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. (c) At what temperature will the volume be 15.00 L if the pressure is 116.8 kPa

hi everyone for this problem, we're told to consider a 9.20 liter sample of bromine at 132.5 Kill a pascal's and 25 degrees Celsius, calculate the temperature at which the volume will be 12 liters at 121.1 killer pascal's. So in order to solve this problem, we're going to remember, we're going to need to remember the combined gas law which tells us that P one times V one over T one is equal to P two times V two over T two. And so the problem is, is asking us for the temperature at which the volume will be 12 liters at 121.1 killer pascal's. So we're looking to solve for T two here. And so when we rearrange this equation we're going to get T two is equal to P two times V two times T one Over P one times v one. So we can write out what we're given. And the problem so that we can see if we're missing anything and then we'll be ready to plug in. So we're told that our first pressure RP one is equal to 132.5 killer pascal's. Our volume V one is 9.20 leaders And our T one Is 25°C. We need to convert this to kelvin so we can add 273.15 to this and that will give us 298.15 Kelvin. So that's T one P Two We're told is 121 .1 Killer Pascal's and V two is 12 leaders. Okay, so we have everything so let's go ahead and plug in. So T two is going to equal RP two is 121.1 killer Pascal's times. V two 12 liters times T one Is .15 Kelvin over. P one 132.5 kill a pascal's Times v. 1 9.20 Leaders. Okay, So our t. two Once we solve it is going to equal 355.54, Sorry, 355.43 Calvin. And so since the temperature and the problem was given and Celsius, we're going to convert this to Celsius by subtracting 273.15 So T two and degrees Celsius is going to equal 82.3°C. This is our final answer and we're able to solve it. Using the combined gas law, I hope this was helpful

Ch.10 - Gases

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Brown 14th Edition

Ch.10 - Gases

Problem 43c

Chapter 10, Problem 43c

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. (c) At what temperature will the volume be 15.00 L if the pressure is 116.8 kPa

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Identify the initial and final conditions of the gas: Initial volume \( V_1 = 8.70 \text{ L} \), initial pressure \( P_1 = 119.3 \text{ kPa} \), initial temperature \( T_1 = 24^\circ \text{C} \), final volume \( V_2 = 15.00 \text{ L} \), and final pressure \( P_2 = 116.8 \text{ kPa} \).

Convert the initial temperature from Celsius to Kelvin using the formula \( T(K) = T(^\circ C) + 273.15 \).

Use the combined gas law, which is \( \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \), to relate the initial and final states of the gas.

Rearrange the combined gas law to solve for the final temperature \( T_2 \): \( T_2 = \frac{P_2 V_2 T_1}{P_1 V_1} \).

Substitute the known values into the equation and solve for \( T_2 \) in Kelvin.

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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 helps to determine how changes in temperature and pressure affect the volume of chlorine gas.

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 crucial for solving the problem, as it allows us to predict how the volume of Cl2 gas will change with temperature adjustments while considering the pressure changes.

Pressure-Volume Relationship

The relationship between pressure and volume of a gas is described by Boyle's Law, which states that at constant temperature, the pressure of a gas is inversely proportional to its volume. Understanding this relationship is essential for analyzing how the pressure of chlorine gas changes when the volume is altered, as seen in the given problem.

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Textbook Question

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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Textbook Question

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Textbook Question

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. (c) At what temperature will the volume be 15.00 L if the pressure is 116.8 kPa

Verified video answer for a similar problem:

Key Concepts

Ideal Gas Law

Charles's Law

Pressure-Volume Relationship

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. (c) At what temperature will the volume be 15.00 L if the pressure is 116.8 kPa