (atm), pascals (Pa), and millimeters of mercury (mmHg). In this context, it is important to ensure that pressure units are consistent when applying gas laws. Converting between units may be necessary to solve problems accurately.