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Ch.10 - Gases: Their Properties & Behavior
McMurry - Chemistry 8th Edition
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Capitolo 10, Problema 23

A glass tube has one end in a dish of mercury and the other end closed by a stopcock. The distance from the surface of the mercury to the bottom of the stopcock is 850 mm. The apparatus is at 25 °C, and the mercury level in the tube is the same as that in the dish. Diagram of a mercury manometer showing mercury level at 850 mm at 25 °C.
(a) Show on drawing (1) what the approximate level of mercury in the tube will be when the temperature of the entire apparatus is lowered from +25 °C to -25 °C.

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1
Identify the initial conditions: The temperature is 25 °C, and the mercury level in the tube is the same as that in the dish, which is 850 mm from the surface of the mercury to the bottom of the stopcock.
Understand that when the temperature decreases, the volume of the gas inside the tube will decrease due to the gas laws (specifically, Charles's Law: V1/T1 = V2/T2).
Calculate the new temperature in Kelvin: Convert both temperatures from Celsius to Kelvin (T1 = 25 + 273.15, T2 = -25 + 273.15).
Apply Charles's Law to find the new volume of the gas: V2 = V1 * (T2/T1). Since the initial volume is proportional to the height of the mercury column, the new height can be found using the same ratio.
Determine the new height of the mercury column: The new height will be less than 850 mm because the volume of the gas decreases as the temperature decreases. Draw the new mercury level in the tube accordingly.

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Thermal Expansion

Thermal expansion refers to the increase in volume of a substance as its temperature rises. In liquids, such as mercury, this expansion occurs because the molecules move faster and push each other apart when heated. Conversely, when the temperature decreases, the liquid contracts, leading to a drop in the liquid level in a manometer. Understanding this concept is crucial for predicting how the mercury level will change when the temperature is lowered.
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Thermal Equilibrium

Manometer Functionality

A manometer is a device used to measure the pressure of gases or liquids by comparing the height of a liquid column in a tube to the atmospheric pressure. In this case, the mercury level in the tube reflects the pressure exerted by the gas above it. The height of the mercury column changes with temperature due to thermal expansion, which is essential for determining the new mercury level when the temperature is altered.
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Gas Laws

Gas laws describe the relationships between pressure, volume, and temperature of gases. The ideal gas law, PV=nRT, illustrates how changes in temperature (T) can affect pressure (P) and volume (V). In the context of the manometer, as the temperature decreases, the pressure exerted by the gas may also change, influencing the mercury level. Understanding these relationships helps in predicting the behavior of gases in response to temperature changes.
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