Chlorine is widely used to purify municipal water supplies and to treat swimming pool waters. Suppose that the volume of a particular sample of Cl₂ gas is 8.70 L at 119.3 kPa and 24 °C. (d) At what pressure will the volume equal 5.00 L if the temperature is 58 °C?

검증된 단계별 안내

Identify the initial conditions: The initial volume (V1) is 8.70 L, the initial pressure (P1) is 119.3 kPa, and the initial temperature (T1) is 24 °C. Convert the temperature to Kelvin by adding 273.15, so T1 = 24 + 273.15 K.

Identify the final conditions: The final volume (V2) is 5.00 L, and the final temperature (T2) is 58 °C. Convert this temperature to Kelvin as well, so T2 = 58 + 273.15 K. The final pressure (P2) is what we need to find.

Use the combined gas law, which relates pressure, volume, and temperature: \( \frac{P1 \cdot V1}{T1} = \frac{P2 \cdot V2}{T2} \). This equation allows us to solve for the unknown pressure P2.

Rearrange the combined gas law to solve for P2: \( P2 = \frac{P1 \cdot V1 \cdot T2}{V2 \cdot T1} \).

Substitute the known values into the equation: P1 = 119.3 kPa, V1 = 8.70 L, T1 = (24 + 273.15) K, V2 = 5.00 L, and T2 = (58 + 273.15) K. Calculate P2 using these values.

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주요 개념

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

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is fundamental in understanding gas behavior under varying conditions. In this scenario, it allows us to calculate the pressure of chlorine gas when the volume and temperature change.

Charles's Law

Charles's Law states that the volume of a gas is directly proportional to its temperature (in Kelvin) when pressure is held constant. This principle is essential for understanding how changes in temperature affect the volume of a gas, which is relevant when determining the new pressure of Cl2 gas at a different volume and temperature.

Boyle's Law

Boyle's Law states that the pressure of a gas is inversely proportional to its volume when temperature is held constant. This concept is crucial for solving the problem, as it helps to understand how a decrease in volume (from 8.70 L to 5.00 L) will affect the pressure of the gas, given the temperature change.

Chlorine is widely used to purify municipal water supplies and to treat swimming pool waters. Suppose that the volume of a particular sample of Cl2 gas is 8.70 L at 119.3 kPa and 24 °C. (d) At what pressure will the volume equal 5.00 L if the temperature is 58 °C?