Chlorine is widely used to purify municipal water supplies and to treat swimming pool waters. Suppose that the volume of a particular sample of Cl 2 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?

Hi everyone here we have a question that says a high pressure vessel contains 214 liters of nitrogen gas with a pressure of 17,800 Kill pascal's at 21 degrees Celsius. If it was transferred to a 67 liter vessel at 22 degrees Celsius, what would be the pressure of the gas? So first we need to change our temperatures to kelvin. So we have our first temperature Is 21 and we're gonna add 273.15 and that equals 294.15 Kelvin. We have our second temperature Which equals plus 273.15 equals 295.15 Kelvin. Now we're going to use the Formula P one B one over T one equals P two, Me too over T two. And we can rearrange this to give us p. two equals P one B one, T 2 over T one the two. So that's our second pressure equals our first pressure times our first volume times our second temperature over our first temperature times our second volume. So P two plugging in what we know equals 17,800 Kill A pascal's Times 20 214 L Times 295.15 Kelvin over 294. Kelvin Times 67 l and that equals 57047. Kill a Pascal's. And that is our final answer, thank you for watching. Bye

Ch.10 - Gases

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Brown 14th Edition

Ch.10 - Gases

Problem 43d

Chapter 10, Problem 43d

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?

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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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Key Concepts

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

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.

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Boyle's Law

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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. (b) What volume will the Cl₂occupy at STP?

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Many gases are shipped in high-pressure containers. Consider a steel tank whose volume is 210.0 L that contains O₂ gas at a pressure of 16,500 kPa at 23 °C. (b) What volume would the gas occupy at STP?

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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?

Verified video answer for a similar problem:

Key Concepts

Ideal Gas Law

Charles's Law

Boyle's Law

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?