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Ch.10 - Gases: Their Properties & Behavior
Chapter 10, Problem 26c

Assume that you have a sample of gas in a cylinder with a movable piston, as shown in the following drawing:
Redraw the apparatus to show what the sample will look like after (c) the temperature is decreased from 300 K to 200 K and the pressure is decreased from 3 atm to 2 atm.

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Identify the initial conditions of the gas sample, which are a temperature of 300 K and a pressure of 3 atm.
Note the final conditions that the gas sample needs to reach, which are a temperature of 200 K and a pressure of 2 atm.
Understand that according to the combined gas law, which is expressed as \(\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}\), where P is pressure, V is volume, and T is temperature, a decrease in both temperature and pressure will affect the volume of the gas.
Since both the temperature and the pressure of the gas are decreasing, the volume of the gas will also decrease. This is because the decrease in temperature tends to decrease the kinetic energy of the gas molecules, leading to a decrease in volume, and the decrease in pressure allows the gas to occupy less space.
Redraw the apparatus showing the piston at a lower position than initially, indicating a decrease in the volume of the gas. The space above the piston in the cylinder should be smaller, reflecting the combined effect of reduced temperature and pressure.

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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 helps predict how a gas will behave under changing conditions, making it essential for understanding the effects of temperature and pressure on gas samples.
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Ideal Gas Law Formula

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 concept is crucial for predicting how the volume of the gas in the cylinder will change as the temperature decreases from 300 K to 200 K.
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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 principle is important for understanding how the pressure change from 3 atm to 2 atm will affect the volume of the gas in the cylinder, especially when combined with the temperature change.
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Related Practice
Textbook Question
A glass tube has one end in a dish of mercury and the otherend closed by a stopcock. The distance from the surface ofthe mercury to the bottom of the stopcock is 850 mm. Theapparatus is at 25 °C, and the mercury level in the tube isthe same as that in the dish.

(a) Show on drawing (1) what the approximate level ofmercury in the tube will be when the temperature of theentire apparatus is lowered from +25 °C to -25 °C.
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Textbook Question

Assume that you have a sample of gas in a cylinder with a movable piston, as shown in the following drawing:

Redraw the apparatus to show what the sample will look like after (a) the temperature is increased from 300 K to 450 K at constant pressure

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Textbook Question

Assume that you have a sample of gas in a cylinder with a movable piston, as shown in the following drawing:

Redraw the apparatus to show what the sample will look like after (b) the pressure is increased from 1 atm to 2 atm at constant temperature

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Textbook Question
Show the approximate level of the movable piston in drawings (a), (b), and (c) after the indicated changes have been made to the gas.

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Textbook Question
A 1:1 mixture of helium (red) and argon (blue) at 300 K isportrayed below on the left. Draw the same mixture whenthe temperature is lowered to 150 K.
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Textbook Question
Yet another common measure of pressure is the unit pounds per square inch (psi). How many pounds per square inch correspond to 1.00 atm? To 1.00 mm Hg?
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