A sample of nitrogen gas in a 1.75-L container exerts a pressure of 1.35 atm at 25 °C. What is the pressure if the volume of the container is maintained constant and the temperature is raised to 355 °C?

검증된 단계별 안내

Identify the initial and final conditions of the gas: initial pressure \( P_1 = 1.35 \text{ atm} \), initial temperature \( T_1 = 25 \degree C \), and final temperature \( T_2 = 355 \degree C \).

Convert the temperatures from Celsius to Kelvin by adding 273.15 to each temperature: \( T_1 = 25 + 273.15 \) and \( T_2 = 355 + 273.15 \).

Use the ideal gas law relationship for constant volume, which is \( \frac{P_1}{T_1} = \frac{P_2}{T_2} \), where \( P_2 \) is the final pressure.

Rearrange the equation to solve for \( P_2 \): \( P_2 = P_1 \times \frac{T_2}{T_1} \).

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

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

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

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law helps predict how gases behave under different conditions.

Charles's Law

Charles's Law states that the volume of a gas is directly proportional to its temperature when pressure is held constant. This means that as the temperature increases, the volume increases, and vice versa. In this scenario, since the volume is constant, we can use the relationship between temperature and pressure to find the new pressure after the temperature change.

Temperature Conversion

In gas law calculations, temperatures must be expressed in Kelvin rather than Celsius. The conversion from Celsius to Kelvin is done by adding 273.15 to the Celsius temperature. This is crucial because gas laws are derived based on absolute temperature, ensuring accurate calculations of pressure and volume changes.